direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C23⋊C8, C46⋊C8, C92.3C4, C4.14D46, C4.3Dic23, C92.14C22, C22.2Dic23, C23⋊2(C2×C8), (C2×C46).2C4, (C2×C92).6C2, C46.6(C2×C4), (C2×C4).5D23, C2.1(C2×Dic23), SmallGroup(368,8)
Series: Derived ►Chief ►Lower central ►Upper central
| C23 — C2×C23⋊C8 |
Generators and relations for C2×C23⋊C8
G = < a,b,c | a2=b23=c8=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×C23⋊C8
►Regular action on 368 points
Generators in S368
(1 93)(2 94)(3 95)(4 96)(5 97)(6 98)(7 99)(8 100)(9 101)(10 102)(11 103)(12 104)(13 105)(14 106)(15 107)(16 108)(17 109)(18 110)(19 111)(20 112)(21 113)(22 114)(23 115)(24 116)(25 117)(26 118)(27 119)(28 120)(29 121)(30 122)(31 123)(32 124)(33 125)(34 126)(35 127)(36 128)(37 129)(38 130)(39 131)(40 132)(41 133)(42 134)(43 135)(44 136)(45 137)(46 138)(47 139)(48 140)(49 141)(50 142)(51 143)(52 144)(53 145)(54 146)(55 147)(56 148)(57 149)(58 150)(59 151)(60 152)(61 153)(62 154)(63 155)(64 156)(65 157)(66 158)(67 159)(68 160)(69 161)(70 162)(71 163)(72 164)(73 165)(74 166)(75 167)(76 168)(77 169)(78 170)(79 171)(80 172)(81 173)(82 174)(83 175)(84 176)(85 177)(86 178)(87 179)(88 180)(89 181)(90 182)(91 183)(92 184)(185 298)(186 299)(187 277)(188 278)(189 279)(190 280)(191 281)(192 282)(193 283)(194 284)(195 285)(196 286)(197 287)(198 288)(199 289)(200 290)(201 291)(202 292)(203 293)(204 294)(205 295)(206 296)(207 297)(208 317)(209 318)(210 319)(211 320)(212 321)(213 322)(214 300)(215 301)(216 302)(217 303)(218 304)(219 305)(220 306)(221 307)(222 308)(223 309)(224 310)(225 311)(226 312)(227 313)(228 314)(229 315)(230 316)(231 334)(232 335)(233 336)(234 337)(235 338)(236 339)(237 340)(238 341)(239 342)(240 343)(241 344)(242 345)(243 323)(244 324)(245 325)(246 326)(247 327)(248 328)(249 329)(250 330)(251 331)(252 332)(253 333)(254 350)(255 351)(256 352)(257 353)(258 354)(259 355)(260 356)(261 357)(262 358)(263 359)(264 360)(265 361)(266 362)(267 363)(268 364)(269 365)(270 366)(271 367)(272 368)(273 346)(274 347)(275 348)(276 349)
(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)(277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299)(300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322)(323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345)(346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368)
(1 346 70 310 24 326 47 287)(2 368 71 309 25 325 48 286)(3 367 72 308 26 324 49 285)(4 366 73 307 27 323 50 284)(5 365 74 306 28 345 51 283)(6 364 75 305 29 344 52 282)(7 363 76 304 30 343 53 281)(8 362 77 303 31 342 54 280)(9 361 78 302 32 341 55 279)(10 360 79 301 33 340 56 278)(11 359 80 300 34 339 57 277)(12 358 81 322 35 338 58 299)(13 357 82 321 36 337 59 298)(14 356 83 320 37 336 60 297)(15 355 84 319 38 335 61 296)(16 354 85 318 39 334 62 295)(17 353 86 317 40 333 63 294)(18 352 87 316 41 332 64 293)(19 351 88 315 42 331 65 292)(20 350 89 314 43 330 66 291)(21 349 90 313 44 329 67 290)(22 348 91 312 45 328 68 289)(23 347 92 311 46 327 69 288)(93 273 162 224 116 246 139 197)(94 272 163 223 117 245 140 196)(95 271 