direct product, metabelian, supersoluble, monomial, A-group
Aliases: C8×C3⋊Dic3, C24⋊4Dic3, C32⋊9(C4×C8), (C3×C24)⋊11C4, C6.14(S3×C8), C3⋊3(C8×Dic3), C12.79(C4×S3), (C6×C24).22C2, (C2×C24).32S3, C32⋊4C8⋊13C4, (C2×C12).417D6, (C3×C6).18C42, C62.71(C2×C4), C6.14(C4×Dic3), C12.58(C2×Dic3), (C6×C12).339C22, C2.2(C8×C3⋊S3), C4.20(C4×C3⋊S3), (C2×C6).46(C4×S3), (C3×C6).34(C2×C8), C22.8(C4×C3⋊S3), C2.2(C4×C3⋊Dic3), (C2×C8).10(C3⋊S3), C4.11(C2×C3⋊Dic3), (C3×C12).134(C2×C4), (C4×C3⋊Dic3).24C2, (C2×C3⋊Dic3).25C4, (C2×C32⋊4C8).22C2, (C2×C4).90(C2×C3⋊S3), SmallGroup(288,288)
Series: Derived ►Chief ►Lower central ►Upper central
| C32 — C8×C3⋊Dic3 |
Generators and relations for C8×C3⋊Dic3
G = < a,b,c,d | a8=b3=c6=1, d2=c3, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b-1, dcd-1=c-1 >
Subgroups: 308 in 132 conjugacy classes, 77 normal (17 characteristic)
C1, C2, C2, C3, C4, C4, C22, C6, C8, C8, C2×C4, C2×C4, C32, Dic3, C12, C2×C6, C42, C2×C8, C2×C8, C3×C6, C3×C6, C3⋊C8, C24, C2×Dic3, C2×C12, C4×C8, C3⋊Dic3, C3×C12, C62, C2×C3⋊C8, C4×Dic3, C2×C24, C32⋊4C8, C3×C24, C2×C3⋊Dic3, C6×C12, C8×Dic3, C2×C32⋊4C8, C4×C3⋊Dic3, C6×C24, C8×C3⋊Dic3
Quotients: C1, C2, C4, C22, S3, C8, C2×C4, Dic3, D6, C42, C2×C8, C3⋊S3, C4×S3, C2×Dic3, C4×C8, C3⋊Dic3, C2×C3⋊S3, S3×C8, C4×Dic3, C4×C3⋊S3, C2×C3⋊Dic3, C8×Dic3, C8×C3⋊S3, C4×C3⋊Dic3, C8×C3⋊Dic3
►Regular action on 288 points
Generators in S288
(1 2 3 4 5 6 7 8)(9 10 11 12 13 14 15 16)(17 18 19 20 21 22 23 24)(25 26 27 28 29 30 31 32)(33 34 35 36 37 38 39 40)(41 42 43 44 45 46 47 48)(49 50 51 52 53 54 55 56)(57 58 59 60 61 62 63 64)(65 66 67 68 69 70 71 72)(73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88)(89 90 91 92 93 94 95 96)(97 98 99 100 101 102 103 104)(105 106 107 108 109 110 111 112)(113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128)(129 130 131 132 133 134 135 136)(137 138 139 140 141 142 143 144)(145 146 147 148 149 150 151 152)(153 154 155 156 157 158 159 160)(161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176)(177 178 179 180 181 182 183 184)(185 186 187 188 189 190 191 192)(193 194 195 196 197 198 199 200)(201 202 203 204 205 206 207 208)(209 210 211 212 213 214 215 216)(217 218 219 220 221 222 223 224)(225 226 227 228 229 230 231 232)(233 234 235 236 237 238 239 240)(241 242 243 244 245 246 247 248)(249 250 251 252 253 254 255 256)(257 258 259 260 261 262 263 264)(265 266 267 268 269 270 271 272)(273 274 275 276 277 278 279 280)(281 282 283 284 285 286 287 288)
(1 208 225)(2 201 226)(3 202 227)(4 203 228)(5 204 229)(6 205 230)(7 206 231)(8 207 232)(9 31 124)(10 32 125)(11 25 126)(12 26 127)(13 27 128)(14 28 121)(15 29 122)(16 30 123)(17 111 260)(18 112 261)(19 105 262)(20 106 263)(21 107 264)(22 108 257)(23 109 258)(24 110 259)(33 137 98)(34 138 99)(35 139 100)(36 140 101)(37 141 102)(38 142 103)(39 143 104)(40 144 97)(41 215 234)(42 216 235)(43 209 236)(44 210 237)(45 211 238)(46 212 239)(47 213 240)(48 214 233)(49 