Bootstrap

267种64阶群

gap> NumberSmallGroups(64);
267
gap> for n in [1..267] do G:=SmallGroup(64,n);idn:=IdGroup(G);Print(idn);Print(":");L:=List(Elements(G),Order);;M:=[1,2,4,8,16,32,64];;for i in M do Print(Size(Positions(L,i)),","); od;Print("\n");od;
[ 64, 1 ]:1,1,2,4,8,16,32,
[ 64, 2 ]:1,3,12,48,0,0,0,
[ 64, 3 ]:1,3,12,48,0,0,0,
[ 64, 4 ]:1,15,16,32,0,0,0,
[ 64, 5 ]:1,7,24,32,0,0,0,
[ 64, 6 ]:1,11,20,32,0,0,0,
[ 64, 7 ]:1,3,28,32,0,0,0,
[ 64, 8 ]:1,15,32,16,0,0,0,
[ 64, 9 ]:1,7,40,16,0,0,0,
[ 64, 10 ]:1,11,20,32,0,0,0,
[ 64, 11 ]:1,3,28,32,0,0,0,
[ 64, 12 ]:1,19,12,32,0,0,0,
[ 64, 13 ]:1,3,28,32,0,0,0,
[ 64, 14 ]:1,3,28,32,0,0,0,
[ 64, 15 ]:1,3,12,48,0,0,0,
[ 64, 16 ]:1,3,12,48,0,0,0,
[ 64, 17 ]:1,7,24,32,0,0,0,
[ 64, 18 ]:1,7,40,16,0,0,0,
[ 64, 19 ]:1,7,8,48,0,0,0,
[ 64, 20 ]:1,7,40,16,0,0,0,
[ 64, 21 ]:1,7,40,16,0,0,0,
[ 64, 22 ]:1,7,8,48,0,0,0,
[ 64, 23 ]:1,15,48,0,0,0,0,
[ 64, 24 ]:1,7,24,32,0,0,0,
[ 64, 25 ]:1,7,24,32,0,0,0,
[ 64, 26 ]:1,3,12,16,32,0,0,
[ 64, 27 ]:1,3,12,16,32,0,0,
[ 64, 28 ]:1,3,12,16,32,0,0,
[ 64, 29 ]:1,7,8,16,32,0,0,
[ 64, 30 ]:1,7,8,16,32,0,0,
[ 64, 31 ]:1,7,8,16,32,0,0,
[ 64, 32 ]:1,19,28,16,0,0,0,
[ 64, 33 ]:1,11,36,16,0,0,0,
[ 64, 34 ]:1,19,44,0,0,0,0,
[ 64, 35 ]:1,11,52,0,0,0,0,
[ 64, 36 ]:1,11,20,32,0,0,0,
[ 64, 37 ]:1,3,28,32,0,0,0,
[ 64, 38 ]:1,19,20,8,16,0,0,
[ 64, 39 ]:1,3,36,8,16,0,0,
[ 64, 40 ]:1,11,12,24,16,0,0,
[ 64, 41 ]:1,11,28,8,16,0,0,
[ 64, 42 ]:1,19,4,24,16,0,0,
[ 64, 43 ]:1,3,20,24,16,0,0,
[ 64, 44 ]:1,3,12,16,32,0,0,
[ 64, 45 ]:1,3,12,16,32,0,0,
[ 64, 46 ]:1,3,20,24,16,0,0,
[ 64, 47 ]:1,3,36,8,16,0,0,
[ 64, 48 ]:1,3,36,8,16,0,0,
[ 64, 49 ]:1,3,4,40,16,0,0,
[ 64, 50 ]:1,3,4,8,16,32,0,
[ 64, 51 ]:1,3,4,8,16,32,0,
[ 64, 52 ]:1,33,2,4,8,16,0,
[ 64, 53 ]:1,17,18,4,8,16,0,
[ 64, 54 ]:1,1,34,4,8,16,0,
[ 64, 55 ]:1,7,56,0,0,0,0,
[ 64, 56 ]:1,15,48,0,0,0,0,
[ 64, 57 ]:1,7,56,0,0,0,0,
[ 64, 58 ]:1,15,48,0,0,0,0,
[ 64, 59 ]:1,7,56,0,0,0,0,
[ 64, 60 ]:1,31,32,0,0,0,0,
[ 64, 61 ]:1,15,48,0,0,0,0,
[ 64, 62 ]:1,15,48,0,0,0,0,
[ 64, 63 ]:1,7,56,0,0,0,0,
[ 64, 64 ]:1,7,56,0,0,0,0,
[ 64, 65 ]:1,7,56,0,0,0,0,
[ 64, 66 ]:1,15,48,0,0,0,0,
[ 64, 67 ]:1,23,40,0,0,0,0,
[ 64, 68 ]:1,7,56,0,0,0,0,
[ 64, 69 ]:1,15,48,0,0,0,0,
[ 64, 70 ]:1,7,56,0,0,0,0,
[ 64, 71 ]:1,23,40,0,0,0,0,
[ 64, 72 ]:1,7,56,0,0,0,0,
[ 64, 73 ]:1,31,32,0,0,0,0,
[ 64, 74 ]:1,15,48,0,0,0,0,
[ 64, 75 ]:1,23,40,0,0,0,0,
[ 64, 76 ]:1,7,56,0,0,0,0,
[ 64, 77 ]:1,15,48,0,0,0,0,
[ 64, 78 ]:1,15,48,0,0,0,0,
[ 64, 79 ]:1,7,56,0,0,0,0,
[ 64, 80 ]:1,15,48,0,0,0,0,
[ 64, 81 ]:1,7,56,0,0,0,0,
[ 64, 82 ]:1,7,56,0,0,0,0,
[ 64, 83 ]:1,7,24,32,0,0,0,
[ 64, 84 ]:1,7,24,32,0,0,0,
[ 64, 85 ]:1,7,24,32,0,0,0,
[ 64, 86 ]:1,7,24,32,0,0,0,
[ 64, 87 ]:1,15,16,32,0,0,0,
[ 64, 88 ]:1,15,16,32,0,0,0,
[ 64, 89 ]:1,15,16,32,0,0,0,
[ 64, 90 ]:1,23,40,0,0,0,0,
[ 64, 91 ]:1,15,48,0,0,0,0,
[ 64, 92 ]:1,23,8,32,0,0,0,
[ 64, 93 ]:1,7,24,32,0,0,0,
[ 64, 94 ]:1,15,16,32,0,0,0,
[ 64, 95 ]:1,23,24,16,0,0,0,
[ 64, 96 ]:1,7,40,16,0,0,0,
[ 64, 97 ]:1,15,32,16,0,0,0,
[ 64, 98 ]:1,15,32,16,0,0,0,
[ 64, 99 ]:1,23,24,16,0,0,0,
[ 64, 100 ]:1,7,40,16,0,0,0,
[ 64, 101 ]:1,15,32,16,0,0,0,
[ 64, 102 ]:1,15,32,16,0,0,0,
[ 64, 103 ]:1,7,24,32,0,0,0,
[ 64, 104 ]:1,7,24,32,0,0,0,
[ 64, 105 ]:1,7,24,32,0,0,0,
[ 64, 106 ]:1,7,40,16,0,0,0,
[ 64, 107 ]:1,7,40,16,0,0,0,
[ 64, 108 ]:1,7,40,16,0,0,0,
[ 64, 109 ]:1,7,40,16,0,0,0,
[ 64, 110 ]:1,7,8,48,0,0,0,
[ 64, 111 ]:1,7,8,48,0,0,0,
[ 64, 112 ]:1,7,24,32,0,0,0,
[ 64, 113 ]:1,7,24,32,0,0,0,
[ 64, 114 ]:1,7,24,32,0,0,0,
[ 64, 115 ]:1,11,20,32,0,0,0,
[ 64, 116 ]:1,11,20,32,0,0,0,
[ 64, 117 ]:1,11,20,32,0,0,0,
[ 64, 118 ]:1,19,28,16,0,0,0,
[ 64, 119 ]:1,11,36,16,0,0,0,
[ 64, 120 ]:1,3,44,16,0,0,0,
[ 64, 121 ]:1,11,36,16,0,0,0,
[ 64, 122 ]:1,3,44,16,0,0,0,
[ 64, 123 ]:1,19,28,16,0,0,0,
[ 64, 124 ]:1,11,20,32,0,0,0,
[ 64, 125 ]:1,11,20,32,0,0,0,