164 222 118 244 141 195)(96 270 165 221 119 243 142 194)(97 269 166 220 120 242 143 193)(98 268 167 219 121 241 144 192)(99 267 168 218 122 240 145 191)(100 266 169 217 123 239 146 190)(101 265 170 216 124 238 147 189)(102 264 171 215 125 237 148 188)(103 263 172 214 126 236 149 187)(104 262 173 213 127 235 150 186)(105 261 174 212 128 234 151 185)(106 260 175 211 129 233 152 207)(107 259 176 210 130 232 153 206)(108 258 177 209 131 231 154 205)(109 257 178 208 132 253 155 204)(110 256 179 230 133 252 156 203)(111 255 180 229 134 251 157 202)(112 254 181 228 135 250 158 201)(113 276 182 227 136 249 159 200)(114 275 183 226 137 248 160 199)(115 274 184 225 138 247 161 198)
G:=sub<Sym(368)| (1,93)(2,94)(3,95)(4,96)(5,97)(6,98)(7,99)(8,100)(9,101)(10,102)(11,103)(12,104)(13,105)(14,106)(15,107)(16,108)(17,109)(18,110)(19,111)(20,112)(21,113)(22,114)(23,115)(24,116)(25,117)(26,118)(27,119)(28,120)(29,121)(30,122)(31,123)(32,124)(33,125)(34,126)(35,127)(36,128)(37,129)(38,130)(39,131)(40,132)(41,133)(42,134)(43,135)(44,136)(45,137)(46,138)(47,139)(48,140)(49,141)(50,142)(51,143)(52,144)(53,145)(54,146)(55,147)(56,148)(57,149)(58,150)(59,151)(60,152)(61,153)(62,154)(63,155)(64,156)(65,157)(66,158)(67,159)(68,160)(69,161)(70,162)(71,163)(72,164)(73,165)(74,166)(75,167)(76,168)(77,169)(78,170)(79,171)(80,172)(81,173)(82,174)(83,175)(84,176)(85,177)(86,178)(87,179)(88,180)(89,181)(90,182)(91,183)(92,184)(185,298)(186,299)(187,277)(188,278)(189,279)(190,280)(191,281)(192,282)(193,283)(194,284)(195,285)(196,286)(197,287)(198,288)(199,289)(200,290)(201,291)(202,292)(203,293)(204,294)(205,295)(206,296)(207,297)(208,317)(209,318)(210,319)(211,320)(212,321)(213,322)(214,300)(215,301)(216,302)(217,303)(218,304)(219,305)(220,306)(221,307)(222,308)(223,309)(224,310)(225,311)(226,312)(227,313)(228,314)(229,315)(230,316)(231,334)(232,335)(233,336)(234,337)(235,338)(236,339)(237,340)(238,341)(239,342)(240,343)(241,344)(242,345)(243,323)(244,324)(245,325)(246,326)(247,327)(248,328)(249,329)(250,330)(251,331)(252,332)(253,333)(254,350)(255,351)(256,352)(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)(264,360)(265,361)(266,362)(267,363)(268,364)(269,365)(270,366)(271,367)(272,368)(273,346)(274,347)(275,348)(276,349), (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)(277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299)(300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322)(323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345)(346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368), (1,346,70,310,24,326,47,287)(2,368,71,309,25,325,48,286)(3,367,72,308,26,324,49,285)(4,366,73,307,27,323,50,284)(5,365,74,306,28,345,51,283)(6,364,75,305,29,344,52,282)(7,363,76,304,30,343,53,281)(8,362,77,303,31,342,54,280)(9,361,78,302,32,341,55,279)(10,360,79,301,33,340,56,278)(11,359,80,300,34,339,57,277)(12,358,81,322,35,338,58,299)(13,357,82,321,36,337,59,298)(14,356,83,320,37,336,60,297)(15,355,84,319,38,335,61,296)(16,354,85,318,39,334,62,295)(17,353,86,317,40,333,63,294)(18,352,87,316,41,332,64,293)(19