direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C21⋊C8, C42⋊1C8, C84.3C4, C4.14D42, C28.49D6, C12.50D14, C4.3Dic21, C28.3Dic3, C12.3Dic7, C84.56C22, C22.2Dic21, C6⋊(C7⋊C8), C14⋊(C3⋊C8), C21⋊7(C2×C8), (C2×C84).8C2, (C2×C42).2C4, (C2×C28).6S3, (C2×C4).5D21, (C2×C12).6D7, C42.29(C2×C4), (C2×C6).2Dic7, C6.6(C2×Dic7), (C2×C14).2Dic3, C2.1(C2×Dic21), C14.6(C2×Dic3), C3⋊2(C2×C7⋊C8), C7⋊2(C2×C3⋊C8), SmallGroup(336,95)
Series: Derived ►Chief ►Lower central ►Upper central
| C21 — C2×C21⋊C8 |
Generators and relations for C2×C21⋊C8
G = < a,b,c | a2=b21=c8=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×C21⋊C8
►Regular action on 336 points
Generators in S336
(1 85)(2 86)(3 87)(4 88)(5 89)(6 90)(7 91)(8 92)(9 93)(10 94)(11 95)(12 96)(13 97)(14 98)(15 99)(16 100)(17 101)(18 102)(19 103)(20 104)(21 105)(22 106)(23 107)(24 108)(25 109)(26 110)(27 111)(28 112)(29 113)(30 114)(31 115)(32 116)(33 117)(34 118)(35 119)(36 120)(37 121)(38 122)(39 123)(40 124)(41 125)(42 126)(43 129)(44 130)(45 131)(46 132)(47 133)(48 134)(49 135)(50 136)(51 137)(52 138)(53 139)(54 140)(55 141)(56 142)(57 143)(58 144)(59 145)(60 146)(61 147)(62 127)(63 128)(64 158)(65 159)(66 160)(67 161)(68 162)(69 163)(70 164)(71 165)(72 166)(73 167)(74 168)(75 148)(76 149)(77 150)(78 151)(79 152)(80 153)(81 154)(82 155)(83 156)(84 157)(169 254)(170 255)(171 256)(172 257)(173 258)(174 259)(175 260)(176 261)(177 262)(178 263)(179 264)(180 265)(181 266)(182 267)(183 268)(184 269)(185 270)(186 271)(187 272)(188 273)(189 253)(190 291)(191 292)(192 293)(193 294)(194 274)(195 275)(196 276)(197 277)(198 278)(199 279)(200 280)(201 281)(202 282)(203 283)(204 284)(205 285)(206 286)(207 287)(208 288)(209 289)(210 290)(211 313)(212 314)(213 315)(214 295)(215 296)(216 297)(217 298)(218 299)(219 300)(220 301)(221 302)(222 303)(223 304)(224 305)(225 306)(226 307)(227 308)(228 309)(229 310)(230 311)(231 312)(232 323)(233 324)(234 325)(235 326)(236 327)(237 328)(238 329)(239 330)(240 331)(241 332)(242 333)(243 334)(244 335)(245 336)(246 316)(247 317)(248 318)(249 319)(250 320)(251 321)(252 322)
(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)
(1 317 73 289 37 304 56 255)(2 316 74 288 38 303 57 254)(3 336 75 287 39 302 58 253)(4 335 76 286 40 301 59 273)(5 334 77 285 41 300 60 272)(6 333 78 284 42 299 61 271)(7 332 79 283 22 298 62 270)(8 331 80 282 23 297 63 269)(9 330 81 281 24 296 43 268)(10 329 82 280 25 295 44 267)(11 328 83 279 26 315 45 266)(12 327 84 278 27 314 46 265)(13 326 64 277 28 313 47 264)(14 325 65 276 29 312 48 263)(15 324 66 275 30 311 49 262)(16 323 67 274 31 310 50 261)(17 322 68 294 32 309 51 260)(18 321 69 293 33 308 52 259)(19 320 70 292 34 307 53 258)(20 319 71 291 35 306 54 257)(21 318 72 290 36 305 55 256)(85 247 167 209 121 223 142 170)(86 246 168 208 122 222 143 169)(87 