[ 64, 126 ]:1,3,28,32,0,0,0,
[ 64, 127 ]:1,3,28,32,0,0,0,
[ 64, 128 ]:1,31,16,16,0,0,0,
[ 64, 129 ]:1,15,32,16,0,0,0,
[ 64, 130 ]:1,23,24,16,0,0,0,
[ 64, 131 ]:1,23,24,16,0,0,0,
[ 64, 132 ]:1,7,40,16,0,0,0,
[ 64, 133 ]:1,15,32,16,0,0,0,
[ 64, 134 ]:1,27,20,16,0,0,0,
[ 64, 135 ]:1,19,28,16,0,0,0,
[ 64, 136 ]:1,19,28,16,0,0,0,
[ 64, 137 ]:1,11,36,16,0,0,0,
[ 64, 138 ]:1,27,36,0,0,0,0,
[ 64, 139 ]:1,19,44,0,0,0,0,
[ 64, 140 ]:1,27,20,16,0,0,0,
[ 64, 141 ]:1,19,28,16,0,0,0,
[ 64, 142 ]:1,11,36,16,0,0,0,
[ 64, 143 ]:1,3,44,16,0,0,0,
[ 64, 144 ]:1,19,28,16,0,0,0,
[ 64, 145 ]:1,11,36,16,0,0,0,
[ 64, 146 ]:1,15,32,16,0,0,0,
[ 64, 147 ]:1,23,24,16,0,0,0,
[ 64, 148 ]:1,7,40,16,0,0,0,
[ 64, 149 ]:1,15,32,16,0,0,0,
[ 64, 150 ]:1,23,24,16,0,0,0,
[ 64, 151 ]:1,7,40,16,0,0,0,
[ 64, 152 ]:1,15,16,32,0,0,0,
[ 64, 153 ]:1,23,8,32,0,0,0,
[ 64, 154 ]:1,7,24,32,0,0,0,
[ 64, 155 ]:1,11,36,16,0,0,0,
[ 64, 156 ]:1,3,44,16,0,0,0,
[ 64, 157 ]:1,11,36,16,0,0,0,
[ 64, 158 ]:1,3,44,16,0,0,0,
[ 64, 159 ]:1,11,36,16,0,0,0,
[ 64, 160 ]:1,3,44,16,0,0,0,
[ 64, 161 ]:1,15,32,16,0,0,0,
[ 64, 162 ]:1,15,32,16,0,0,0,
[ 64, 163 ]:1,15,32,16,0,0,0,
[ 64, 164 ]:1,7,40,16,0,0,0,
[ 64, 165 ]:1,7,40,16,0,0,0,
[ 64, 166 ]:1,7,40,16,0,0,0,
[ 64, 167 ]:1,19,28,16,0,0,0,
[ 64, 168 ]:1,3,44,16,0,0,0,
[ 64, 169 ]:1,11,36,16,0,0,0,
[ 64, 170 ]:1,11,36,16,0,0,0,
[ 64, 171 ]:1,19,28,16,0,0,0,
[ 64, 172 ]:1,3,44,16,0,0,0,
[ 64, 173 ]:1,19,28,16,0,0,0,
[ 64, 174 ]:1,35,12,16,0,0,0,
[ 64, 175 ]:1,3,44,16,0,0,0,
[ 64, 176 ]:1,19,28,16,0,0,0,
[ 64, 177 ]:1,27,20,16,0,0,0,
[ 64, 178 ]:1,11,36,16,0,0,0,
[ 64, 179 ]:1,3,44,16,0,0,0,
[ 64, 180 ]:1,3,44,16,0,0,0,
[ 64, 181 ]:1,3,44,16,0,0,0,
[ 64, 182 ]:1,3,44,16,0,0,0,
[ 64, 183 ]:1,7,8,16,32,0,0,
[ 64, 184 ]:1,7,8,16,32,0,0,
[ 64, 185 ]:1,7,8,16,32,0,0,
[ 64, 186 ]:1,35,4,8,16,0,0,
[ 64, 187 ]:1,19,20,8,16,0,0,
[ 64, 188 ]:1,3,36,8,16,0,0,
[ 64, 189 ]:1,19,20,8,16,0,0,
[ 64, 190 ]:1,27,12,8,16,0,0,
[ 64, 191 ]:1,11,28,8,16,0,0,
[ 64, 192 ]:1,15,48,0,0,0,0,
[ 64, 193 ]:1,31,32,0,0,0,0,
[ 64, 194 ]:1,15,48,0,0,0,0,
[ 64, 195 ]:1,15,48,0,0,0,0,
[ 64, 196 ]:1,23,40,0,0,0,0,
[ 64, 197 ]:1,7,56,0,0,0,0,
[ 64, 198 ]:1,15,48,0,0,0,0,
[ 64, 199 ]:1,23,40,0,0,0,0,
[ 64, 200 ]:1,7,56,0,0,0,0,
[ 64, 201 ]:1,15,48,0,0,0,0,
[ 64, 202 ]:1,39,24,0,0,0,0,
[ 64, 203 ]:1,31,32,0,0,0,0,
[ 64, 204 ]:1,15,48,0,0,0,0,
[ 64, 205 ]:1,23,40,0,0,0,0,
[ 64, 206 ]:1,23,40,0,0,0,0,
[ 64, 207 ]:1,23,40,0,0,0,0,
[ 64, 208 ]:1,7,56,0,0,0,0,
[ 64, 209 ]:1,15,48,0,0,0,0,
[ 64, 210 ]:1,15,48,0,0,0,0,
[ 64, 211 ]:1,39,24,0,0,0,0,
[ 64, 212 ]:1,7,56,0,0,0,0,
[ 64, 213 ]:1,23,40,0,0,0,0,
[ 64, 214 ]:1,7,56,0,0,0,0,
[ 64, 215 ]:1,31,32,0,0,0,0,
[ 64, 216 ]:1,31,32,0,0,0,0,
[ 64, 217 ]:1,15,48,0,0,0,0,
[ 64, 218 ]:1,23,40,0,0,0,0,
[ 64, 219 ]:1,23,40,0,0,0,0,
[ 64, 220 ]:1,15,48,0,0,0,0,
[ 64, 221 ]:1,23,40,0,0,0,0,
[ 64, 222 ]:1,7,56,0,0,0,0,
[ 64, 223 ]:1,15,48,0,0,0,0,
[ 64, 224 ]:1,15,48,0,0,0,0,
[ 64, 225 ]:1,7,56,0,0,0,0,
[ 64, 226 ]:1,35,28,0,0,0,0,
[ 64, 227 ]:1,27,36,0,0,0,0,
[ 64, 228 ]:1,19,44,0,0,0,0,
[ 64, 229 ]:1,19,44,0,0,0,0,
[ 64, 230 ]:1,11,52,0,0,0,0,
[ 64, 231 ]:1,27,36,0,0,0,0,
[ 64, 232 ]:1,19,44,0,0,0,0,
[ 64, 233 ]:1,11,52,0,0,0,0,
[ 64, 234 ]:1,19,44,0,0,0,0,
[ 64, 235 ]:1,11,52,0,0,0,0,
[ 64, 236 ]:1,19,44,0,0,0,0,
[ 64, 237 ]:1,11,52,0,0,0,0,
[ 64, 238 ]:1,3,60,0,0,0,0,
[ 64, 239 ]:1,3,60,0,0,0,0,
[ 64, 240 ]:1,19,44,0,0,0,0,
[ 64, 241 ]:1,27,36,0,0,0,0,
[ 64, 242 ]:1,27,36,0,0,0,0,
[ 64, 243 ]:1,19,44,0,0,0,0,
[ 64, 244 ]:1,11,52,0,0,0,0,
[ 64, 245 ]:1,3,60,0,0,0,0,
[ 64, 246 ]:1,15,16,32,0,0,0,
[ 64, 247 ]:1,15,16,32,0,0,0,
[ 64, 248 ]:1,15,16,32,0,0,0,
[ 64, 249 ]:1,15,16,32,0,0,0,
[ 64, 250 ]:1,39,8,16,0,0,0,
[ 64, 251 ]:1,23,24,16,0,0,0,
[ 64, 252 ]:1,7,40,16,0,0,0,
[ 64, 253 ]:1,23,24,16,0,0,0,
[ 64, 254 ]:1,31,16,16,0,0,0,