196 80)(50 197 73)(51 198 74)(52 199 75)(53 200 76)(54 193 77)(55 194 78)(56 195 79)(57 186 218)(58 187 219)(59 188 220)(60 189 221)(61 190 222)(62 191 223)(63 192 224)(64 185 217)(65 81 96)(66 82 89)(67 83 90)(68 84 91)(69 85 92)(70 86 93)(71 87 94)(72 88 95)(113 153 249)(114 154 250)(115 155 251)(116 156 252)(117 157 253)(118 158 254)(119 159 255)(120 160 256)(129 151 242)(130 152 243)(131 145 244)(132 146 245)(133 147 246)(134 148 247)(135 149 248)(136 150 241)(161 271 176)(162 272 169)(163 265 170)(164 266 171)(165 267 172)(166 268 173)(167 269 174)(168 270 175)(177 273 281)(178 274 282)(179 275 283)(180 276 284)(181 277 285)(182 278 286)(183 279 287)(184 280 288)
(1 141 195 66 45 59)(2 142 196 67 46 60)(3 143 197 68 47 61)(4 144 198 69 48 62)(5 137 199 70 41 63)(6 138 200 71 42 64)(7 139 193 72 43 57)(8 140 194 65 44 58)(9 261 149 268 119 285)(10 262 150 269 120 286)(11 263 151 270 113 287)(12 264 152 271 114 288)(13 257 145 272 115 281)(14 258 146 265 116 282)(15 259 147 266 117 283)(16 260 148 267 118 284)(17 247 172 158 180 30)(18 248 173 159 181 31)(19 241 174 160 182 32)(20 242 175 153 183 25)(21 243 176 154 184 26)(22 244 169 155 177 27)(23 245 170 156 178 28)(24 246 171 157 179 29)(33 52 93 234 224 229)(34 53 94 235 217 230)(35 54 95 236 218 231)(36 55 96 237 219 232)(37 56 89 238 220 225)(38 49 90 239 221 226)(39 50 91 240 222 227)(40 51 92 233 223 228)(73 84 213 190 202 104)(74 85 214 191 203 97)(75 86 215 192 204 98)(76 87 216 185 205 99)(77 88 209 186 206 100)(78 81 210 187 207 101)(79 82 211 188 208 102)(80 83 212 189 201 103)(105 136 167 256 278 125)(106 129 168 249 279 126)(107 130 161 250 280 127)(108 131 162 251 273 128)(109 132 163 252 274 121)(110 133 164 253 275 122)(111 134 165 254 276 123)(112 135 166 255 277 124)
(1 272 66 13)(2 265 67 14)(3 266 68 15)(4 267 69 16)(5 268 70 9)(6 269 71 10)(7 270 72 11)(8 271 65 12)(17 223 158 51)(18 224 159 52)(19 217 160 53)(20 218 153 54)(21 219 154 55)(22 220 155 56)(23 221 156 49)(24 222 157 50)(25 231 175 95)(26 232 176 96)(27 225 169 89)(28 226 170 90)(29 227 171 91)(30 228 172 92)(31 229 173 93)(32 230 174 94)(33 248 234 181)(34 241 235 182)(35 242 236 183)(36 243 237 184)(37 244 238 177)(38 245 239 178)(39 246 240 179)(40 247 233 180)(41 285 137 149)(42 286 138 150)(43 287 139 151)(44 288 140 152)(45 281 141 145)(46 282 142 146)(47 283 143 147)(48 284 144 148)(57 113 193 263)(58 114 194 264)(59 115 195 257)(60 116 196 258)(61 117 197 259)(62 118 198 260)(63 119 199 261)(64 120 200 262)(73 110 190 253)(74 111 191 254)(75 112 192 255)(76 105 185 256)(77 106 186 249)(78 107 187 250)(79 108 188 251)(80 109 189 252)(81 127 207 161)(82 128 208 162)(83 121 201 163)(84 122 202 164)(85 123 203 165)(86 124 204 166)(87 125 205 167)(88 126 206 168)(97 134 214 276)(98 135 215 277)(99 136 216 278)(100 129 209 279)(101 130 210 280)(102 131 211 273)(103 132 212 274)(104 133 213 275)