245 148 207 123 221 144 189)(88 244 149 206 124 220 145 188)(89 243 150 205 125 219 146 187)(90 242 151 204 126 218 147 186)(91 241 152 203 106 217 127 185)(92 240 153 202 107 216 128 184)(93 239 154 201 108 215 129 183)(94 238 155 200 109 214 130 182)(95 237 156 199 110 213 131 181)(96 236 157 198 111 212 132 180)(97 235 158 197 112 211 133 179)(98 234 159 196 113 231 134 178)(99 233 160 195 114 230 135 177)(100 232 161 194 115 229 136 176)(101 252 162 193 116 228 137 175)(102 251 163 192 117 227 138 174)(103 250 164 191 118 226 139 173)(104 249 165 190 119 225 140 172)(105 248 166 210 120 224 141 171)
G:=sub<Sym(336)| (1,85)(2,86)(3,87)(4,88)(5,89)(6,90)(7,91)(8,92)(9,93)(10,94)(11,95)(12,96)(13,97)(14,98)(15,99)(16,100)(17,101)(18,102)(19,103)(20,104)(21,105)(22,106)(23,107)(24,108)(25,109)(26,110)(27,111)(28,112)(29,113)(30,114)(31,115)(32,116)(33,117)(34,118)(35,119)(36,120)(37,121)(38,122)(39,123)(40,124)(41,125)(42,126)(43,129)(44,130)(45,131)(46,132)(47,133)(48,134)(49,135)(50,136)(51,137)(52,138)(53,139)(54,140)(55,141)(56,142)(57,143)(58,144)(59,145)(60,146)(61,147)(62,127)(63,128)(64,158)(65,159)(66,160)(67,161)(68,162)(69,163)(70,164)(71,165)(72,166)(73,167)(74,168)(75,148)(76,149)(77,150)(78,151)(79,152)(80,153)(81,154)(82,155)(83,156)(84,157)(169,254)(170,255)(171,256)(172,257)(173,258)(174,259)(175,260)(176,261)(177,262)(178,263)(179,264)(180,265)(181,266)(182,267)(183,268)(184,269)(185,270)(186,271)(187,272)(188,273)(189,253)(190,291)(191,292)(192,293)(193,294)(194,274)(195,275)(196,276)(197,277)(198,278)(199,279)(200,280)(201,281)(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)(208,288)(209,289)(210,290)(211,313)(212,314)(213,315)(214,295)(215,296)(216,297)(217,298)(218,299)(219,300)(220,301)(221,302)(222,303)(223,304)(224,305)(225,306)(226,307)(227,308)(228,309)(229,310)(230,311)(231,312)(232,323)(233,324)(234,325)(235,326)(236,327)(237,328)(238,329)(239,330)(240,331)(241,332)(242,333)(243,334)(244,335)(245,336)(246,316)(247,317)(248,318)(249,319)(250,320)(251,321)(252,322), (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), (1,317,73,289,37,304,56,255)(2,316,74,288,38,303,57,254)(3,336,75,287,39,302,58,253)(4,335,76,286,40,301,59,273)(5,334,77,285,41,300,60,272)(6,333,78,284,42,299,61,271)(7,332,79,283,22,298,62,270)(8,331,80,282,23,297,63,269)(9,330,81,281,24,296,43,268)(10,329,82,280,25,295,44,267)(11,328,83,279,26,315,45,266)(12,327,84,278,27,314,46,265)(13,326,64,277,28,313,47,264)(14,325,65,276,29,312,48,263)(15,324,66,275,30,311,49,262)(16,323,67,274,31,310,50,261)(17,322,68,294,32,309,51,260)(18,321,69,293,33,308,52,259)(19,320,70,292,34,307,53,258)(20,319,71,291,35,306,54,257)(21,318,72,290,36,305,55,256)(85,247,167,209,121,223,142,170)(86,246,168,208,122,222,143,169)(87,245,148,207,123,221,144,189)(88