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G = C2×C21⋊C8order 336 = 24·3·7

Direct product of C2 and C21⋊C8

direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: C2×C21⋊C8, C421C8, C84.3C4, C4.14D42, C28.49D6, C12.50D14, C4.3Dic21, C28.3Dic3, C12.3Dic7, C84.56C22, C22.2Dic21, C6⋊(C7⋊C8), C14⋊(C3⋊C8), C217(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), C32(C2×C7⋊C8), C72(C2×C3⋊C8), SmallGroup(336,95)

Series: Derived Chief Lower central Upper central

C1C21 — C2×C21⋊C8
C1C7C21C42C84C21⋊C8 — C2×C21⋊C8
C21 — C2×C21⋊C8
C1C2×C4

Generators and relations for C2×C21⋊C8
 G = < a,b,c | a2=b21=c8=1, ab=ba, ac=ca, cbc-1=b-1 >

21C8
21C8
21C2×C8
7C3⋊C8
7C3⋊C8
3C7⋊C8
3C7⋊C8
7C2×C3⋊C8
3C2×C7⋊C8

Smallest permutation representation of C2×C21⋊C8
Regular action on 336 points
Generators in S336
(1 100)(2 101)(3 102)(4 103)(5 104)(6 105)(7 85)(8 86)(9 87)(10 88)(11 89)(12 90)(13 91)(14 92)(15 93)(16 94)(17 95)(18 96)(19 97)(20 98)(21 99)(22 110)(23 111)(24 112)(25 113)(26 114)(27 115)(28 116)(29 117)(30 118)(31 119)(32 120)(33 121)(34 122)(35 123)(36 124)(37 125)(38 126)(39 106)(40 107)(41 108)(42 109)(43 131)(44 132)(45 133)(46 134)(47 135)(48 136)(49 137)(50 138)(51 139)(52 140)(53 141)(54 142)(55 143)(56 144)(57 145)(58 146)(59 147)(60 127)(61 128)(62 129)(63 130)(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)(190 282)(191 283)(192 284)(193 285)(194 286)(195 287)(196 288)(197 289)(198 290)(199 291)(200 292)(201 293)(202 294)(203 274)(204 275)(205 276)(206 277)(207 278)(208 279)(209 280)(210 281)(211 296)(212 297)(213 298)(214 299)(215 300)(216 301)(217 302)(218 303)(219 304)(220 305)(221 306)(222 307)(223 308)(224 309)(225 310)(226 311)(227 312)(228 313)(229 314)(230 315)(231 295)(232 332)(233 333)(234 334)(235 335)(236 336)(237 316)(238 317)(239 318)(240 319)(241 320)(242 321)(243 322)(244 323)(245 324)(246 325)(247 326)(248 327)(249 328)(250 329)(251 330)(252 331)
(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)
(1 330 73 280 33 297 52 263)(2 329 74 279 34 296 53 262)(3 328 75 278 35 295 54 261)(4 327 76 277 36 315 55 260)(5 326 77 276 37 314 56 259)(6 325 78 275 38 313 57 258)(7 324 79 274 39 312 58 257)(8 323 80 294 40 311 59 256)(9 322 81 293 41 310 60 255)(10 321 82 292 42 309 61 254)(11 320 83 291 22 308 62 253)(12 319 84 290 23 307 63 273)(13 318 64 289 24 306 43 272)(14 317 65 288 25 305 44 271)(15 316 66 287 26 304 45 270)(16 336 67 286 27 303 46 269)(17 335 68 285 28 302 47 268)(18 334 69 284 29 301 48 267)(19 333 70 283 30 300 49 266)(20 332 71 282 31 299 50 265)(21 331 72 281 32 298 51 264)(85 245 152 203 106 227 146 172)(86 244 153 202 107 226 147 171)(87 243 154 201 108 225 127 170)(88 242 155 200 109 224 128 169)(89 241 156 199 110 223 129 189)(90 240 157 198 111 222 130 188)(91 239 158 197 112 221 131 187)(92 238 159 196 113 220 132 186)(93 237 160 195 114 219 133 185)(94 236 161 194 115 218 134 184)(95 235 162 193 116 217 135 183)(96 234 163 192 117 216 136 182)(97 233 164 191 118 215 137 181)(98 232 165 190 119 214 138 180)(99 252 166 210 120 213 139 179)(100 251 167 209 121 212 140 178)(101 250 168 208 122 211 141 177)(102 249 148 207 123 231 142 176)(103 248 149 206 124 230 143 175)(104 247 150 205 125 229 144 174)(105 246 151 204 126 228 145 173)