G:=sub<Sym(288)| (1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64)(65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104)(105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128)(129,130,131,132,133,134,135,136)(137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152)(153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176)(177,178,179,180,181,182,183,184)(185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224)(225,226,227,228,229,230,231,232)(233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248)(249,250,251,252,253,254,255,256)(257,258,259,260,261,262,263,264)(265,266,267,268,269,270,271,272)(273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288), (1,208,225)(2,201,226)(3,202,227)(4,203,228)(5,204,229)(6,205,230)(7,206,231)(8,207,232)(9,31,124)(10,32,125)(11,25,126)(12,26,127)(13,27,128)(14,28,121)(15,29,122)(16,30,123)(17,111,260)(18,112,261)(19,105,262)(20,106,263)(21,107,264)(22,108,257)(23,109,258)(24,110,259)(33,137,98)(34,138,99)(35,139,100)(36,140,101)(37,141,102)(38,142,103)(39,143,104)(40,144,97)(41,215,234)(42,216,235)(43,209,236)(44,210,237)(45,211,238)(46,212,239)(47,213,240)(48,214,233)(49,196,80)(50,197,73)(51,198,74)(52,199,75)(53,200,76)(54,193,77)(55,194,78)(56,195,79)(57,186,218)(58,187,219)(59,188,220)(60,189,221)(61,190,222)(62,191,223)(63,192,224)(64,185,217)(65,81,96)(66,82,89)(67,83,90)(68,84,91)(69,85,92)(70,86,93)(71,87,94)(72,88,95)(113,153,249)(114,154,250)(115,155,251)(116,156,252)(117,157,253)(118,158,254)(119,159,255)(120,160,256)(129,151,242)(130,152,243)(131,145,244)(132,146,245)(133,147,246)(134,148,247)(135,149,248)(136,150,241)(161,271,176)(162,272,169)(163,265,170)(164,266,171)(165,267,172)(166,268,173)(167,269,174)(168,270,175)(177,273,281)(178,274,282)(179,275,283)(180,276,284)(181,277,285)(182,278,286)(183,279,287)(184,280,288), (1,141,195,66,45,59)(2,142,196,67,46,60)(3,143,197,68,47,61)(4,144,198,69,48,62)(5,137,199,70,41,63)(6,138,200,71,42,64)(7,139,193,72,43,57)(8,140,194,65,44,58)(9,261,149,268,119,285)(10,262,150,269,120,286)(11,263,151,270,113,287)(12,264,152,271,114,288)(13,257,145,272,115,281)(14,258,146,265,116,282)(15,259,147,266,117,283)(16,260,148,267,118,284)(17,247,172,158,180,30)(18,248,173,159,181,31)(19,241,174,160,182,32)(20,242,175,153,183,25)(21,243,176,154,184,26)(22,244,169,155,177,27)(23,245,170,156,178,28)(24,246,171,157,179,29)(33,52,93,234,224,229)(34,53,94,235,217,230)(35,54,95,236,218,231)(36,55,96,237,219,232)(37,56,89,238,220,225)(38,49,90,239,221,226)(39,50,91,240,222,227)(40,51,92,233,223,228)(73,84,213,190,202,104)(74,85,214,191,203,97)(75,86,215,192,204,98)(76,87,216,185,205,99)(77,88,209,186,206,100)(78,81,210,187,207,101)(79,82,211,188,208,102)(80,83,212,189,201,103)(105,136,167,256,278,125)(106,129,168,249,279,126)(107,130,161,250,280,127)(108,131,162,251,273,128)(109,132,163,252,274,121)(110,133,164,253,275,122)(111,134,165,254,276,123)(112,135,166,255,277,124), (1,272,66,13)(2,265,67,14