direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Dic46, C46⋊Q8, C4.11D46, C46.1C23, C22.8D46, C92.11C22, Dic23.1C22, C23⋊1(C2×Q8), (C2×C92).4C2, (C2×C4).4D23, (C2×C46).8C22, C2.3(C22×D23), (C2×Dic23).3C2, SmallGroup(368,27)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Dic46
G = < a,b,c | a2=b92=1, c2=b46, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×Dic46
►Regular action on 368 points
Generators in S368
(1 166)(2 167)(3 168)(4 169)(5 170)(6 171)(7 172)(8 173)(9 174)(10 175)(11 176)(12 177)(13 178)(14 179)(15 180)(16 181)(17 182)(18 183)(19 184)(20 93)(21 94)(22 95)(23 96)(24 97)(25 98)(26 99)(27 100)(28 101)(29 102)(30 103)(31 104)(32 105)(33 106)(34 107)(35 108)(36 109)(37 110)(38 111)(39 112)(40 113)(41 114)(42 115)(43 116)(44 117)(45 118)(46 119)(47 120)(48 121)(49 122)(50 123)(51 124)(52 125)(53 126)(54 127)(55 128)(56 129)(57 130)(58 131)(59 132)(60 133)(61 134)(62 135)(63 136)(64 137)(65 138)(66 139)(67 140)(68 141)(69 142)(70 143)(71 144)(72 145)(73 146)(74 147)(75 148)(76 149)(77 150)(78 151)(79 152)(80 153)(81 154)(82 155)(83 156)(84 157)(85 158)(86 159)(87 160)(88 161)(89 162)(90 163)(91 164)(92 165)(185 346)(186 347)(187 348)(188 349)(189 350)(190 351)(191 352)(192 353)(193 354)(194 355)(195 356)(196 357)(197 358)(198 359)(199 360)(200 361)(201 362)(202 363)(203 364)(204 365)(205 366)(206 367)(207 368)(208 277)(209 278)(210 279)(211 280)(212 281)(213 282)(214 283)(215 284)(216 285)(217 286)(218 287)(219 288)(220 289)(221 290)(222 291)(223 292)(224 293)(225 294)(226 295)(227 296)(228 297)(229 298)(230 299)(231 300)(232 301)(233 302)(234 303)(235 304)(236 305)(237 306)(238 307)(239 308)(240 309)(241 310)(242 311)(243 312)(244 313)(245 314)(246 315)(247 316)(248 317)(249 318)(250 319)(251 320)(252 321)(253 322)(254 323)(255 324)(256 325)(257 326)(258 327)(259 328)(260 329)(261 330)(262 331)(263 332)(264 333)(265 334)(266 335)(267 336)(268 337)(269 338)(270 339)(271 340)(272 341)(273 342)(274 343)(275 344)(276 345)
(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)
(1 231 47 185)(2 230 48 276)(3 229 49 275)(4 228 50 274)(5 227 51 273)(6 226 52 272)(7 225 53 271)(8 224 54 270)(9 223 55 269)(10 222 56 268)(11 221 57 267)(12 220 58 266)(13 219 59 265)(14 218 60 264)(15 217 61 263)(16 216 62 262)(17 215 63 261)(18 214 64 260)(19 213 65 259)(20 212 66 258)(21 211 67 257)(22 210 68 256)(23 209 69 255)(24 208 70 254)(25 207 71 253)(26 206 72 252)(27 205 73 251)(28 204 74 250)(29 203 75 249)(30 202 76 248)(31 201 77 247)(32 200 78 246)(33 199 79 245)(34 198 80 244)(35 197 81 243)(36 196 82 242)(37 195 83 241)(38 194 84 240)(39 193 85 239)(40 192 86 238)(41 191 87 237)(42 190 88 236)(43 189 89 235)(44 188 90 234)(45 187 91 233)(46 186 92 232)(93 281 139 327)(94 280 140 326)(95 279 141 325)(96 278 142 324)(97 277 143 323)(98 368 144 322)(99 367 145 321)(100 366 146 320)(101 365 147 