[ 64, 255 ]:1,15,32,16,0,0,0,
[ 64, 256 ]:1,23,24,16,0,0,0,
[ 64, 257 ]:1,31,16,16,0,0,0,
[ 64, 258 ]:1,23,24,16,0,0,0,
[ 64, 259 ]:1,15,32,16,0,0,0,
[ 64, 260 ]:1,31,32,0,0,0,0,
[ 64, 261 ]:1,47,16,0,0,0,0,
[ 64, 262 ]:1,15,48,0,0,0,0,
[ 64, 263 ]:1,31,32,0,0,0,0,
[ 64, 264 ]:1,39,24,0,0,0,0,
[ 64, 265 ]:1,23,40,0,0,0,0,
[ 64, 266 ]:1,31,32,0,0,0,0,
[ 64, 267 ]:1,63,0,0,0,0,0,
gap> for n in [1..267] do G:=SmallGroup(64,n);idn:=IdGroup(G);Print(idn);Print(":");L:=List(Elements(G),Order);;M:=[1,2,4,8,16,32,64];;for i in M do Print(Size(Positions(L,i)),","); od;arr:=[];;idn:=IdGroup(G);Append(arr,"秩:");;Append(arr,String(RankPGroup(G)));;cl:=ConjugacyClasses(G);;Append(arr,"共轭类数:");;Append(arr,String(Size(cl)));Append(arr,"中心:");;Append(arr,String(IdGroup(Center(G))));;Append(arr,"换位子群:");;Append(arr,String(IdGroup(DerivedSubgroup(G))));;Append(arr,"自同构群:");;Append(arr,String(Order(AutomorphismGroup(G))));;cl:=NormalSubgroups(G);;Append(arr,"正规子群个数:");;len:=Size(cl);;Append(arr,String(len));;Print(arr);Print("\n");od;
[ 64, 1 ]:1,1,2,4,8,16,
32,秩:1共轭类数:64中心:[ 64, 1 ]换位子群:[ 1, 1 ]自同构群:32正规子群个数:7
[ 64, 2 ]:1,3,12,48,0,0,
0,秩:2共轭类数:64中心:[ 64, 2 ]换位子群:[ 1, 1 ]自同构群:1536正规子群个数:37
[ 64, 3 ]:1,3,12,48,0,0,
0,秩:2共轭类数:40中心:[ 16, 2 ]换位子群:[ 2, 1 ]自同构群:512正规子群个数:29
[ 64, 4 ]:1,15,16,32,0,0,
0,秩:2共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:256正规子群个数:19
[ 64, 5 ]:1,7,24,32,0,0,
0,秩:2共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:256正规子群个数:19
[ 64, 6 ]:1,11,20,32,0,0,
0,秩:2共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:128正规子群个数:21
[ 64, 7 ]:1,3,28,32,0,0,
0,秩:2共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:128正规子群个数:21
[ 64, 8 ]:1,15,32,16,0,0,
0,秩:2共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:128正规子群个数:17
[ 64, 9 ]:1,7,40,16,0,0,
0,秩:2共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:128正规子群个数:17
[ 64, 10 ]:1,11,20,32,0,0,
0,秩:2共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:15
[ 64, 11 ]:1,3,28,32,0,0,
0,秩:2共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:15
[ 64, 12 ]:1,19,12,32,0,0,
0,秩:2共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:512正规子群个数:19
[ 64, 13 ]:1,3,28,32,0,0,
0,秩:2共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:19
[ 64, 14 ]:1,3,28,32,0,0,
0,秩:2共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:512正规子群个数:19
[ 64, 15 ]:1,3,12,48,0,0,
0,秩:2共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:256正规子群个数:21
[ 64, 16 ]:1,3,12,48,0,0,
0,秩:2共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:256正规子群个数:21
[ 64, 17 ]:1,7,24,32,0,0,
0,秩:2共轭类数:40中心:[ 16, 10 ]换位子群:[ 2, 1 ]自同构群:512正规子群个数:41
[ 64, 18 ]:1,7,40,16,0,0,
0,秩:2共轭类数:22中心:[ 4, 1 ]换位子群:[ 4, 1 ]自同构群:512正规子群个数:27
[ 64, 19 ]:1,7,8,48,0,0,
0,秩:2共轭类数:22中心:[ 4, 1 ]换位子群:[ 4, 1 ]自同构群:1536正规子群个数:27
[ 64, 20 ]:1,7,40,16,0,0,
0,秩:2共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:256正规子群个数:29
[ 64, 21 ]:1,7,40,16,0,0,
0,秩:2共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 1 ]自同构群:512正规子群个数:37
[ 64, 22 ]:1,7,8,48,0,0,
0,秩:2共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:512正规子群个数:29
[ 64, 23 ]:1,15,48,0,0,0,
0,秩:2共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:512正规子群个数:29
[ 64, 24 ]:1,7,24,32,0,0,
0,秩:2共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:512正规子群个数:29
[ 64, 25 ]:1,7,24,32,0,0,
0,秩:2共轭类数:22中心:[ 4, 1 ]换位子群:[ 4, 2 ]自同构群:256正规子群个数:27
[ 64, 26 ]:1,3,12,16,32,0,
0,秩:2共轭类数:64中心:[ 64, 26 ]换位子群:[ 1, 1 ]自同构群:256正规子群个数:29
[ 64, 27 ]:1,3,12,16,32,0,
0,秩:2共轭类数:40中心:[ 16, 5 ]换位子群:[ 2, 1 ]自同构群:256正规子群个数:25
[ 64, 28 ]:1,3,12,16,32,0,
0,秩:2共轭类数:22中心:[ 4, 1 ]换位子群:[ 4, 1 ]自同构群:128正规子群个数:19
[ 64, 29 ]:1,7,8,16,32,0,
0,秩:2共轭类数:40中心:[ 16, 5 ]换位子群:[ 2, 1 ]自同构群:128正规子群个数:21
[ 64, 30 ]:1,7,8,16,32,0,
0,秩:2共轭类数:22中心:[ 4, 1 ]换位子群:[ 4, 2 ]自同构群:128正规子群个数:17
[ 64, 31 ]:1,7,8,16,32,0,