)(3,266,68,15)(4,267,69,16)(5,268,70,9)(6,269,71,10)(7,270,72,11)(8,271,65,12)(17,223,158,51)(18,224,159,52)(19,217,160,53)(20,218,153,54)(21,219,154,55)(22,220,155,56)(23,221,156,49)(24,222,157,50)(25,231,175,95)(26,232,176,96)(27,225,169,89)(28,226,170,90)(29,227,171,91)(30,228,172,92)(31,229,173,93)(32,230,174,94)(33,248,234,181)(34,241,235,182)(35,242,236,183)(36,243,237,184)(37,244,238,177)(38,245,239,178)(39,246,240,179)(40,247,233,180)(41,285,137,149)(42,286,138,150)(43,287,139,151)(44,288,140,152)(45,281,141,145)(46,282,142,146)(47,283,143,147)(48,284,144,148)(57,113,193,263)(58,114,194,264)(59,115,195,257)(60,116,196,258)(61,117,197,259)(62,118,198,260)(63,119,199,261)(64,120,200,262)(73,110,190,253)(74,111,191,254)(75,112,192,255)(76,105,185,256)(77,106,186,249)(78,107,187,250)(79,108,188,251)(80,109,189,252)(81,127,207,161)(82,128,208,162)(83,121,201,163)(84,122,202,164)(85,123,203,165)(86,124,204,166)(87,125,205,167)(88,126,206,168)(97,134,214,276)(98,135,215,277)(99,136,216,278)(100,129,209,279)(101,130,210,280)(102,131,211,273)(103,132,212,274)(104,133,213,275)>;
G:=Group( (1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64)(65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104)(105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128)(129,130,131,132,133,134,135,136)(137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152)(153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176)(177,178,179,180,181,182,183,184)(185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224)(225,226,227,228,229,230,231,232)(233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248)(249,250,251,252,253,254,255,256)(257,258,259,260,261,262,263,264)(265,266,267,268,269,270,271,272)(273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288), (1,208,225)(2,201,226)(3,202,227)(4,203,228)(5,204,229)(6,205,230)(7,206,231)(8,207,232)(9,31,124)(10,32,125)(11,25,126)(12,26,127)(13,27,128)(14,28,121)(15,29,122)(16,30,123)(17,111,260)(18,112,261)(19,105,262)(20,106,263)(21,107,264)(22,108,257)(23,109,258)(24,110,259)(33,137,98)(34,138,99)(35,139,100)(36,140,101)(37,141,102)(38,142,103)(39,143,104)(40,144,97)(41,215,234)(42,216,235)(43,209,236)(44,210,237)(45,211,238)(46,212,239)(47,213,240)(48,214,233)(49,196,80)(50,197,73)(51,198,74)(52,199,75)(53,200,76)(54,193,77)(55,194,78)(56,195,79)(57,186,218)(58,187,219)(59,188,220)(60,189,221)(61,190,222)(62,191,223)(63,192,224)(64,185,217)(65,81,96)(66,82,89)(67,83,90)(68,84,91)(69,85,92)(70,86,93)(71,87,94)(72,88,95)(113,153,249)(114,154,250)(115,155,251)(116,156,252)(117,157,253)(118,158,254)(119,159,255)(120,160,256)(129,151,242)(130,152,243)(131,145,244)(132,146,245)(133,147,246)(134,148,247)(135,149,248)(136,150,241)(161,271,176)(162,272,169)(163,265,170)(164,266,171)(165,267,172)(166,268,173)(167,269,174)(168,270,175)(177,273,281)(178,274,282)(179,275,283)(180,276,284)(181,277,285)(182,278,286)(183,279,287)(184,280,288