,244,149,206,124,220,145,188)(89,243,150,205,125,219,146,187)(90,242,151,204,126,218,147,186)(91,241,152,203,106,217,127,185)(92,240,153,202,107,216,128,184)(93,239,154,201,108,215,129,183)(94,238,155,200,109,214,130,182)(95,237,156,199,110,213,131,181)(96,236,157,198,111,212,132,180)(97,235,158,197,112,211,133,179)(98,234,159,196,113,231,134,178)(99,233,160,195,114,230,135,177)(100,232,161,194,115,229,136,176)(101,252,162,193,116,228,137,175)(102,251,163,192,117,227,138,174)(103,250,164,191,118,226,139,173)(104,249,165,190,119,225,140,172)(105,248,166,210,120,224,141,171)>;
G:=Group( (1,85)(2,86)(3,87)(4,88)(5,89)(6,90)(7,91)(8,92)(9,93)(10,94)(11,95)(12,96)(13,97)(14,98)(15,99)(16,100)(17,101)(18,102)(19,103)(20,104)(21,105)(22,106)(23,107)(24,108)(25,109)(26,110)(27,111)(28,112)(29,113)(30,114)(31,115)(32,116)(33,117)(34,118)(35,119)(36,120)(37,121)(38,122)(39,123)(40,124)(41,125)(42,126)(43,129)(44,130)(45,131)(46,132)(47,133)(48,134)(49,135)(50,136)(51,137)(52,138)(53,139)(54,140)(55,141)(56,142)(57,143)(58,144)(59,145)(60,146)(61,147)(62,127)(63,128)(64,158)(65,159)(66,160)(67,161)(68,162)(69,163)(70,164)(71,165)(72,166)(73,167)(74,168)(75,148)(76,149)(77,150)(78,151)(79,152)(80,153)(81,154)(82,155)(83,156)(84,157)(169,254)(170,255)(171,256)(172,257)(173,258)(174,259)(175,260)(176,261)(177,262)(178,263)(179,264)(180,265)(181,266)(182,267)(183,268)(184,269)(185,270)(186,271)(187,272)(188,273)(189,253)(190,291)(191,292)(192,293)(193,294)(194,274)(195,275)(196,276)(197,277)(198,278)(199,279)(200,280)(201,281)(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)(208,288)(209,289)(210,290)(211,313)(212,314)(213,315)(214,295)(215,296)(216,297)(217,298)(218,299)(219,300)(220,301)(221,302)(222,303)(223,304)(224,305)(225,306)(226,307)(227,308)(228,309)(229,310)(230,311)(231,312)(232,323)(233,324)(234,325)(235,326)(236,327)(237,328)(238,329)(239,330)(240,331)(241,332)(242,333)(243,334)(244,335)(245,336)(246,316)(247,317)(248,318)(249,319)(250,320)(251,321)(252,322), (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), (1,317,73,289,37,304,56,255)(2,316,74,288,38,303,57,254)(3,336,75,287,39,302,58,253)(4,335,76,286,40,301,59,273)(5,334,77,285,41,300,60,272)(6,333,78,284,42,299,61,271)(7,332,79,283,22,298,62,270)(8,331,80,282,23,297,63,269)(9,330,81,281,24,296,43,268)(10,329,82,280,25,295,44,267)(11,328,83,279,26,315,45,266)(12,327,84,278,27,314,46,265)(13,326,64,277,28,313,47,264)(14,325,65,276,29,312,48,263)(15,324,66,275,30,311,49,262)(16,323,67,274,31,310,50,261)(17,322,68,294,32,309,51,260)(18,321,69,293,33,308,52,259)(19,320,70,292,34,307,53,258)(20,319,71,291,35,306,54,257)(21,318,72,290,36,305,55,256)(85,247,167,209,121,223,142,170)(86,246,168,208,122,222,143,169)(87,245,148,207,123,221,144,189)(88,244,149,206,124,220,145,188)(89,243,150