0,秩:2共轭类数:28中心:[ 8, 1 ]换位子群:[ 4, 1 ]自同构群:64正规子群个数:17
[ 64, 32 ]:1,19,28,16,0,0,
0,秩:2共轭类数:13中心:[ 2, 1 ]换位子群:[ 8, 5 ]自同构群:128正规子群个数:13
[ 64, 33 ]:1,11,36,16,0,0,
0,秩:2共轭类数:13中心:[ 2, 1 ]换位子群:[ 8, 5 ]自同构群:128正规子群个数:13
[ 64, 34 ]:1,19,44,0,0,0,
0,秩:2共轭类数:13中心:[ 2, 1 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:13
[ 64, 35 ]:1,11,52,0,0,0,
0,秩:2共轭类数:13中心:[ 2, 1 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:13
[ 64, 36 ]:1,11,20,32,0,0,
0,秩:2共轭类数:13中心:[ 2, 1 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:13
[ 64, 37 ]:1,3,28,32,0,0,
0,秩:2共轭类数:13中心:[ 2, 1 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:13
[ 64, 38 ]:1,19,20,8,16,0,
0,秩:2共轭类数:22中心:[ 4, 2 ]换位子群:[ 8, 1 ]自同构群:256正规子群个数:17
[ 64, 39 ]:1,3,36,8,16,0,
0,秩:2共轭类数:22中心:[ 4, 2 ]换位子群:[ 8, 1 ]自同构群:256正规子群个数:17
[ 64, 40 ]:1,11,12,24,16,0,
0,秩:2共轭类数:22中心:[ 4, 1 ]换位子群:[ 8, 1 ]自同构群:128正规子群个数:15
[ 64, 41 ]:1,11,28,8,16,0,
0,秩:2共轭类数:16中心:[ 2, 1 ]换位子群:[ 8, 1 ]自同构群:128正规子群个数:15
[ 64, 42 ]:1,19,4,24,16,0,
0,秩:2共轭类数:16中心:[ 2, 1 ]换位子群:[ 8, 1 ]自同构群:256正规子群个数:15
[ 64, 43 ]:1,3,20,24,16,0,
0,秩:2共轭类数:16中心:[ 2, 1 ]换位子群:[ 8, 1 ]自同构群:256正规子群个数:15
[ 64, 44 ]:1,3,12,16,32,0,
0,秩:2共轭类数:40中心:[ 16, 5 ]换位子群:[ 2, 1 ]自同构群:128正规子群个数:21
[ 64, 45 ]:1,3,12,16,32,0,
0,秩:2共轭类数:28中心:[ 8, 1 ]换位子群:[ 4, 1 ]自同构群:128正规子群个数:17
[ 64, 46 ]:1,3,20,24,16,0,
0,秩:2共轭类数:16中心:[ 2, 1 ]换位子群:[ 8, 1 ]自同构群:128正规子群个数:15
[ 64, 47 ]:1,3,36,8,16,0,
0,秩:2共轭类数:22中心:[ 4, 2 ]换位子群:[ 8, 1 ]自同构群:512正规子群个数:17
[ 64, 48 ]:1,3,36,8,16,0,
0,秩:2共轭类数:22中心:[ 4, 2 ]换位子群:[ 8, 1 ]自同构群:512正规子群个数:17
[ 64, 49 ]:1,3,4,40,16,0,
0,秩:2共轭类数:22中心:[ 4, 1 ]换位子群:[ 8, 1 ]自同构群:256正规子群个数:15
[ 64, 50 ]:1,3,4,8,16,32,
0,秩:2共轭类数:64中心:[ 64, 50 ]换位子群:[ 1, 1 ]自同构群:64正规子群个数:17
[ 64, 51 ]:1,3,4,8,16,32,
0,秩:2共轭类数:40中心:[ 16, 1 ]换位子群:[ 2, 1 ]自同构群:64正规子群个数:15
[ 64, 52 ]:1,33,2,4,8,16,
0,秩:2共轭类数:19中心:[ 2, 1 ]换位子群:[ 16, 1 ]自同构群:512正规子群个数:9
[ 64, 53 ]:1,17,18,4,8,16,
0,秩:2共轭类数:19中心:[ 2, 1 ]换位子群:[ 16, 1 ]自同构群:256正规子群个数:9
[ 64, 54 ]:1,1,34,4,8,16,
0,秩:2共轭类数:19中心:[ 2, 1 ]换位子群:[ 16, 1 ]自同构群:512正规子群个数:9
[ 64, 55 ]:1,7,56,0,0,0,
0,秩:3共轭类数:64中心:[ 64, 55 ]换位子群:[ 1, 1 ]自同构群:86016正规子群个数:129
[ 64, 56 ]:1,15,48,0,0,0,
0,秩:3共轭类数:40中心:[ 16, 14 ]换位子群:[ 2, 1 ]自同构群:12288正规子群个数:105
[ 64, 57 ]:1,7,56,0,0,0,
0,秩:3共轭类数:40中心:[ 16, 10 ]换位子群:[ 2, 1 ]自同构群:12288正规子群个数:65
[ 64, 58 ]:1,15,48,0,0,0,
0,秩:3共轭类数:40中心:[ 16, 10 ]换位子群:[ 2, 1 ]自同构群:2048正规子群个数:73
[ 64, 59 ]:1,7,56,0,0,0,
0,秩:3共轭类数:40中心:[ 16, 10 ]换位子群:[ 2, 1 ]自同构群:2048正规子群个数:73
[ 64, 60 ]:1,31,32,0,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:12288正规子群个数:65
[ 64, 61 ]:1,15,48,0,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:2048正规子群个数:57
[ 64, 62 ]:1,15,48,0,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:4096正规子群个数:49
[ 64, 63 ]:1,7,56,0,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:4096正规子群个数:49
[ 64, 64 ]:1,7,56,0,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:6144正规子群个数:41
[ 64, 65 ]:1,7,56,0,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:12288正规子群个数:65
[ 64, 66 ]:1,15,48,0,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:1024正规子群个数:53
[ 64, 67 ]:1,23,40,0,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:1024正规子群个数:53
[ 64, 68 ]:1,7,56,0,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:512正规子群个数:45
[ 64, 69 ]:1,15,48,0,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:512正规子群个数:45
[ 64, 70 ]:1,7,56,0,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:1024正规子群个数:53
[ 64, 71 ]:1,23,40,0,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:2048正规子群个数:53
[ 64, 72 ]:1,7,56,0,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:2048正规子群个数:53
[ 64, 73 ]:1,31,32,0,0,0,
0,秩:3共轭类数:22中心:[ 8, 5 ]换位子群:[ 8, 5 ]自同构群:3072正规子群个数:43
[ 64, 74 ]:1,15,48,0,0,0,
0,秩:3共轭类数:22中心:[ 8, 5 ]换位子群:[ 8, 5 ]自同构群:3072正规子群个数:39
[ 64, 75 ]:1,23,40,0,0,0,
0,秩:3共轭类数:22中心:[ 8, 5 ]换位子群:[ 8, 5 ]自同构群:1024正规子群个数:39
