direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×Dic47, C94⋊C4, C2.2D94, C22.D47, C94.4C22, C47⋊2(C2×C4), (C2×C94).C2, SmallGroup(376,6)
Series: Derived ►Chief ►Lower central ►Upper central
| C47 — C2×Dic47 |
Generators and relations for C2×Dic47
G = < a,b,c | a2=b94=1, c2=b47, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×Dic47
►Regular action on 376 points
Generators in S376
(1 151)(2 152)(3 153)(4 154)(5 155)(6 156)(7 157)(8 158)(9 159)(10 160)(11 161)(12 162)(13 163)(14 164)(15 165)(16 166)(17 167)(18 168)(19 169)(20 170)(21 171)(22 172)(23 173)(24 174)(25 175)(26 176)(27 177)(28 178)(29 179)(30 180)(31 181)(32 182)(33 183)(34 184)(35 185)(36 186)(37 187)(38 188)(39 95)(40 96)(41 97)(42 98)(43 99)(44 100)(45 101)(46 102)(47 103)(48 104)(49 105)(50 106)(51 107)(52 108)(53 109)(54 110)(55 111)(56 112)(57 113)(58 114)(59 115)(60 116)(61 117)(62 118)(63 119)(64 120)(65 121)(66 122)(67 123)(68 124)(69 125)(70 126)(71 127)(72 128)(73 129)(74 130)(75 131)(76 132)(77 133)(78 134)(79 135)(80 136)(81 137)(82 138)(83 139)(84 140)(85 141)(86 142)(87 143)(88 144)(89 145)(90 146)(91 147)(92 148)(93 149)(94 150)(189 283)(190 284)(191 285)(192 286)(193 287)(194 288)(195 289)(196 290)(197 291)(198 292)(199 293)(200 294)(201 295)(202 296)(203 297)(204 298)(205 299)(206 300)(207 301)(208 302)(209 303)(210 304)(211 305)(212 306)(213 307)(214 308)(215 309)(216 310)(217 311)(218 312)(219 313)(220 314)(221 315)(222 316)(223 317)(224 318)(225 319)(226 320)(227 321)(228 322)(229 323)(230 324)(231 325)(232 326)(233 327)(234 328)(235 329)(236 330)(237 331)(238 332)(239 333)(240 334)(241 335)(242 336)(243 337)(244 338)(245 339)(246 340)(247 341)(248 342)(249 343)(250 344)(251 345)(252 346)(253 347)(254 348)(255 349)(256 350)(257 351)(258 352)(259 353)(260 354)(261 355)(262 356)(263 357)(264 358)(265 359)(266 360)(267 361)(268 362)(269 363)(270 364)(271 365)(272 366)(273 367)(274 368)(275 369)(276 370)(277 371)(278 372)(279 373)(280 374)(281 375)(282 376)
(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)(283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376)
(1 189 48 236)(2 282 49 235)(3 281 50 234)(4 280 51 233)(5 279 52 232)(6 278 53 231)(7 277 54 230)(8 276 55 229)(9 275 56 228)(10 274 57 227)(11 273 58 226)(12 272 59 225)(13 271 60 224)(14 270 61 223)(15 269 62 222)(16 268 63 221)(17 267 64 220)(18 266 65 219)(19 265 66 218)(20 264 67 217)(21 263 68 216)(22 262 69 215)(23 261 70 214)(24 260 71 213)(25 259 72 212)(26 258 73 211)(27 257 74 210)(28 256 75 209)(29 255 76 208)(30 254 77 207)(31 253 78 206)(32 252 79 205)(33 251 80 204)(34 250 81 203)(35 249 82 202)(36 248 83 201)(37 247 84 200)(38 246 85 199)(39 245 86 198)(40 244 87 197)(41 243 88 196)(42 242 89 195)(43 241 90 194)(44 240 91 193)(45 239 92 192)(46 238 93 191)(47 237 94 190)(95 339 142 292)(96 338 143 291)(97 337 144 290)(98 336 145 289)(99 335 146 288)(100 334 147 287)(101 333 148 286)(102 332 149 285)(103 331 150 284)(104 330 151 