,351,88,315,42,331,65,292)(20,350,89,314,43,330,66,291)(21,349,90,313,44,329,67,290)(22,348,91,312,45,328,68,289)(23,347,92,311,46,327,69,288)(93,273,162,224,116,246,139,197)(94,272,163,223,117,245,140,196)(95,271,164,222,118,244,141,195)(96,270,165,221,119,243,142,194)(97,269,166,220,120,242,143,193)(98,268,167,219,121,241,144,192)(99,267,168,218,122,240,145,191)(100,266,169,217,123,239,146,190)(101,265,170,216,124,238,147,189)(102,264,171,215,125,237,148,188)(103,263,172,214,126,236,149,187)(104,262,173,213,127,235,150,186)(105,261,174,212,128,234,151,185)(106,260,175,211,129,233,152,207)(107,259,176,210,130,232,153,206)(108,258,177,209,131,231,154,205)(109,257,178,208,132,253,155,204)(110,256,179,230,133,252,156,203)(111,255,180,229,134,251,157,202)(112,254,181,228,135,250,158,201)(113,276,182,227,136,249,159,200)(114,275,183,226,137,248,160,199)(115,274,184,225,138,247,161,198)>;
G:=Group( (1,93)(2,94)(3,95)(4,96)(5,97)(6,98)(7,99)(8,100)(9,101)(10,102)(11,103)(12,104)(13,105)(14,106)(15,107)(16,108)(17,109)(18,110)(19,111)(20,112)(21,113)(22,114)(23,115)(24,116)(25,117)(26,118)(27,119)(28,120)(29,121)(30,122)(31,123)(32,124)(33,125)(34,126)(35,127)(36,128)(37,129)(38,130)(39,131)(40,132)(41,133)(42,134)(43,135)(44,136)(45,137)(46,138)(47,139)(48,140)(49,141)(50,142)(51,143)(52,144)(53,145)(54,146)(55,147)(56,148)(57,149)(58,150)(59,151)(60,152)(61,153)(62,154)(63,155)(64,156)(65,157)(66,158)(67,159)(68,160)(69,161)(70,162)(71,163)(72,164)(73,165)(74,166)(75,167)(76,168)(77,169)(78,170)(79,171)(80,172)(81,173)(82,174)(83,175)(84,176)(85,177)(86,178)(87,179)(88,180)(89,181)(90,182)(91,183)(92,184)(185,298)(186,299)(187,277)(188,278)(189,279)(190,280)(191,281)(192,282)(193,283)(194,284)(195,285)(196,286)(197,287)(198,288)(199,289)(200,290)(201,291)(202,292)(203,293)(204,294)(205,295)(206,296)(207,297)(208,317)(209,318)(210,319)(211,320)(212,321)(213,322)(214,300)(215,301)(216,302)(217,303)(218,304)(219,305)(220,306)(221,307)(222,308)(223,309)(224,310)(225,311)(226,312)(227,313)(228,314)(229,315)(230,316)(231,334)(232,335)(233,336)(234,337)(235,338)(236,339)(237,340)(238,341)(239,342)(240,343)(241,344)(242,345)(243,323)(244,324)(245,325)(246,326)(247,327)(248,328)(249,329)(250,330)(251,331)(252,332)(253,333)(254,350)(255,351)(256,352)(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)(264,360)(265,361)(266,362)(267,363)(268,364)(269,365)(270,366)(271,367)(272,368)(273,346)(274,347)(275,348)(276,349), (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)(277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299)(300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322)(323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345)(346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368), (1,346,70,310,24,326,47,287)(2,368,71,309,25,325,48,286)(3,367,72,308,26,324,49,285)(4,366,73,307,27,323,50,284)(5,365,74,306,28,345,51,283)(6,364,75,305,29,344,52,282)(7,363,76,304,30,343,53,281)(8,362,77,303,31,342,54,280)(9,361,78,302,32,341,55,279)(10,360,79,301,33,340,56,278)(11,359,80,300,34,339,57,