[ 64, 76 ]:1,7,56,0,0,0,
0,秩:3共轭类数:22中心:[ 8, 5 ]换位子群:[ 8, 5 ]自同构群:3072正规子群个数:43
[ 64, 77 ]:1,15,48,0,0,0,
0,秩:3共轭类数:22中心:[ 8, 5 ]换位子群:[ 8, 5 ]自同构群:1536正规子群个数:39
[ 64, 78 ]:1,15,48,0,0,0,
0,秩:3共轭类数:22中心:[ 8, 5 ]换位子群:[ 8, 5 ]自同构群:1024正规子群个数:35
[ 64, 79 ]:1,7,56,0,0,0,
0,秩:3共轭类数:22中心:[ 8, 5 ]换位子群:[ 8, 5 ]自同构群:1024正规子群个数:39
[ 64, 80 ]:1,15,48,0,0,0,
0,秩:3共轭类数:22中心:[ 8, 5 ]换位子群:[ 8, 5 ]自同构群:3072正规子群个数:39
[ 64, 81 ]:1,7,56,0,0,0,
0,秩:3共轭类数:22中心:[ 8, 5 ]换位子群:[ 8, 5 ]自同构群:1024正规子群个数:35
[ 64, 82 ]:1,7,56,0,0,0,
0,秩:3共轭类数:22中心:[ 8, 5 ]换位子群:[ 8, 5 ]自同构群:10752正规子群个数:31
[ 64, 83 ]:1,7,24,32,0,0,
0,秩:3共轭类数:64中心:[ 64, 83 ]换位子群:[ 1, 1 ]自同构群:2048正规子群个数:81
[ 64, 84 ]:1,7,24,32,0,0,
0,秩:3共轭类数:40中心:[ 16, 10 ]换位子群:[ 2, 1 ]自同构群:2048正规子群个数:65
[ 64, 85 ]:1,7,24,32,0,0,
0,秩:3共轭类数:40中心:[ 16, 2 ]换位子群:[ 2, 1 ]自同构群:1024正规子群个数:61
[ 64, 86 ]:1,7,24,32,0,0,
0,秩:3共轭类数:40中心:[ 16, 5 ]换位子群:[ 2, 1 ]自同构群:512正规子群个数:57
[ 64, 87 ]:1,15,16,32,0,0,
0,秩:3共轭类数:40中心:[ 16, 10 ]换位子群:[ 2, 1 ]自同构群:1024正规子群个数:57
[ 64, 88 ]:1,15,16,32,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 2 ]自同构群:1024正规子群个数:45
[ 64, 89 ]:1,15,16,32,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 2 ]自同构群:512正规子群个数:41
[ 64, 90 ]:1,23,40,0,0,0,
0,秩:3共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:512正规子群个数:41
[ 64, 91 ]:1,15,48,0,0,0,
0,秩:3共轭类数:22中心:[ 4, 1 ]换位子群:[ 4, 2 ]自同构群:512正规子群个数:39
[ 64, 92 ]:1,23,8,32,0,0,
0,秩:3共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:1024正规子群个数:41
[ 64, 93 ]:1,7,24,32,0,0,
0,秩:3共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:1024正规子群个数:41
[ 64, 94 ]:1,15,16,32,0,0,
0,秩:3共轭类数:22中心:[ 4, 1 ]换位子群:[ 4, 2 ]自同构群:512正规子群个数:39
[ 64, 95 ]:1,23,24,16,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 1 ]自同构群:1024正规子群个数:49
[ 64, 96 ]:1,7,40,16,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 1 ]自同构群:1024正规子群个数:49
[ 64, 97 ]:1,15,32,16,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:512正规子群个数:41
[ 64, 98 ]:1,15,32,16,0,0,
0,秩:3共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 1 ]自同构群:512正规子群个数:41
[ 64, 99 ]:1,23,24,16,0,0,
0,秩:3共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 1 ]自同构群:1024正规子群个数:41
[ 64, 100 ]:1,7,40,16,0,0,
0,秩:3共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 1 ]自同构群:1024正规子群个数:41
[ 64, 101 ]:1,15,32,16,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:256正规子群个数:41
[ 64, 102 ]:1,15,32,16,0,0,
0,秩:3共轭类数:22中心:[ 4, 1 ]换位子群:[ 4, 1 ]自同构群:256正规子群个数:39
[ 64, 103 ]:1,7,24,32,0,0,
0,秩:3共轭类数:40中心:[ 16, 10 ]换位子群:[ 2, 1 ]自同构群:1024正规子群个数:57
[ 64, 104 ]:1,7,24,32,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 2 ]自同构群:1024正规子群个数:45
[ 64, 105 ]:1,7,24,32,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 2 ]自同构群:512正规子群个数:41
[ 64, 106 ]:1,7,40,16,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 1 ]自同构群:2048正规子群个数:49
[ 64, 107 ]:1,7,40,16,0,0,
0,秩:3共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 1 ]自同构群:2048正规子群个数:49
[ 64, 108 ]:1,7,40,16,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:1024正规子群个数:41
[ 64, 109 ]:1,7,40,16,0,0,
0,秩:3共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 1 ]自同构群:512正规子群个数:41
[ 64, 110 ]:1,7,8,48,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:512正规子群个数:41
[ 64, 111 ]:1,7,8,48,0,0,
0,秩:3共轭类数:22中心:[ 4, 1 ]换位子群:[ 4, 1 ]自同构群:512正规子群个数:39
[ 64, 112 ]:1,7,24,32,0,0,
0,秩:3共轭类数:40中心:[ 16, 2 ]换位子群:[ 2, 1 ]自同构群:512正规子群个数:45
[ 64, 113 ]:1,7,24,32,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 2 ]自同构群:512正规子群个数:37
[ 64, 114 ]:1,7,24,32,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 2 ]自同构群:256正规子群个数:33
[ 64, 115 ]:1,11,20,32,0,0,
0,秩:3共轭类数:40中心:[ 16, 5 ]换位子群:[ 2, 1 ]自同构群:256正规子群个数:45
[ 64, 116 ]:1,11,20,32,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 2 ]自同构群:128正规子群个数:37
[ 64, 117 ]:1,11,20,32,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 2 ]自同构群:256正规子群个数:37