319)(102 364 148 318)(103 363 149 317)(104 362 150 316)(105 361 151 315)(106 360 152 314)(107 359 153 313)(108 358 154 312)(109 357 155 311)(110 356 156 310)(111 355 157 309)(112 354 158 308)(113 353 159 307)(114 352 160 306)(115 351 161 305)(116 350 162 304)(117 349 163 303)(118 348 164 302)(119 347 165 301)(120 346 166 300)(121 345 167 299)(122 344 168 298)(123 343 169 297)(124 342 170 296)(125 341 171 295)(126 340 172 294)(127 339 173 293)(128 338 174 292)(129 337 175 291)(130 336 176 290)(131 335 177 289)(132 334 178 288)(133 333 179 287)(134 332 180 286)(135 331 181 285)(136 330 182 284)(137 329 183 283)(138 328 184 282)
G:=sub<Sym(368)| (1,166)(2,167)(3,168)(4,169)(5,170)(6,171)(7,172)(8,173)(9,174)(10,175)(11,176)(12,177)(13,178)(14,179)(15,180)(16,181)(17,182)(18,183)(19,184)(20,93)(21,94)(22,95)(23,96)(24,97)(25,98)(26,99)(27,100)(28,101)(29,102)(30,103)(31,104)(32,105)(33,106)(34,107)(35,108)(36,109)(37,110)(38,111)(39,112)(40,113)(41,114)(42,115)(43,116)(44,117)(45,118)(46,119)(47,120)(48,121)(49,122)(50,123)(51,124)(52,125)(53,126)(54,127)(55,128)(56,129)(57,130)(58,131)(59,132)(60,133)(61,134)(62,135)(63,136)(64,137)(65,138)(66,139)(67,140)(68,141)(69,142)(70,143)(71,144)(72,145)(73,146)(74,147)(75,148)(76,149)(77,150)(78,151)(79,152)(80,153)(81,154)(82,155)(83,156)(84,157)(85,158)(86,159)(87,160)(88,161)(89,162)(90,163)(91,164)(92,165)(185,346)(186,347)(187,348)(188,349)(189,350)(190,351)(191,352)(192,353)(193,354)(194,355)(195,356)(196,357)(197,358)(198,359)(199,360)(200,361)(201,362)(202,363)(203,364)(204,365)(205,366)(206,367)(207,368)(208,277)(209,278)(210,279)(211,280)(212,281)(213,282)(214,283)(215,284)(216,285)(217,286)(218,287)(219,288)(220,289)(221,290)(222,291)(223,292)(224,293)(225,294)(226,295)(227,296)(228,297)(229,298)(230,299)(231,300)(232,301)(233,302)(234,303)(235,304)(236,305)(237,306)(238,307)(239,308)(240,309)(241,310)(242,311)(243,312)(244,313)(245,314)(246,315)(247,316)(248,317)(249,318)(250,319)(251,320)(252,321)(253,322)(254,323)(255,324)(256,325)(257,326)(258,327)(259,328)(260,329)(261,330)(262,331)(263,332)(264,333)(265,334)(266,335)(267,336)(268,337)(269,338)(270,339)(271,340)(272,341)(273,342)(274,343)(275,344)(276,345), (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), (1,231,47,185)(2,230,48,276)(3,229,49,275)(4,228,50,274)(5,227,51,273)(6,226,52,272)(7,225,53,271)(8,224,54,270)(9,223,55,269)(10,222,56,268)(11,221,57,267)(12,220,58,266)(13,219,59,265)(14,218,60,264)(15,217,61,263)(16,216,62,262)(17,215,63,261)(18,214,64,260)(19,213,65,259)(20,212,66,258)(21,211,67,257)(22,210,68,256)(23,209,69,255)(24,208,70,254)(25,207,71,253)(26,206,72,252)(27,205,73,251)(28,204,74,250)(29,203,75,249)(30,202,76,248)(31,201,77,247)(32,200,78,246)(33,199,79,245)(34,198,80,244)(35,197,81,243)(36,196,82,242)(37,195,83,241)(38,194,84,240)(39,193,85,239)(40,192,86,238)(41,191,87,237)(42