G:=sub<Sym(336)| (1,100)(2,101)(3,102)(4,103)(5,104)(6,105)(7,85)(8,86)(9,87)(10,88)(11,89)(12,90)(13,91)(14,92)(15,93)(16,94)(17,95)(18,96)(19,97)(20,98)(21,99)(22,110)(23,111)(24,112)(25,113)(26,114)(27,115)(28,116)(29,117)(30,118)(31,119)(32,120)(33,121)(34,122)(35,123)(36,124)(37,125)(38,126)(39,106)(40,107)(41,108)(42,109)(43,131)(44,132)(45,133)(46,134)(47,135)(48,136)(49,137)(50,138)(51,139)(52,140)(53,141)(54,142)(55,143)(56,144)(57,145)(58,146)(59,147)(60,127)(61,128)(62,129)(63,130)(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)(190,282)(191,283)(192,284)(193,285)(194,286)(195,287)(196,288)(197,289)(198,290)(199,291)(200,292)(201,293)(202,294)(203,274)(204,275)(205,276)(206,277)(207,278)(208,279)(209,280)(210,281)(211,296)(212,297)(213,298)(214,299)(215,300)(216,301)(217,302)(218,303)(219,304)(220,305)(221,306)(222,307)(223,308)(224,309)(225,310)(226,311)(227,312)(228,313)(229,314)(230,315)(231,295)(232,332)(233,333)(234,334)(235,335)(236,336)(237,316)(238,317)(239,318)(240,319)(241,320)(242,321)(243,322)(244,323)(245,324)(246,325)(247,326)(248,327)(249,328)(250,329)(251,330)(252,331), (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), (1,330,73,280,33,297,52,263)(2,329,74,279,34,296,53,262)(3,328,75,278,35,295,54,261)(4,327,76,277,36,315,55,260)(5,326,77,276,37,314,56,259)(6,325,78,275,38,313,57,258)(7,324,79,274,39,312,58,257)(8,323,80,294,40,311,59,256)(9,322,81,293,41,310,60,255)(10,321,82,292,42,309,61,254)(11,320,83,291,22,308,62,253)(12,319,84,290,23,307,63,273)(13,318,64,289,24,306,43,272)(14,317,65,288,25,305,44,271)(15,316,66,287,26,304,45,270)(16,336,67,286,27,303,46,269)(17,335,68,285,28,302,47,268)(18,334,69,284,29,301,48,267)(19,333,70,283,30,300,49,266)(20,332,71,282,31,299,50,265)(21,331,72,281,32,298,51,264)(85,245,152,203,106,227,146,172)(86,244,153,202,107,226,147,171)(87,243,154,201,108,225,127,170)(88,242,155,200,109,224,128,169)(89,241,156,199,110,223,129,189)(90,240,157,198,111,222,130,188)(91,239,158,197,112,221,131,187)(92,238,159,196,113,220,132,186)(93,237,160,195,114,219,133,185)(94,236,161,194,115,218,134,184)(95,235,162,193,116,217,135,183)(96,234,163,192,117,216,136,182)(97,233,164,191,118,215,137,181)(98,232,165,190,119,214,138,180)(99,252,166,210,120,213,139,179)(100,251,167,209,121,212,140,178)(101,250,168,208,122,211,141,177)(102,249,148,207,123,231,142,176)(103,248,149,206,124,230,143,175)(104,247,150,205,125,229,144,174)(105,246,151,204,126,228,145,173)>;