[ 64, 118 ]:1,19,28,16,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:512正规子群个数:37
[ 64, 119 ]:1,11,36,16,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:256正规子群个数:37
[ 64, 120 ]:1,3,44,16,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:512正规子群个数:37
[ 64, 121 ]:1,11,36,16,0,0,
0,秩:3共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 1 ]自同构群:256正规子群个数:35
[ 64, 122 ]:1,3,44,16,0,0,
0,秩:3共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 1 ]自同构群:512正规子群个数:35
[ 64, 123 ]:1,19,28,16,0,0,
0,秩:3共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 1 ]自同构群:512正规子群个数:35
[ 64, 124 ]:1,11,20,32,0,0,
0,秩:3共轭类数:28中心:[ 8, 1 ]换位子群:[ 4, 1 ]自同构群:128正规子群个数:33
[ 64, 125 ]:1,11,20,32,0,0,
0,秩:3共轭类数:22中心:[ 4, 1 ]换位子群:[ 4, 1 ]自同构群:128正规子群个数:33
[ 64, 126 ]:1,3,28,32,0,0,
0,秩:3共轭类数:40中心:[ 16, 5 ]换位子群:[ 2, 1 ]自同构群:768正规子群个数:45
[ 64, 127 ]:1,3,28,32,0,0,
0,秩:3共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 2 ]自同构群:256正规子群个数:37
[ 64, 128 ]:1,31,16,16,0,0,
0,秩:3共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:512正规子群个数:31
[ 64, 129 ]:1,15,32,16,0,0,
0,秩:3共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:512正规子群个数:31
[ 64, 130 ]:1,23,24,16,0,0,
0,秩:3共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:29
[ 64, 131 ]:1,23,24,16,0,0,
0,秩:3共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:512正规子群个数:31
[ 64, 132 ]:1,7,40,16,0,0,
0,秩:3共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:512正规子群个数:31
[ 64, 133 ]:1,15,32,16,0,0,
0,秩:3共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:29
[ 64, 134 ]:1,27,20,16,0,0,
0,秩:3共轭类数:16中心:[ 2, 1 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:27
[ 64, 135 ]:1,19,28,16,0,0,
0,秩:3共轭类数:16中心:[ 2, 1 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:27
[ 64, 136 ]:1,19,28,16,0,0,
0,秩:3共轭类数:16中心:[ 2, 1 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:27
[ 64, 137 ]:1,11,36,16,0,0,
0,秩:3共轭类数:16中心:[ 2, 1 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:27
[ 64, 138 ]:1,27,36,0,0,0,
0,秩:3共轭类数:16中心:[ 2, 1 ]换位子群:[ 8, 5 ]自同构群:384正规子群个数:27
[ 64, 139 ]:1,19,44,0,0,0,
0,秩:3共轭类数:16中心:[ 2, 1 ]换位子群:[ 8, 5 ]自同构群:384正规子群个数:27
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0,秩:3共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:512正规子群个数:29
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0,秩:3共轭类数:19中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:27
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0,秩:3共轭类数:22中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:512正规子群个数:29
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0,秩:3共轭类数:16中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:256正规子群个数:27
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0,秩:3共轭类数:16中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:512正规子群个数:27
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0,秩:3共轭类数:16中心:[ 4, 2 ]换位子群:[ 8, 2 ]自同构群:512正规子群个数:27
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[ 64, 186 ]:1,35,4,8,16,0,
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0,秩:3共轭类数:22中心:[ 4, 1 ]换位子群:[ 8, 1 ]自同构群:256正规子群个数:23
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0,秩:3共轭类数:16中心:[ 2, 1 ]换位子群:[ 8, 1 ]自同构群:256正规子群个数:23
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0,秩:4共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:4096正规子群个数:97
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0,秩:4共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:8192正规子群个数:89
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0,秩:4共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:8192正规子群个数:89
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0,秩:4共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 2 ]自同构群:6144正规子群个数:81