277)(12,358,81,322,35,338,58,299)(13,357,82,321,36,337,59,298)(14,356,83,320,37,336,60,297)(15,355,84,319,38,335,61,296)(16,354,85,318,39,334,62,295)(17,353,86,317,40,333,63,294)(18,352,87,316,41,332,64,293)(19,351,88,315,42,331,65,292)(20,350,89,314,43,330,66,291)(21,349,90,313,44,329,67,290)(22,348,91,312,45,328,68,289)(23,347,92,311,46,327,69,288)(93,273,162,224,116,246,139,197)(94,272,163,223,117,245,140,196)(95,271,164,222,118,244,141,195)(96,270,165,221,119,243,142,194)(97,269,166,220,120,242,143,193)(98,268,167,219,121,241,144,192)(99,267,168,218,122,240,145,191)(100,266,169,217,123,239,146,190)(101,265,170,216,124,238,147,189)(102,264,171,215,125,237,148,188)(103,263,172,214,126,236,149,187)(104,262,173,213,127,235,150,186)(105,261,174,212,128,234,151,185)(106,260,175,211,129,233,152,207)(107,259,176,210,130,232,153,206)(108,258,177,209,131,231,154,205)(109,257,178,208,132,253,155,204)(110,256,179,230,133,252,156,203)(111,255,180,229,134,251,157,202)(112,254,181,228,135,250,158,201)(113,276,182,227,136,249,159,200)(114,275,183,226,137,248,160,199)(115,274,184,225,138,247,161,198) );
G=PermutationGroup([[(1,93),(2,94),(3,95),(4,96),(5,97),(6,98),(7,99),(8,100),(9,101),(10,102),(11,103),(12,104),(13,105),(14,106),(15,107),(16,108),(17,109),(18,110),(19,111),(20,112),(21,113),(22,114),(23,115),(24,116),(25,117),(26,118),(27,119),(28,120),(29,121),(30,122),(31,123),(32,124),(33,125),(34,126),(35,127),(36,128),(37,129),(38,130),(39,131),(40,132),(41,133),(42,134),(43,135),(44,136),(45,137),(46,138),(47,139),(48,140),(49,141),(50,142),(51,143),(52,144),(53,145),(54,146),(55,147),(56,148),(57,149),(58,150),(59,151),(60,152),(61,153),(62,154),(63,155),(64,156),(65,157),(66,158),(67,159),(68,160),(69,161),(70,162),(71,163),(72,164),(73,165),(74,166),(75,167),(76,168),(77,169),(78,170),(79,171),(80,172),(81,173),(82,174),(83,175),(84,176),(85,177),(86,178),(87,179),(88,180),(89,181),(90,182),(91,183),(92,184),(185,298),(186,299),(187,277),(188,278),(189,279),(190,280),(191,281),(192,282),(193,283),(194,284),(195,285),(196,286),(197,287),(198,288),(199,289),(200,290),(201,291),(202,292),(203,293),(204,294),(205,295),(206,296),(207,297),(208,317),(209,318),(210,319),(211,320),(212,321),(213,322),(214,300),(215,301),(216,302),(217,303),(218,304),(219,305),(220,306),(221,307),(222,308),(223,309),(224,310),(225,311),(226,312),(227,313),(228,314),(229,315),(230,316),(231,334),(232,335),(233,336),(234,337),(235,338),(236,339),(237,340),(238,341),(239,342),(240,343),(241,344),(242,345),(243,323),(244,324),(245,325),(246,326),(247,327),(248,328),(249,329),(250,330),(251,331),(252,332),(253,333),(254,350),(255,351),(256,352),(257,353),(258,354),(259,355),(260,356),(261,357),(262,358),(263,359),(264,360),(265,361),(266,362),(267,363),(268,364),(269,365),(270,366),(271,367),(272,368),(273,346),(274,347),(275,348),(276,349)], [(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),(277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299),(300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322),(323