,205,125,219,146,187)(90,242,151,204,126,218,147,186)(91,241,152,203,106,217,127,185)(92,240,153,202,107,216,128,184)(93,239,154,201,108,215,129,183)(94,238,155,200,109,214,130,182)(95,237,156,199,110,213,131,181)(96,236,157,198,111,212,132,180)(97,235,158,197,112,211,133,179)(98,234,159,196,113,231,134,178)(99,233,160,195,114,230,135,177)(100,232,161,194,115,229,136,176)(101,252,162,193,116,228,137,175)(102,251,163,192,117,227,138,174)(103,250,164,191,118,226,139,173)(104,249,165,190,119,225,140,172)(105,248,166,210,120,224,141,171) );
G=PermutationGroup([[(1,85),(2,86),(3,87),(4,88),(5,89),(6,90),(7,91),(8,92),(9,93),(10,94),(11,95),(12,96),(13,97),(14,98),(15,99),(16,100),(17,101),(18,102),(19,103),(20,104),(21,105),(22,106),(23,107),(24,108),(25,109),(26,110),(27,111),(28,112),(29,113),(30,114),(31,115),(32,116),(33,117),(34,118),(35,119),(36,120),(37,121),(38,122),(39,123),(40,124),(41,125),(42,126),(43,129),(44,130),(45,131),(46,132),(47,133),(48,134),(49,135),(50,136),(51,137),(52,138),(53,139),(54,140),(55,141),(56,142),(57,143),(58,144),(59,145),(60,146),(61,147),(62,127),(63,128),(64,158),(65,159),(66,160),(67,161),(68,162),(69,163),(70,164),(71,165),(72,166),(73,167),(74,168),(75,148),(76,149),(77,150),(78,151),(79,152),(80,153),(81,154),(82,155),(83,156),(84,157),(169,254),(170,255),(171,256),(172,257),(173,258),(174,259),(175,260),(176,261),(177,262),(178,263),(179,264),(180,265),(181,266),(182,267),(183,268),(184,269),(185,270),(186,271),(187,272),(188,273),(189,253),(190,291),(191,292),(192,293),(193,294),(194,274),(195,275),(196,276),(197,277),(198,278),(199,279),(200,280),(201,281),(202,282),(203,283),(204,284),(205,285),(206,286),(207,287),(208,288),(209,289),(210,290),(211,313),(212,314),(213,315),(214,295),(215,296),(216,297),(217,298),(218,299),(219,300),(220,301),(221,302),(222,303),(223,304),(224,305),(225,306),(226,307),(227,308),(228,309),(229,310),(230,311),(231,312),(232,323),(233,324),(234,325),(235,326),(236,327),(237,328),(238,329),(239,330),(240,331),(241,332),(242,333),(243,334),(244,335),(245,336),(246,316),(247,317),(248,318),(249,319),(250,320),(251,321),(252,322)], [(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)], [(1,317,73,289,37,304,56,255),(2,316,74,288,38,303,57,254),(3,336,75,287,39,302,58,253),(4,335,76,286,40,301,59,273),(5,334,77,285,41,300,60,272),(6,333,78,284,42,299,61,271),(7,332,79,283,22,298,62,270),(8,331,80,282,23,297,63,269),(9,330,81,281,24,296,43,268),(10,329,82,280,25,295,44,267),(11,328,83,279,26,315,45,266),(12,327,84,278,27,314,46,265),(13,326,64,277,28,313,47,264),(14,325,65,276,29,312,48,263),(15,324,66,275,30,311,49,262),(16,323,67,274,31,310,50,261),(17,322,68,294,32,309,51,260),(18,321,69,293,33,308,52,259),(19,320,70,292,34,307,53,258),(20,319,71,291,35,306,54,257),(21,318