283)(105 329 152 376)(106 328 153 375)(107 327 154 374)(108 326 155 373)(109 325 156 372)(110 324 157 371)(111 323 158 370)(112 322 159 369)(113 321 160 368)(114 320 161 367)(115 319 162 366)(116 318 163 365)(117 317 164 364)(118 316 165 363)(119 315 166 362)(120 314 167 361)(121 313 168 360)(122 312 169 359)(123 311 170 358)(124 310 171 357)(125 309 172 356)(126 308 173 355)(127 307 174 354)(128 306 175 353)(129 305 176 352)(130 304 177 351)(131 303 178 350)(132 302 179 349)(133 301 180 348)(134 300 181 347)(135 299 182 346)(136 298 183 345)(137 297 184 344)(138 296 185 343)(139 295 186 342)(140 294 187 341)(141 293 188 340)
G:=sub<Sym(376)| (1,151)(2,152)(3,153)(4,154)(5,155)(6,156)(7,157)(8,158)(9,159)(10,160)(11,161)(12,162)(13,163)(14,164)(15,165)(16,166)(17,167)(18,168)(19,169)(20,170)(21,171)(22,172)(23,173)(24,174)(25,175)(26,176)(27,177)(28,178)(29,179)(30,180)(31,181)(32,182)(33,183)(34,184)(35,185)(36,186)(37,187)(38,188)(39,95)(40,96)(41,97)(42,98)(43,99)(44,100)(45,101)(46,102)(47,103)(48,104)(49,105)(50,106)(51,107)(52,108)(53,109)(54,110)(55,111)(56,112)(57,113)(58,114)(59,115)(60,116)(61,117)(62,118)(63,119)(64,120)(65,121)(66,122)(67,123)(68,124)(69,125)(70,126)(71,127)(72,128)(73,129)(74,130)(75,131)(76,132)(77,133)(78,134)(79,135)(80,136)(81,137)(82,138)(83,139)(84,140)(85,141)(86,142)(87,143)(88,144)(89,145)(90,146)(91,147)(92,148)(93,149)(94,150)(189,283)(190,284)(191,285)(192,286)(193,287)(194,288)(195,289)(196,290)(197,291)(198,292)(199,293)(200,294)(201,295)(202,296)(203,297)(204,298)(205,299)(206,300)(207,301)(208,302)(209,303)(210,304)(211,305)(212,306)(213,307)(214,308)(215,309)(216,310)(217,311)(218,312)(219,313)(220,314)(221,315)(222,316)(223,317)(224,318)(225,319)(226,320)(227,321)(228,322)(229,323)(230,324)(231,325)(232,326)(233,327)(234,328)(235,329)(236,330)(237,331)(238,332)(239,333)(240,334)(241,335)(242,336)(243,337)(244,338)(245,339)(246,340)(247,341)(248,342)(249,343)(250,344)(251,345)(252,346)(253,347)(254,348)(255,349)(256,350)(257,351)(258,352)(259,353)(260,354)(261,355)(262,356)(263,357)(264,358)(265,359)(266,360)(267,361)(268,362)(269,363)(270,364)(271,365)(272,366)(273,367)(274,368)(275,369)(276,370)(277,371)(278,372)(279,373)(280,374)(281,375)(282,376), (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)(283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376), (1,189,48,236)(2,282,49,235)(3,281,50,234)(4,280,51,233)(5,279,52,232)(6,278,53,231)(7,277,54,230)(8,276,55,229)(9,275,56,228)(10,274,57,227)(11,273,58,226)(12,272,59,225)(13,271,60,224)(14,270,61,223)(15,269,62,222)(16,268,63,221)(17,267,64,220)(18,266,65,219)(19,265,66,218)(20,264,67,217)(21,263,68,216)(22,262,69,215)(23,261,70,214)(24,260,71,213)(25,259,72,212)(26,258,73,211)(27,257,74,210)(28,256,75,209)(29,255,76,208)(30,254,77,207)(31,253,78,206)(32,252,79,205)(33,251,80,204)(34,250,81,203)(35,249,82,202)(36,248,83,201)(37,247,84,200)(38,246,85,199)(39,245,86,198)(40,244,87,197)(41,243,88