,190,88,236)(43,189,89,235)(44,188,90,234)(45,187,91,233)(46,186,92,232)(93,281,139,327)(94,280,140,326)(95,279,141,325)(96,278,142,324)(97,277,143,323)(98,368,144,322)(99,367,145,321)(100,366,146,320)(101,365,147,319)(102,364,148,318)(103,363,149,317)(104,362,150,316)(105,361,151,315)(106,360,152,314)(107,359,153,313)(108,358,154,312)(109,357,155,311)(110,356,156,310)(111,355,157,309)(112,354,158,308)(113,353,159,307)(114,352,160,306)(115,351,161,305)(116,350,162,304)(117,349,163,303)(118,348,164,302)(119,347,165,301)(120,346,166,300)(121,345,167,299)(122,344,168,298)(123,343,169,297)(124,342,170,296)(125,341,171,295)(126,340,172,294)(127,339,173,293)(128,338,174,292)(129,337,175,291)(130,336,176,290)(131,335,177,289)(132,334,178,288)(133,333,179,287)(134,332,180,286)(135,331,181,285)(136,330,182,284)(137,329,183,283)(138,328,184,282)>;
G:=Group( (1,166)(2,167)(3,168)(4,169)(5,170)(6,171)(7,172)(8,173)(9,174)(10,175)(11,176)(12,177)(13,178)(14,179)(15,180)(16,181)(17,182)(18,183)(19,184)(20,93)(21,94)(22,95)(23,96)(24,97)(25,98)(26,99)(27,100)(28,101)(29,102)(30,103)(31,104)(32,105)(33,106)(34,107)(35,108)(36,109)(37,110)(38,111)(39,112)(40,113)(41,114)(42,115)(43,116)(44,117)(45,118)(46,119)(47,120)(48,121)(49,122)(50,123)(51,124)(52,125)(53,126)(54,127)(55,128)(56,129)(57,130)(58,131)(59,132)(60,133)(61,134)(62,135)(63,136)(64,137)(65,138)(66,139)(67,140)(68,141)(69,142)(70,143)(71,144)(72,145)(73,146)(74,147)(75,148)(76,149)(77,150)(78,151)(79,152)(80,153)(81,154)(82,155)(83,156)(84,157)(85,158)(86,159)(87,160)(88,161)(89,162)(90,163)(91,164)(92,165)(185,346)(186,347)(187,348)(188,349)(189,350)(190,351)(191,352)(192,353)(193,354)(194,355)(195,356)(196,357)(197,358)(198,359)(199,360)(200,361)(201,362)(202,363)(203,364)(204,365)(205,366)(206,367)(207,368)(208,277)(209,278)(210,279)(211,280)(212,281)(213,282)(214,283)(215,284)(216,285)(217,286)(218,287)(219,288)(220,289)(221,290)(222,291)(223,292)(224,293)(225,294)(226,295)(227,296)(228,297)(229,298)(230,299)(231,300)(232,301)(233,302)(234,303)(235,304)(236,305)(237,306)(238,307)(239,308)(240,309)(241,310)(242,311)(243,312)(244,313)(245,314)(246,315)(247,316)(248,317)(249,318)(250,319)(251,320)(252,321)(253,322)(254,323)(255,324)(256,325)(257,326)(258,327)(259,328)(260,329)(261,330)(262,331)(263,332)(264,333)(265,334)(266,335)(267,336)(268,337)(269,338)(270,339)(271,340)(272,341)(273,342)(274,343)(275,344)(276,345), (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), (1,231,47,185)(2,230,48,276)(3,229,49,275)(4,228,50,274)(5,227,51,273)(6,226,52,272)(7,225,53,271)(8,224,54,270)(9,223,55,269)(10,222,56,268)(11,221,57,267)(12,220,58,266)(13,219,59,265)(14,218,60,264)(15,217,61,263)(16,216,62,262)(17,215,63,261)(18,214,64,260)(19,213,65,259)(20,212,66,258)(21,211,67,257)(22,210,68,256)(23,209,69,255)(24,208,70,254)(25,207,71,253)(26,206,72,252)(27,205,73,251