), (1,141,195,66,45,59)(2,142,196,67,46,60)(3,143,197,68,47,61)(4,144,198,69,48,62)(5,137,199,70,41,63)(6,138,200,71,42,64)(7,139,193,72,43,57)(8,140,194,65,44,58)(9,261,149,268,119,285)(10,262,150,269,120,286)(11,263,151,270,113,287)(12,264,152,271,114,288)(13,257,145,272,115,281)(14,258,146,265,116,282)(15,259,147,266,117,283)(16,260,148,267,118,284)(17,247,172,158,180,30)(18,248,173,159,181,31)(19,241,174,160,182,32)(20,242,175,153,183,25)(21,243,176,154,184,26)(22,244,169,155,177,27)(23,245,170,156,178,28)(24,246,171,157,179,29)(33,52,93,234,224,229)(34,53,94,235,217,230)(35,54,95,236,218,231)(36,55,96,237,219,232)(37,56,89,238,220,225)(38,49,90,239,221,226)(39,50,91,240,222,227)(40,51,92,233,223,228)(73,84,213,190,202,104)(74,85,214,191,203,97)(75,86,215,192,204,98)(76,87,216,185,205,99)(77,88,209,186,206,100)(78,81,210,187,207,101)(79,82,211,188,208,102)(80,83,212,189,201,103)(105,136,167,256,278,125)(106,129,168,249,279,126)(107,130,161,250,280,127)(108,131,162,251,273,128)(109,132,163,252,274,121)(110,133,164,253,275,122)(111,134,165,254,276,123)(112,135,166,255,277,124), (1,272,66,13)(2,265,67,14)(3,266,68,15)(4,267,69,16)(5,268,70,9)(6,269,71,10)(7,270,72,11)(8,271,65,12)(17,223,158,51)(18,224,159,52)(19,217,160,53)(20,218,153,54)(21,219,154,55)(22,220,155,56)(23,221,156,49)(24,222,157,50)(25,231,175,95)(26,232,176,96)(27,225,169,89)(28,226,170,90)(29,227,171,91)(30,228,172,92)(31,229,173,93)(32,230,174,94)(33,248,234,181)(34,241,235,182)(35,242,236,183)(36,243,237,184)(37,244,238,177)(38,245,239,178)(39,246,240,179)(40,247,233,180)(41,285,137,149)(42,286,138,150)(43,287,139,151)(44,288,140,152)(45,281,141,145)(46,282,142,146)(47,283,143,147)(48,284,144,148)(57,113,193,263)(58,114,194,264)(59,115,195,257)(60,116,196,258)(61,117,197,259)(62,118,198,260)(63,119,199,261)(64,120,200,262)(73,110,190,253)(74,111,191,254)(75,112,192,255)(76,105,185,256)(77,106,186,249)(78,107,187,250)(79,108,188,251)(80,109,189,252)(81,127,207,161)(82,128,208,162)(83,121,201,163)(84,122,202,164)(85,123,203,165)(86,124,204,166)(87,125,205,167)(88,126,206,168)(97,134,214,276)(98,135,215,277)(99,136,216,278)(100,129,209,279)(101,130,210,280)(102,131,211,273)(103,132,212,274)(104,133,213,275) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8),(9,10,11,12,13,14,15,16),(17,18,19,20,21,22,23,24),(25,26,27,28,29,30,31,32),(33,34,35,36,37,38,39,40),(41,42,43,44,45,46,47,48),(49,50,51,52,53,54,55,56),(57,58,59,60,61,62,63,64),(65,66,67,68,69,70,71,72),(73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88),(89,90,91,92,93,94,95,96),(97,98,99,100,101,102,103,104),(105,106,107,108,109,110,111,112),(113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128),(129,130,131,132,133,134,135,136),(137,138,139,140,141,142,143,144),(145,146,147,148,149,150,151,152),(153,154,155,156,157,158,159,160),(161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176),(177,178,179,180,181,182,183,184),(185,