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345),(346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368)], [(1,346,70,310,24,326,47,287),(2,368,71,309,25,325,48,286),(3,367,72,308,26,324,49,285),(4,366,73,307,27,323,50,284),(5,365,74,306,28,345,51,283),(6,364,75,305,29,344,52,282),(7,363,76,304,30,343,53,281),(8,362,77,303,31,342,54,280),(9,361,78,302,32,341,55,279),(10,360,79,301,33,340,56,278),(11,359,80,300,34,339,57,277),(12,358,81,322,35,338,58,299),(13,357,82,321,36,337,59,298),(14,356,83,320,37,336,60,297),(15,355,84,319,38,335,61,296),(16,354,85,318,39,334,62,295),(17,353,86,317,40,333,63,294),(18,352,87,316,41,332,64,293),(19,351,88,315,42,331,65,292),(20,350,89,314,43,330,66,291),(21,349,90,313,44,329,67,290),(22,348,91,312,45,328,68,289),(23,347,92,311,46,327,69,288),(93,273,162,224,116,246,139,197),(94,272,163,223,117,245,140,196),(95,271,164,222,118,244,141,195),(96,270,165,221,119,243,142,194),(97,269,166,220,120,242,143,193),(98,268,167,219,121,241,144,192),(99,267,168,218,122,240,145,191),(100,266,169,217,123,239,146,190),(101,265,170,216,124,238,147,189),(102,264,171,215,125,237,148,188),(103,263,172,214,126,236,149,187),(104,262,173,213,127,235,150,186),(105,261,174,212,128,234,151,185),(106,260,175,211,129,233,152,207),(107,259,176,210,130,232,153,206),(108,258,177,209,131,231,154,205),(109,257,178,208,132,253,155,204),(110,256,179,230,133,252,156,203),(111,255,180,229,134,251,157,202),(112,254,181,228,135,250,158,201),(113,276,182,227,136,249,159,200),(114,275,183,226,137,248,160,199),(115,274,184,225,138,247,161,198)]])
104 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 8A | ··· | 8H | 23A | ··· | 23K | 46A | ··· | 46AG | 92A | ··· | 92AR |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 23 | ··· | 23 | 46 | ··· | 46 | 92 | ··· | 92 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 23 | ··· | 23 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
104 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | ||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | D23 | Dic23 | D46 | Dic23 | C23⋊C8 |
| kernel | C2×C23⋊C8 | C23⋊C8 | C2×C92 | C92 | C2×C46 | C46 | C2×C4 | C4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 8 | 11 | 11 | 11 | 11 | 44 |
Matrix representation of C2×C23⋊C8 ►in GL4(𝔽1289) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1288 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 181 | 1288 |
| 0 | 0 | 1 | 0 |
| 497 | 0 | 0 | 0 |
| 0 | 479 | 0 | 0 |
| 0 | 0 | 123 | 510 |
| 0 | 0 | 860 | 1166 |
G:=sub<GL(4,GF(1289))| [1,0,0,0,0,1288,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,181,1,0,0,1288,0],[497,0,0,0,0,479,0,0,0,0,123,860,0,0,510,1166] >;
C2×C23⋊C8 in GAP, Magma, Sage, TeX
C_2\times C_{23}\rtimes C_8 % in TeX
G:=Group("C2xC23:C8"); // GroupNames label
G:=SmallGroup(368,8);
// by ID
G=gap.SmallGroup(368,8);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-23,20,42,8804]);
// Polycyclic
G:=Group<a,b,c|a^2=b^23=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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