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0,秩:4共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 2 ]自同构群:512正规子群个数:77
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0,秩:4共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:2048正规子群个数:81
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0,秩:4共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:2048正规子群个数:81
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0,秩:4共轭类数:25中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:1536正规子群个数:83
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0,秩:4共轭类数:25中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:3072正规子群个数:91
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0,秩:4共轭类数:25中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:3072正规子群个数:83
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0,秩:4共轭类数:25中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:512正规子群个数:75
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0,秩:4共轭类数:25中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:1024正规子群个数:75
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0,秩:4共轭类数:25中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:3072正规子群个数:83
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0,秩:4共轭类数:25中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:18432正规子群个数:91
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0,秩:4共轭类数:25中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:2048正规子群个数:75
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0,秩:4共轭类数:19中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:9216正规子群个数:71
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0,秩:4共轭类数:19中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:1024正规子群个数:71
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0,秩:4共轭类数:19中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:1024正规子群个数:71
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0,秩:4共轭类数:19中心:[ 4, 2 ]换位子群:[ 4, 2 ]自同构群:15360正规子群个数:71
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[ 64, 248 ]:1,15,16,32,0,0,
0,秩:4共轭类数:40中心:[ 16, 5 ]换位子群:[ 2, 1 ]自同构群:1536正规子群个数:121
[ 64, 249 ]:1,15,16,32,0,0,
0,秩:4共轭类数:34中心:[ 4, 1 ]换位子群:[ 2, 1 ]自同构群:1536正规子群个数:119
[ 64, 250 ]:1,39,8,16,0,0,
0,秩:4共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 1 ]自同构群:12288正规子群个数:89
[ 64, 251 ]:1,23,24,16,0,0,
0,秩:4共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 1 ]自同构群:6144正规子群个数:89
[ 64, 252 ]:1,7,40,16,0,0,
0,秩:4共轭类数:28中心:[ 8, 5 ]换位子群:[ 4, 1 ]自同构群:12288正规子群个数:89
[ 64, 253 ]:1,23,24,16,0,0,
0,秩:4共轭类数:28中心:[ 8, 2 ]换位子群:[ 4, 1 ]自同构群:1024正规子群个数:81
[ 64, 254 ]:1,31,16,16,0,0,
0,秩:4共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 1 ]自同构群:1024正规子群个数:81
[ 64, 255 ]:1,15,32,16,0,0,
0,秩:4共轭类数:22中心:[ 4, 2 ]换位子群:[ 4, 1 ]自同构群:1024正规子群个数:81
[ 64, 256 ]:1,23,24,16,0,0,
0,秩:4共轭类数:22中心:[ 4, 1 ]换位子群:[ 4, 1 ]自同构群:512正规子群个数:79
[ 64, 257 ]:1,31,16,16,0,0,
0,秩:4共轭类数:22中心:[ 2, 1 ]换位子群:[ 4, 1 ]自同构群:768正规子群个数:79
[ 64, 258 ]:1,23,24,16,0,0,
0,秩:4共轭类数:22中心:[ 2, 1 ]换位子群:[ 4, 1 ]自同构群:384正规子群个数:79
[ 64, 259 ]:1,15,32,16,0,0,
0,秩:4共轭类数:22中心:[ 2, 1 ]换位子群:[ 4, 1 ]自同构群:768正规子群个数:79
[ 64, 260 ]:1,31,32,0,0,0,
0,秩:5共轭类数:64中心:[ 64, 260 ]换位子群:[ 1, 1 ]自同构群:10321920正规子群个数:681
[ 64, 261 ]:1,47,16,0,0,0,
0,秩:5共轭类数:40中心:[ 16, 14 ]换位子群:[ 2, 1 ]自同构群:688128正规子群个数:425
[ 64, 262 ]:1,15,48,0,0,0,
0,秩:5共轭类数:40中心:[ 16, 14 ]换位子群:[ 2, 1 ]自同构群:2064384正规子群个数:425
[ 64, 263 ]:1,31,32,0,0,0,
0,秩:5共轭类数:40中心:[ 16, 10 ]换位子群:[ 2, 1 ]自同构群:73728正规子群个数:385
[ 64, 264 ]:1,39,24,0,0,0,
0,秩:5共轭类数:34中心:[ 4, 2 ]换位子群:[ 2, 1 ]自同构群:36864正规子群个数:377
[ 64, 265 ]:1,23,40,0,0,0,
0,秩:5共轭类数:34中心:[ 4, 2 ]换位子群:[ 2, 1 ]自同构群:61440正规子群个数:377
[ 64, 266 ]:1,31,32,0,0,0,
0,秩:5共轭类数:34中心:[ 4, 1 ]换位子群:[ 2, 1 ]自同构群:23040正规子群个数:375
[ 64, 267 ]:1,63,0,0,0,0,
0
 ,秩:6共轭类数:64中心:[ 64, 267 ]换位子群:[ 1, 1 ]自同构群:20158709760正规子群个数:2825