186,187,188,189,190,191,192),(193,194,195,196,197,198,199,200),(201,202,203,204,205,206,207,208),(209,210,211,212,213,214,215,216),(217,218,219,220,221,222,223,224),(225,226,227,228,229,230,231,232),(233,234,235,236,237,238,239,240),(241,242,243,244,245,246,247,248),(249,250,251,252,253,254,255,256),(257,258,259,260,261,262,263,264),(265,266,267,268,269,270,271,272),(273,274,275,276,277,278,279,280),(281,282,283,284,285,286,287,288)], [(1,208,225),(2,201,226),(3,202,227),(4,203,228),(5,204,229),(6,205,230),(7,206,231),(8,207,232),(9,31,124),(10,32,125),(11,25,126),(12,26,127),(13,27,128),(14,28,121),(15,29,122),(16,30,123),(17,111,260),(18,112,261),(19,105,262),(20,106,263),(21,107,264),(22,108,257),(23,109,258),(24,110,259),(33,137,98),(34,138,99),(35,139,100),(36,140,101),(37,141,102),(38,142,103),(39,143,104),(40,144,97),(41,215,234),(42,216,235),(43,209,236),(44,210,237),(45,211,238),(46,212,239),(47,213,240),(48,214,233),(49,196,80),(50,197,73),(51,198,74),(52,199,75),(53,200,76),(54,193,77),(55,194,78),(56,195,79),(57,186,218),(58,187,219),(59,188,220),(60,189,221),(61,190,222),(62,191,223),(63,192,224),(64,185,217),(65,81,96),(66,82,89),(67,83,90),(68,84,91),(69,85,92),(70,86,93),(71,87,94),(72,88,95),(113,153,249),(114,154,250),(115,155,251),(116,156,252),(117,157,253),(118,158,254),(119,159,255),(120,160,256),(129,151,242),(130,152,243),(131,145,244),(132,146,245),(133,147,246),(134,148,247),(135,149,248),(136,150,241),(161,271,176),(162,272,169),(163,265,170),(164,266,171),(165,267,172),(166,268,173),(167,269,174),(168,270,175),(177,273,281),(178,274,282),(179,275,283),(180,276,284),(181,277,285),(182,278,286),(183,279,287),(184,280,288)], [(1,141,195,66,45,59),(2,142,196,67,46,60),(3,143,197,68,47,61),(4,144,198,69,48,62),(5,137,199,70,41,63),(6,138,200,71,42,64),(7,139,193,72,43,57),(8,140,194,65,44,58),(9,261,149,268,119,285),(10,262,150,269,120,286),(11,263,151,270,113,287),(12,264,152,271,114,288),(13,257,145,272,115,281),(14,258,146,265,116,282),(15,259,147,266,117,283),(16,260,148,267,118,284),(17,247,172,158,180,30),(18,248,173,159,181,31),(19,241,174,160,182,32),(20,242,175,153,183,25),(21,243,176,154,184,26),(22,244,169,155,177,27),(23,245,170,156,178,28),(24,246,171,157,179,29),(33,52,93,234,224,229),(34,53,94,235,217,230),(35,54,95,236,218,231),(36,55,96,237,219,232),(37,56,89,238,220,225),(38,49,90,239,221,226),(39,50,91,240,222,227),(40,51,92,233,223,228),(73,84,213,190,202,104),(74,85,214,191,203,97),(75,86,215,192,204,98),(76,87,216,185,205,99),(77,88,209,186,206,100),(78,81,210,187,207,101),(79,82,211,188,208,102),(80,83,212,189,201,103),(105,136,167,256,278,125),(106,129,168,249,279,126),(107,130,161,250,280,127),(108,131,162,251,273,128),(109,132,163,252,274,121),(110,133,164,253,275,122),(111,134,165,254,276,123),(112,135,166,255,277,124)], [(1,272,66,13),(2,265,67,14),(3,266,68,15),(4,267,69,16),(5,268,70,9),(6,269,71,10),(7,270,72,11),(8,271,65