G:=Group( (1,100)(2,101)(3,102)(4,103)(5,104)(6,105)(7,85)(8,86)(9,87)(10,88)(11,89)(12,90)(13,91)(14,92)(15,93)(16,94)(17,95)(18,96)(19,97)(20,98)(21,99)(22,110)(23,111)(24,112)(25,113)(26,114)(27,115)(28,116)(29,117)(30,118)(31,119)(32,120)(33,121)(34,122)(35,123)(36,124)(37,125)(38,126)(39,106)(40,107)(41,108)(42,109)(43,131)(44,132)(45,133)(46,134)(47,135)(48,136)(49,137)(50,138)(51,139)(52,140)(53,141)(54,142)(55,143)(56,144)(57,145)(58,146)(59,147)(60,127)(61,128)(62,129)(63,130)(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)(190,282)(191,283)(192,284)(193,285)(194,286)(195,287)(196,288)(197,289)(198,290)(199,291)(200,292)(201,293)(202,294)(203,274)(204,275)(205,276)(206,277)(207,278)(208,279)(209,280)(210,281)(211,296)(212,297)(213,298)(214,299)(215,300)(216,301)(217,302)(218,303)(219,304)(220,305)(221,306)(222,307)(223,308)(224,309)(225,310)(226,311)(227,312)(228,313)(229,314)(230,315)(231,295)(232,332)(233,333)(234,334)(235,335)(236,336)(237,316)(238,317)(239,318)(240,319)(241,320)(242,321)(243,322)(244,323)(245,324)(246,325)(247,326)(248,327)(249,328)(250,329)(251,330)(252,331), (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), (1,330,73,280,33,297,52,263)(2,329,74,279,34,296,53,262)(3,328,75,278,35,295,54,261)(4,327,76,277,36,315,55,260)(5,326,77,276,37,314,56,259)(6,325,78,275,38,313,57,258)(7,324,79,274,39,312,58,257)(8,323,80,294,40,311,59,256)(9,322,81,293,41,310,60,255)(10,321,82,292,42,309,61,254)(11,320,83,291,22,308,62,253)(12,319,84,290,23,307,63,273)(13,318,64,289,24,306,43,272)(14,317,65,288,25,305,44,271)(15,316,66,287,26,304,45,270)(16,336,67,286,27,303,46,269)(17,335,68,285,28,302,47,268)(18,334,69,284,29,301,48,267)(19,333,70,283,30,300,49,266)(20,332,71,282,31,299,50,265)(21,331,72,281,32,298,51,264)(85,245,152,203,106,227,146,172)(86,244,153,202,107,226,147,171)(87,243,154,201,108,225,127,170)(88,242,155,200,109,224,128,169)(89,241,156,199,110,223,129,189)(90,240,157,198,111,222,130,188)(91,239,158,197,112,221,131,187)(92,238,159,196,113,220,132,186)(93,237,160,195,114,219,133,185)(94,236,161,194,115,218,134,184)(95,235,162,193,116,217,135,183)(96,234,163,192,117,216,136,182)(97,233,164,191,118,215,137,181)(98,232,165,190,119,214,138,180)(99,252,166,210,120,213,139,179)(100,251,167,209,121,212,140,178)(101,250,168,208,122,211,141,177)(102,249,148,207,123,231,142,176)(103,248,149,206,124,230,143,175)(104,247,150,205,125,229,144,174)(105,246,151,204,126,228,145,173) );