,196)(42,242,89,195)(43,241,90,194)(44,240,91,193)(45,239,92,192)(46,238,93,191)(47,237,94,190)(95,339,142,292)(96,338,143,291)(97,337,144,290)(98,336,145,289)(99,335,146,288)(100,334,147,287)(101,333,148,286)(102,332,149,285)(103,331,150,284)(104,330,151,283)(105,329,152,376)(106,328,153,375)(107,327,154,374)(108,326,155,373)(109,325,156,372)(110,324,157,371)(111,323,158,370)(112,322,159,369)(113,321,160,368)(114,320,161,367)(115,319,162,366)(116,318,163,365)(117,317,164,364)(118,316,165,363)(119,315,166,362)(120,314,167,361)(121,313,168,360)(122,312,169,359)(123,311,170,358)(124,310,171,357)(125,309,172,356)(126,308,173,355)(127,307,174,354)(128,306,175,353)(129,305,176,352)(130,304,177,351)(131,303,178,350)(132,302,179,349)(133,301,180,348)(134,300,181,347)(135,299,182,346)(136,298,183,345)(137,297,184,344)(138,296,185,343)(139,295,186,342)(140,294,187,341)(141,293,188,340)>;
G:=Group( (1,151)(2,152)(3,153)(4,154)(5,155)(6,156)(7,157)(8,158)(9,159)(10,160)(11,161)(12,162)(13,163)(14,164)(15,165)(16,166)(17,167)(18,168)(19,169)(20,170)(21,171)(22,172)(23,173)(24,174)(25,175)(26,176)(27,177)(28,178)(29,179)(30,180)(31,181)(32,182)(33,183)(34,184)(35,185)(36,186)(37,187)(38,188)(39,95)(40,96)(41,97)(42,98)(43,99)(44,100)(45,101)(46,102)(47,103)(48,104)(49,105)(50,106)(51,107)(52,108)(53,109)(54,110)(55,111)(56,112)(57,113)(58,114)(59,115)(60,116)(61,117)(62,118)(63,119)(64,120)(65,121)(66,122)(67,123)(68,124)(69,125)(70,126)(71,127)(72,128)(73,129)(74,130)(75,131)(76,132)(77,133)(78,134)(79,135)(80,136)(81,137)(82,138)(83,139)(84,140)(85,141)(86,142)(87,143)(88,144)(89,145)(90,146)(91,147)(92,148)(93,149)(94,150)(189,283)(190,284)(191,285)(192,286)(193,287)(194,288)(195,289)(196,290)(197,291)(198,292)(199,293)(200,294)(201,295)(202,296)(203,297)(204,298)(205,299)(206,300)(207,301)(208,302)(209,303)(210,304)(211,305)(212,306)(213,307)(214,308)(215,309)(216,310)(217,311)(218,312)(219,313)(220,314)(221,315)(222,316)(223,317)(224,318)(225,319)(226,320)(227,321)(228,322)(229,323)(230,324)(231,325)(232,326)(233,327)(234,328)(235,329)(236,330)(237,331)(238,332)(239,333)(240,334)(241,335)(242,336)(243,337)(244,338)(245,339)(246,340)(247,341)(248,342)(249,343)(250,344)(251,345)(252,346)(253,347)(254,348)(255,349)(256,350)(257,351)(258,352)(259,353)(260,354)(261,355)(262,356)(263,357)(264,358)(265,359)(266,360)(267,361)(268,362)(269,363)(270,364)(271,365)(272,366)(273,367)(274,368)(275,369)(276,370)(277,371)(278,372)(279,373)(280,374)(281,375)(282,376), (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)(283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376), (1,189,48,236)(2,282,49,235)(3,281,50,234)(4,280,51,233)(5,279,52,232)(6,278,53,231)(7,277,54,230)(8,276,55,229)(9,275,56,228)(10,274,57,227)(11,273,58,226)(12,272,59,225)(13,271,60,224)(14,270,61,223)(15,269,62,222)(16,268,63,221)(17,267,64,220)(18,266,65,219)(19,265,66,218)(20,264,67,217)(21,263,68,216)(22,262,69,215)(23,261,70,214)(24,260,71,