)(28,204,74,250)(29,203,75,249)(30,202,76,248)(31,201,77,247)(32,200,78,246)(33,199,79,245)(34,198,80,244)(35,197,81,243)(36,196,82,242)(37,195,83,241)(38,194,84,240)(39,193,85,239)(40,192,86,238)(41,191,87,237)(42,190,88,236)(43,189,89,235)(44,188,90,234)(45,187,91,233)(46,186,92,232)(93,281,139,327)(94,280,140,326)(95,279,141,325)(96,278,142,324)(97,277,143,323)(98,368,144,322)(99,367,145,321)(100,366,146,320)(101,365,147,319)(102,364,148,318)(103,363,149,317)(104,362,150,316)(105,361,151,315)(106,360,152,314)(107,359,153,313)(108,358,154,312)(109,357,155,311)(110,356,156,310)(111,355,157,309)(112,354,158,308)(113,353,159,307)(114,352,160,306)(115,351,161,305)(116,350,162,304)(117,349,163,303)(118,348,164,302)(119,347,165,301)(120,346,166,300)(121,345,167,299)(122,344,168,298)(123,343,169,297)(124,342,170,296)(125,341,171,295)(126,340,172,294)(127,339,173,293)(128,338,174,292)(129,337,175,291)(130,336,176,290)(131,335,177,289)(132,334,178,288)(133,333,179,287)(134,332,180,286)(135,331,181,285)(136,330,182,284)(137,329,183,283)(138,328,184,282) );
G=PermutationGroup([[(1,166),(2,167),(3,168),(4,169),(5,170),(6,171),(7,172),(8,173),(9,174),(10,175),(11,176),(12,177),(13,178),(14,179),(15,180),(16,181),(17,182),(18,183),(19,184),(20,93),(21,94),(22,95),(23,96),(24,97),(25,98),(26,99),(27,100),(28,101),(29,102),(30,103),(31,104),(32,105),(33,106),(34,107),(35,108),(36,109),(37,110),(38,111),(39,112),(40,113),(41,114),(42,115),(43,116),(44,117),(45,118),(46,119),(47,120),(48,121),(49,122),(50,123),(51,124),(52,125),(53,126),(54,127),(55,128),(56,129),(57,130),(58,131),(59,132),(60,133),(61,134),(62,135),(63,136),(64,137),(65,138),(66,139),(67,140),(68,141),(69,142),(70,143),(71,144),(72,145),(73,146),(74,147),(75,148),(76,149),(77,150),(78,151),(79,152),(80,153),(81,154),(82,155),(83,156),(84,157),(85,158),(86,159),(87,160),(88,161),(89,162),(90,163),(91,164),(92,165),(185,346),(186,347),(187,348),(188,349),(189,350),(190,351),(191,352),(192,353),(193,354),(194,355),(195,356),(196,357),(197,358),(198,359),(199,360),(200,361),(201,362),(202,363),(203,364),(204,365),(205,366),(206,367),(207,368),(208,277),(209,278),(210,279),(211,280),(212,281),(213,282),(214,283),(215,284),(216,285),(217,286),(218,287),(219,288),(220,289),(221,290),(222,291),(223,292),(224,293),(225,294),(226,295),(227,296),(228,297),(229,298),(230,299),(231,300),(232,301),(233,302),(234,303),(235,304),(236,305),(237,306),(238,307),(239,308),(240,309),(241,310),(242,311),(243,312),(244,313),(245,314),(246,315),(247,316),(248,317),(249,318),(250,319),(251,320),(252,321),(253,322),(254,323),(255,324),(256,325),(257,326),(258,327),(259,328),(260,329),(261,330),(262,331),(263,332),(264,333),(265,334),(266,335),(267,336),(268,337),(269,338),(270,339),(271,340),(272,341),(273,342),(274,343),(275,344),(276,345)], [(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