gap> for n in [1..51] do G32:=SmallGroup(32,n);;G:=DirectProduct(G32,CyclicGroup(2));;Print(IdGroup(G32));Print("与C_2的直积=");Print(IdGroup(G));Print("\n");od;
[ 32, 1 ]与C_2的直积=[ 64, 50 ]
[ 32, 2 ]与C_2的直积=[ 64, 56 ]
[ 32, 3 ]与C_2的直积=[ 64, 83 ]
[ 32, 4 ]与C_2的直积=[ 64, 84 ]
[ 32, 5 ]与C_2的直积=[ 64, 87 ]
[ 32, 6 ]与C_2的直积=[ 64, 90 ]
[ 32, 7 ]与C_2的直积=[ 64, 92 ]
[ 32, 8 ]与C_2的直积=[ 64, 93 ]
[ 32, 9 ]与C_2的直积=[ 64, 95 ]
[ 32, 10 ]与C_2的直积=[ 64, 96 ]
[ 32, 11 ]与C_2的直积=[ 64, 101 ]
[ 32, 12 ]与C_2的直积=[ 64, 103 ]
[ 32, 13 ]与C_2的直积=[ 64, 106 ]
[ 32, 14 ]与C_2的直积=[ 64, 107 ]
[ 32, 15 ]与C_2的直积=[ 64, 110 ]
[ 32, 16 ]与C_2的直积=[ 64, 183 ]
[ 32, 17 ]与C_2的直积=[ 64, 184 ]
[ 32, 18 ]与C_2的直积=[ 64, 186 ]
[ 32, 19 ]与C_2的直积=[ 64, 187 ]
[ 32, 20 ]与C_2的直积=[ 64, 188 ]
[ 32, 21 ]与C_2的直积=[ 64, 192 ]
[ 32, 22 ]与C_2的直积=[ 64, 193 ]
[ 32, 23 ]与C_2的直积=[ 64, 194 ]
[ 32, 24 ]与C_2的直积=[ 64, 195 ]
[ 32, 25 ]与C_2的直积=[ 64, 196 ]
[ 32, 26 ]与C_2的直积=[ 64, 197 ]
[ 32, 27 ]与C_2的直积=[ 64, 202 ]
[ 32, 28 ]与C_2的直积=[ 64, 203 ]
[ 32, 29 ]与C_2的直积=[ 64, 204 ]
[ 32, 30 ]与C_2的直积=[ 64, 205 ]
[ 32, 31 ]与C_2的直积=[ 64, 207 ]
[ 32, 32 ]与C_2的直积=[ 64, 208 ]
[ 32, 33 ]与C_2的直积=[ 64, 209 ]
[ 32, 34 ]与C_2的直积=[ 64, 211 ]
[ 32, 35 ]与C_2的直积=[ 64, 212 ]
[ 32, 36 ]与C_2的直积=[ 64, 246 ]
[ 32, 37 ]与C_2的直积=[ 64, 247 ]
[ 32, 38 ]与C_2的直积=[ 64, 248 ]
[ 32, 39 ]与C_2的直积=[ 64, 250 ]
[ 32, 40 ]与C_2的直积=[ 64, 251 ]
[ 32, 41 ]与C_2的直积=[ 64, 252 ]
[ 32, 42 ]与C_2的直积=[ 64, 253 ]
[ 32, 43 ]与C_2的直积=[ 64, 254 ]
[ 32, 44 ]与C_2的直积=[ 64, 255 ]
[ 32, 45 ]与C_2的直积=[ 64, 260 ]
[ 32, 46 ]与C_2的直积=[ 64, 261 ]
[ 32, 47 ]与C_2的直积=[ 64, 262 ]
[ 32, 48 ]与C_2的直积=[ 64, 263 ]
[ 32, 49 ]与C_2的直积=[ 64, 264 ]
[ 32, 50 ]与C_2的直积=[ 64, 265 ]
[ 32, 51 ]与C_2的直积=[ 64, 267 ]
gap> for n in [1..14] do G16:=SmallGroup(16,n);;G:=DirectProduct(G16,CyclicGroup(4));;Print(IdGroup(G16));Print("与C_4的直积=");Print(IdGroup(G));Print("\n");od;
[ 16, 1 ]与C_4的直积=[ 64, 26 ]
[ 16, 2 ]与C_4的直积=[ 64, 55 ]
[ 16, 3 ]与C_4的直积=[ 64, 58 ]
[ 16, 4 ]与C_4的直积=[ 64, 59 ]
[ 16, 5 ]与C_4的直积=[ 64, 83 ]
[ 16, 6 ]与C_4的直积=[ 64, 85 ]
[ 16, 7 ]与C_4的直积=[ 64, 118 ]
[ 16, 8 ]与C_4的直积=[ 64, 119 ]
[ 16, 9 ]与C_4的直积=[ 64, 120 ]
[ 16, 10 ]与C_4的直积=[ 64, 192 ]
[ 16, 11 ]与C_4的直积=[ 64, 196 ]
[ 16, 12 ]与C_4的直积=[ 64, 197 ]
[ 16, 13 ]与C_4的直积=[ 64, 198 ]
[ 16, 14 ]与C_4的直积=[ 64, 260 ]
gap> for n in [1..14] do G16:=SmallGroup(16,n);;G:=DirectProduct(G16,SmallGroup(4,2));;Print(IdGroup(G16));Print("与K_4 的直积=");Print(IdGroup(G));Print("\n");od;
[ 16, 1 ]与K_4的直积=[ 64, 183 ]
[ 16, 2 ]与K_4的直积=[ 64, 192 ]
[ 16, 3 ]与K_4的直积=[ 64, 193 ]
[ 16, 4 ]与K_4的直积=[ 64, 194 ]
[ 16, 5 ]与K_4的直积=[ 64, 246 ]
[ 16, 6 ]与K_4的直积=[ 64, 247 ]
[ 16, 7 ]与K_4的直积=[ 64, 250 ]
[ 16, 8 ]与K_4的直积=[ 64, 251 ]
[ 16, 9 ]与K_4的直积=[ 64, 252 ]
[ 16, 10 ]与K_4的直积=[ 64, 260 ]
[ 16, 11 ]与K_4的直积=[ 64, 261 ]
[ 16, 12 ]与K_4的直积=[ 64, 262 ]
[ 16, 13 ]与K_4的直积=[ 64, 263 ]
[ 16, 14 ]与K_4的直积=[ 64, 267 ]
gap> for n in [1..5] do G8n:=SmallGroup(8,n);;for m in [1..5] do G8m:=SmallGroup(8,m);;G:=DirectProduct(G8n,G8m);;Print(IdGroup(G8n));Print("与");Print(IdGroup(G8m));Print("的直积=");Print(IdGroup(G));Print("\n");od;od;
[ 8, 1 ]与[ 8, 1 ]的直积=[ 64, 2 ]
[ 8, 1 ]与[ 8, 2 ]的直积=[ 64, 83 ]
[ 8, 1 ]与[ 8, 3 ]的直积=[ 64, 115 ]
[ 8, 1 ]与[ 8, 4 ]的直积=[ 64, 126 ]
[ 8, 1 ]与[ 8, 5 ]的直积=[ 64, 246 ]
[ 8, 2 ]与[ 8, 1 ]的直积=[ 64, 83 ]
[ 8, 2 ]与[ 8, 2 ]的直积=[ 64, 192 ]
[ 8, 2 ]与[ 8, 3 ]的直积=[ 64, 196 ]
[ 8, 2 ]与[ 8, 4 ]的直积=[ 64, 197 ]
[ 8, 2 ]与[ 8, 5 ]的直积=[ 64, 260 ]
[ 8, 3 ]与[ 8, 1 ]的直积=[ 64, 115 ]
[ 8, 3 ]与[ 8, 2 ]的直积=[ 64, 196 ]
[ 8, 3 ]与[ 8, 3 ]的直积=[ 64, 226 ]
[ 8, 3 ]与[ 8, 4 ]的直积=[ 64, 230 ]
[ 8, 3 ]与[ 8, 5 ]的直积=[ 64, 261 ]
[ 8, 4 ]与[ 8, 1 ]的直积=[ 64, 126 ]
[ 8, 4 ]与[ 8, 2 ]的直积=[ 64, 197 ]
[ 8, 4 ]与[ 8, 3 ]的直积=[ 64, 230 ]
[ 8, 4 ]与[ 8, 4 ]的直积=[ 64, 239 ]
[ 8, 4 ]与[ 8, 5 ]的直积=[ 64, 262 ]
[ 8, 5 ]与[ 8, 1 ]的直积=[ 64, 246 ]
[ 8, 5 ]与[ 8, 2 ]的直积=[ 64, 260 ]
[ 8, 5 ]与[ 8, 3 ]的直积=[ 64, 261 ]
[ 8, 5 ]与[ 8, 4 ]的直积=[ 64, 262 ]
[ 8, 5 ]与[ 8, 5 ]的直积=[ 64, 267 ]

;