213)(25,259,72,212)(26,258,73,211)(27,257,74,210)(28,256,75,209)(29,255,76,208)(30,254,77,207)(31,253,78,206)(32,252,79,205)(33,251,80,204)(34,250,81,203)(35,249,82,202)(36,248,83,201)(37,247,84,200)(38,246,85,199)(39,245,86,198)(40,244,87,197)(41,243,88,196)(42,242,89,195)(43,241,90,194)(44,240,91,193)(45,239,92,192)(46,238,93,191)(47,237,94,190)(95,339,142,292)(96,338,143,291)(97,337,144,290)(98,336,145,289)(99,335,146,288)(100,334,147,287)(101,333,148,286)(102,332,149,285)(103,331,150,284)(104,330,151,283)(105,329,152,376)(106,328,153,375)(107,327,154,374)(108,326,155,373)(109,325,156,372)(110,324,157,371)(111,323,158,370)(112,322,159,369)(113,321,160,368)(114,320,161,367)(115,319,162,366)(116,318,163,365)(117,317,164,364)(118,316,165,363)(119,315,166,362)(120,314,167,361)(121,313,168,360)(122,312,169,359)(123,311,170,358)(124,310,171,357)(125,309,172,356)(126,308,173,355)(127,307,174,354)(128,306,175,353)(129,305,176,352)(130,304,177,351)(131,303,178,350)(132,302,179,349)(133,301,180,348)(134,300,181,347)(135,299,182,346)(136,298,183,345)(137,297,184,344)(138,296,185,343)(139,295,186,342)(140,294,187,341)(141,293,188,340) );
G=PermutationGroup([[(1,151),(2,152),(3,153),(4,154),(5,155),(6,156),(7,157),(8,158),(9,159),(10,160),(11,161),(12,162),(13,163),(14,164),(15,165),(16,166),(17,167),(18,168),(19,169),(20,170),(21,171),(22,172),(23,173),(24,174),(25,175),(26,176),(27,177),(28,178),(29,179),(30,180),(31,181),(32,182),(33,183),(34,184),(35,185),(36,186),(37,187),(38,188),(39,95),(40,96),(41,97),(42,98),(43,99),(44,100),(45,101),(46,102),(47,103),(48,104),(49,105),(50,106),(51,107),(52,108),(53,109),(54,110),(55,111),(56,112),(57,113),(58,114),(59,115),(60,116),(61,117),(62,118),(63,119),(64,120),(65,121),(66,122),(67,123),(68,124),(69,125),(70,126),(71,127),(72,128),(73,129),(74,130),(75,131),(76,132),(77,133),(78,134),(79,135),(80,136),(81,137),(82,138),(83,139),(84,140),(85,141),(86,142),(87,143),(88,144),(89,145),(90,146),(91,147),(92,148),(93,149),(94,150),(189,283),(190,284),(191,285),(192,286),(193,287),(194,288),(195,289),(196,290),(197,291),(198,292),(199,293),(200,294),(201,295),(202,296),(203,297),(204,298),(205,299),(206,300),(207,301),(208,302),(209,303),(210,304),(211,305),(212,306),(213,307),(214,308),(215,309),(216,310),(217,311),(218,312),(219,313),(220,314),(221,315),(222,316),(223,317),(224,318),(225,319),(226,320),(227,321),(228,322),(229,323),(230,324),(231,325),(232,326),(233,327),(234,328),(235,329),(236,330),(237,331),(238,332),(239,333),(240,334),(241,335),(242,336),(243,337),(244,338),(245,339),(246,340),(247,341),(248,342),(249,343),(250,344),(251,345),(252,346),(253,347),(254,348),(255,349),(256,350),(257,351),(258,352),(259,353),(260,354),(261,355),(262,356),(263,357),(264,358),(265,359),(266,360),(267,361),(268,362),(269,363),(270,364),(271,365),(272,366),(273,367),(274,368),(275,369),(276,370),(277,371),(278,372),(279,373),(280,374),(281,375),(282,376)], [(