,12),(17,223,158,51),(18,224,159,52),(19,217,160,53),(20,218,153,54),(21,219,154,55),(22,220,155,56),(23,221,156,49),(24,222,157,50),(25,231,175,95),(26,232,176,96),(27,225,169,89),(28,226,170,90),(29,227,171,91),(30,228,172,92),(31,229,173,93),(32,230,174,94),(33,248,234,181),(34,241,235,182),(35,242,236,183),(36,243,237,184),(37,244,238,177),(38,245,239,178),(39,246,240,179),(40,247,233,180),(41,285,137,149),(42,286,138,150),(43,287,139,151),(44,288,140,152),(45,281,141,145),(46,282,142,146),(47,283,143,147),(48,284,144,148),(57,113,193,263),(58,114,194,264),(59,115,195,257),(60,116,196,258),(61,117,197,259),(62,118,198,260),(63,119,199,261),(64,120,200,262),(73,110,190,253),(74,111,191,254),(75,112,192,255),(76,105,185,256),(77,106,186,249),(78,107,187,250),(79,108,188,251),(80,109,189,252),(81,127,207,161),(82,128,208,162),(83,121,201,163),(84,122,202,164),(85,123,203,165),(86,124,204,166),(87,125,205,167),(88,126,206,168),(97,134,214,276),(98,135,215,277),(99,136,216,278),(100,129,209,279),(101,130,210,280),(102,131,211,273),(103,132,212,274),(104,133,213,275)]])
96 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 3C | 3D | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 6A | ··· | 6L | 8A | ··· | 8H | 8I | ··· | 8P | 12A | ··· | 12P | 24A | ··· | 24AF |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 6 | ··· | 6 | 8 | ··· | 8 | 8 | ··· | 8 | 12 | ··· | 12 | 24 | ··· | 24 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 9 | ··· | 9 | 2 | ··· | 2 | 1 | ··· | 1 | 9 | ··· | 9 | 2 | ··· | 2 | 2 | ··· | 2 |
96 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | |||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | C4 | C8 | S3 | Dic3 | D6 | C4×S3 | C4×S3 | S3×C8 |
| kernel | C8×C3⋊Dic3 | C2×C32⋊4C8 | C4×C3⋊Dic3 | C6×C24 | C32⋊4C8 | C3×C24 | C2×C3⋊Dic3 | C3⋊Dic3 | C2×C24 | C24 | C2×C12 | C12 | C2×C6 | C6 |
| # reps | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 16 | 4 | 8 | 4 | 8 | 8 | 32 |
Matrix representation of C8×C3⋊Dic3 ►in GL4(𝔽73) generated by
| 72 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 |
| 0 | 0 | 22 | 0 |
| 0 | 0 | 0 | 22 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 72 | 1 |
| 0 | 0 | 72 | 0 |
| 0 | 72 | 0 | 0 |
| 1 | 1 | 0 | 0 |
| 0 | 0 | 72 | 0 |
| 0 | 0 | 0 | 72 |
| 30 | 60 | 0 | 0 |
| 30 | 43 | 0 | 0 |
| 0 | 0 | 13 | 30 |
| 0 | 0 | 43 | 60 |
G:=sub<GL(4,GF(73))| [72,0,0,0,0,72,0,0,0,0,22,0,0,0,0,22],[1,0,0,0,0,1,0,0,0,0,72,72,0,0,1,0],[0,1,0,0,72,1,0,0,0,0,72,0,0,0,0,72],[30,30,0,0,60,43,0,0,0,0,13,43,0,0,30,60] >;
C8×C3⋊Dic3 in GAP, Magma, Sage, TeX
C_8\times C_3\rtimes {\rm Dic}_3 % in TeX
G:=Group("C8xC3:Dic3"); // GroupNames label
G:=SmallGroup(288,288);
// by ID
G=gap.SmallGroup(288,288);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-3,28,64,80,2693,9414]);
// Polycyclic
G:=Group<a,b,c,d|a^8=b^3=c^6=1,d^2=c^3,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^-1>;
// generators/relations