,72,290,36,305,55,256),(85,247,167,209,121,223,142,170),(86,246,168,208,122,222,143,169),(87,245,148,207,123,221,144,189),(88,244,149,206,124,220,145,188),(89,243,150,205,125,219,146,187),(90,242,151,204,126,218,147,186),(91,241,152,203,106,217,127,185),(92,240,153,202,107,216,128,184),(93,239,154,201,108,215,129,183),(94,238,155,200,109,214,130,182),(95,237,156,199,110,213,131,181),(96,236,157,198,111,212,132,180),(97,235,158,197,112,211,133,179),(98,234,159,196,113,231,134,178),(99,233,160,195,114,230,135,177),(100,232,161,194,115,229,136,176),(101,252,162,193,116,228,137,175),(102,251,163,192,117,227,138,174),(103,250,164,191,118,226,139,173),(104,249,165,190,119,225,140,172),(105,248,166,210,120,224,141,171)]])
96 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 6A | 6B | 6C | 7A | 7B | 7C | 8A | ··· | 8H | 12A | 12B | 12C | 12D | 14A | ··· | 14I | 21A | ··· | 21F | 28A | ··· | 28L | 42A | ··· | 42R | 84A | ··· | 84X |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 6 | 6 | 6 | 7 | 7 | 7 | 8 | ··· | 8 | 12 | 12 | 12 | 12 | 14 | ··· | 14 | 21 | ··· | 21 | 28 | ··· | 28 | 42 | ··· | 42 | 84 | ··· | 84 |
| size | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 21 | ··· | 21 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
96 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | + | - | + | - | + | - | + | - | ||||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | S3 | Dic3 | D6 | Dic3 | D7 | C3⋊C8 | Dic7 | D14 | Dic7 | D21 | C7⋊C8 | Dic21 | D42 | Dic21 | C21⋊C8 |
| kernel | C2×C21⋊C8 | C21⋊C8 | C2×C84 | C84 | C2×C42 | C42 | C2×C28 | C28 | C28 | C2×C14 | C2×C12 | C14 | C12 | C12 | C2×C6 | C2×C4 | C6 | C4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 8 | 1 | 1 | 1 | 1 | 3 | 4 | 3 | 3 | 3 | 6 | 12 | 6 | 6 | 6 | 24 |
Matrix representation of C2×C21⋊C8 ►in GL5(𝔽337)
| 336 | 0 | 0 | 0 | 0 |
| 0 | 336 | 0 | 0 | 0 |
| 0 | 0 | 336 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 336 | 227 | 0 | 0 |
| 0 | 110 | 304 | 0 | 0 |
| 0 | 0 | 0 | 73 | 278 |
| 0 | 0 | 0 | 118 | 117 |
| 226 | 0 | 0 | 0 | 0 |
| 0 | 139 | 257 | 0 | 0 |
| 0 | 132 | 198 | 0 | 0 |
| 0 | 0 | 0 | 98 | 29 |
| 0 | 0 | 0 | 122 | 239 |
G:=sub<GL(5,GF(337))| [336,0,0,0,0,0,336,0,0,0,0,0,336,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,336,110,0,0,0,227,304,0,0,0,0,0,73,118,0,0,0,278,117],[226,0,0,0,0,0,139,132,0,0,0,257,198,0,0,0,0,0,98,122,0,0,0,29,239] >;
C2×C21⋊C8 in GAP, Magma, Sage, TeX
C_2\times C_{21}\rtimes C_8 % in TeX
G:=Group("C2xC21:C8"); // GroupNames label
G:=SmallGroup(336,95);
// by ID
G=gap.SmallGroup(336,95);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-3,-7,24,50,964,10373]);
// Polycyclic
G:=Group<a,b,c|a^2=b^21=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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