G=PermutationGroup([(1,100),(2,101),(3,102),(4,103),(5,104),(6,105),(7,85),(8,86),(9,87),(10,88),(11,89),(12,90),(13,91),(14,92),(15,93),(16,94),(17,95),(18,96),(19,97),(20,98),(21,99),(22,110),(23,111),(24,112),(25,113),(26,114),(27,115),(28,116),(29,117),(30,118),(31,119),(32,120),(33,121),(34,122),(35,123),(36,124),(37,125),(38,126),(39,106),(40,107),(41,108),(42,109),(43,131),(44,132),(45,133),(46,134),(47,135),(48,136),(49,137),(50,138),(51,139),(52,140),(53,141),(54,142),(55,143),(56,144),(57,145),(58,146),(59,147),(60,127),(61,128),(62,129),(63,130),(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),(190,282),(191,283),(192,284),(193,285),(194,286),(195,287),(196,288),(197,289),(198,290),(199,291),(200,292),(201,293),(202,294),(203,274),(204,275),(205,276),(206,277),(207,278),(208,279),(209,280),(210,281),(211,296),(212,297),(213,298),(214,299),(215,300),(216,301),(217,302),(218,303),(219,304),(220,305),(221,306),(222,307),(223,308),(224,309),(225,310),(226,311),(227,312),(228,313),(229,314),(230,315),(231,295),(232,332),(233,333),(234,334),(235,335),(236,336),(237,316),(238,317),(239,318),(240,319),(241,320),(242,321),(243,322),(244,323),(245,324),(246,325),(247,326),(248,327),(249,328),(250,329),(251,330),(252,331)], [(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)], [(1,330,73,280,33,297,52,263),(2,329,74,279,34,296,53,262),(3,328,75,278,35,295,54,261),(4,327,76,277,36,315,55,260),(5,326,77,276,37,314,56,259),(6,325,78,275,38,313,57,258),(7,324,79,274,39,312,58,257),(8,323,80,294,40,311,59,256),(9,322,81,293,41,310,60,255),(10,321,82,292,42,309,61,254),(11,320,83,291,22,308,62,253),(12,319,84,290,23,307,63,273),(13,318,64,289,24,306,43,272),(14,317,65,288,25,305,44,271),(15,316,66,287,26,304,45,270),(16,336,67,286,27,303,46,269),(17,335,68,285,28,302,47,268),(18,334,69,284,29,301,48,267),(19,333,70,283,30,300,49,266),(20,332,71,282,31,299,50,265),(21,331,72,281,32,298,51,264),(85,245,152,203,106,227,146,172),(86,244,153,202,107,226,147,171),(87,243,154,201,108,225,127,170),(88,242,155,200,109,224,128,169),(89,241,156,199,110,223,129,189),(90,240,157,198,111,222,130,188),(91,239,158,197,112,221,131,187),(92,238,159,196,113,220,132,186),(93,237,160,195,114,219,133,185),(94,236,161,194,115,218,134,184),(95,235,162,193,116,217,135,183),(96,234,163,192,117,216,136,182),(97,233,164,191,118,215,137,181),(98,232,165,190,119,214,138,180),(99,252,166,210,120,213,139,179),(100,251,167,209,121,212,140,178),(101,250,168,208,122,211,141,177),(102,249,148,207,123,231,142,176),(103,248,149,206,124,230,143,175),(104,247,150,205,125,229,144,174),(105,246,151,204,126,228,145,173)])

96 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D6A6B6C7A7B7C8A···8H12A12B12C12D14A···14I21A···21F28A···28L42A···42R84A···84X
order1222344446667778···81212121214···1421···2128···2842···4284···84
size11112111122222221···2122222···22···22···22···22···2

96 irreducible representations

dim111111222222222222222
type++++-+-+-+-+-+-
imageC1C2C2C4C4C8S3Dic3D6Dic3D7C3⋊C8Dic7D14Dic7D21C7⋊C8Dic21D42Dic21C21⋊C8
kernelC2×C21⋊C8C21⋊C8C2×C84C84C2×C42C42C2×C28C28C28C2×C14C2×C12C14C12C12C2×C6C2×C4C6C4C4C22C2
# reps12122811113433361266624

Matrix representation of C2×C21⋊C8 in GL5(𝔽337)

3360000
0336000
0033600
00010
00001
,
10000
033622700
011030400
00073278
000118117
,
2260000
013925700
013219800
0009829
000122239

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

Export

Subgroup lattice of C2×C21⋊C8 in TeX

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