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),(283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376)], [(1,189,48,236),(2,282,49,235),(3,281,50,234),(4,280,51,233),(5,279,52,232),(6,278,53,231),(7,277,54,230),(8,276,55,229),(9,275,56,228),(10,274,57,227),(11,273,58,226),(12,272,59,225),(13,271,60,224),(14,270,61,223),(15,269,62,222),(16,268,63,221),(17,267,64,220),(18,266,65,219),(19,265,66,218),(20,264,67,217),(21,263,68,216),(22,262,69,215),(23,261,70,214),(24,260,71,213),(25,259,72,212),(26,258,73,211),(27,257,74,210),(28,256,75,209),(29,255,76,208),(30,254,77,207),(31,253,78,206),(32,252,79,205),(33,251,80,204),(34,250,81,203),(35,249,82,202),(36,248,83,201),(37,247,84,200),(38,246,85,199),(39,245,86,198),(40,244,87,197),(41,243,88,196),(42,242,89,195),(43,241,90,194),(44,240,91,193),(45,239,92,192),(46,238,93,191),(47,237,94,190),(95,339,142,292),(96,338,143,291),(97,337,144,290),(98,336,145,289),(99,335,146,288),(100,334,147,287),(101,333,148,286),(102,332,149,285),(103,331,150,284),(104,330,151,283),(105,329,152,376),(106,328,153,375),(107,327,154,374),(108,326,155,373),(109,325,156,372),(110,324,157,371),(111,323,158,370),(112,322,159,369),(113,321,160,368),(114,320,161,367),(115,319,162,366),(116,318,163,365),(117,317,164,364),(118,316,165,363),(119,315,166,362),(120,314,167,361),(121,313,168,360),(122,312,169,359),(123,311,170,358),(124,310,171,357),(125,309,172,356),(126,308,173,355),(127,307,174,354),(128,306,175,353),(129,305,176,352),(130,304,177,351),(131,303,178,350),(132,302,179,349),(133,301,180,348),(134,300,181,347),(135,299,182,346),(136,298,183,345),(137,297,184,344),(138,296,185,343),(139,295,186,342),(140,294,187,341),(141,293,188,340)]])
100 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 47A | ··· | 47W | 94A | ··· | 94BQ |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 47 | ··· | 47 | 94 | ··· | 94 |
| size | 1 | 1 | 1 | 1 | 47 | 47 | 47 | 47 | 2 | ··· | 2 | 2 | ··· | 2 |
100 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | |
| image | C1 | C2 | C2 | C4 | D47 | Dic47 | D94 |
| kernel | C2×Dic47 | Dic47 | C2×C94 | C94 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 4 | 23 | 46 | 23 |
Matrix representation of C2×Dic47 ►in GL4(𝔽941) generated by
| 1 | 0 | 0 | 0 |
| 0 | 940 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 940 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 940 | 478 |
| 97 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 169 | 706 |
| 0 | 0 | 562 | 772 |
G:=sub<GL(4,GF(941))| [1,0,0,0,0,940,0,0,0,0,1,0,0,0,0,1],[940,0,0,0,0,1,0,0,0,0,0,940,0,0,1,478],[97,0,0,0,0,1,0,0,0,0,169,562,0,0,706,772] >;
C2×Dic47 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_{47} % in TeX
G:=Group("C2xDic47"); // GroupNames label
G:=SmallGroup(376,6);
// by ID
G=gap.SmallGroup(376,6);
# by ID
G:=PCGroup([4,-2,-2,-2,-47,16,5891]);
// Polycyclic
G:=Group<a,b,c|a^2=b^94=1,c^2=b^47,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export