)], [(1,231,47,185),(2,230,48,276),(3,229,49,275),(4,228,50,274),(5,227,51,273),(6,226,52,272),(7,225,53,271),(8,224,54,270),(9,223,55,269),(10,222,56,268),(11,221,57,267),(12,220,58,266),(13,219,59,265),(14,218,60,264),(15,217,61,263),(16,216,62,262),(17,215,63,261),(18,214,64,260),(19,213,65,259),(20,212,66,258),(21,211,67,257),(22,210,68,256),(23,209,69,255),(24,208,70,254),(25,207,71,253),(26,206,72,252),(27,205,73,251),(28,204,74,250),(29,203,75,249),(30,202,76,248),(31,201,77,247),(32,200,78,246),(33,199,79,245),(34,198,80,244),(35,197,81,243),(36,196,82,242),(37,195,83,241),(38,194,84,240),(39,193,85,239),(40,192,86,238),(41,191,87,237),(42,190,88,236),(43,189,89,235),(44,188,90,234),(45,187,91,233),(46,186,92,232),(93,281,139,327),(94,280,140,326),(95,279,141,325),(96,278,142,324),(97,277,143,323),(98,368,144,322),(99,367,145,321),(100,366,146,320),(101,365,147,319),(102,364,148,318),(103,363,149,317),(104,362,150,316),(105,361,151,315),(106,360,152,314),(107,359,153,313),(108,358,154,312),(109,357,155,311),(110,356,156,310),(111,355,157,309),(112,354,158,308),(113,353,159,307),(114,352,160,306),(115,351,161,305),(116,350,162,304),(117,349,163,303),(118,348,164,302),(119,347,165,301),(120,346,166,300),(121,345,167,299),(122,344,168,298),(123,343,169,297),(124,342,170,296),(125,341,171,295),(126,340,172,294),(127,339,173,293),(128,338,174,292),(129,337,175,291),(130,336,176,290),(131,335,177,289),(132,334,178,288),(133,333,179,287),(134,332,180,286),(135,331,181,285),(136,330,182,284),(137,329,183,283),(138,328,184,282)]])
98 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 23A | ··· | 23K | 46A | ··· | 46AG | 92A | ··· | 92AR |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 23 | ··· | 23 | 46 | ··· | 46 | 92 | ··· | 92 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 46 | 46 | 46 | 46 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
98 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | + | + | - |
| image | C1 | C2 | C2 | C2 | Q8 | D23 | D46 | D46 | Dic46 |
| kernel | C2×Dic46 | Dic46 | C2×Dic23 | C2×C92 | C46 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 4 | 2 | 1 | 2 | 11 | 22 | 11 | 44 |
Matrix representation of C2×Dic46 ►in GL3(𝔽277) generated by
| 276 | 0 | 0 |
| 0 | 276 | 0 |
| 0 | 0 | 276 |
| 276 | 0 | 0 |
| 0 | 167 | 36 |
| 0 | 241 | 251 |
| 276 | 0 | 0 |
| 0 | 148 | 263 |
| 0 | 239 | 129 |
G:=sub<GL(3,GF(277))| [276,0,0,0,276,0,0,0,276],[276,0,0,0,167,241,0,36,251],[276,0,0,0,148,239,0,263,129] >;
C2×Dic46 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_{46} % in TeX
G:=Group("C2xDic46"); // GroupNames label
G:=SmallGroup(368,27);
// by ID
G=gap.SmallGroup(368,27);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-23,40,182,42,8804]);
// Polycyclic
G:=Group<a,b,c|a^2=b^92=1,c^2=b^46,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export