Copied to
clipboard

G = C22×C84order 336 = 24·3·7

Abelian group of type [2,2,84]

direct product, abelian, monomial, 2-elementary

Aliases: C22×C84, SmallGroup(336,204)

Series: Derived Chief Lower central Upper central

C1 — C22×C84
C1C2C14C42C84C2×C84 — C22×C84
C1 — C22×C84
C1 — C22×C84

Generators and relations for C22×C84
 G = < a,b,c | a2=b2=c84=1, ab=ba, ac=ca, bc=cb >

Subgroups: 108, all normal (16 characteristic)
C1, C2, C2 [×6], C3, C4 [×4], C22 [×7], C6, C6 [×6], C7, C2×C4 [×6], C23, C12 [×4], C2×C6 [×7], C14, C14 [×6], C22×C4, C21, C2×C12 [×6], C22×C6, C28 [×4], C2×C14 [×7], C42, C42 [×6], C22×C12, C2×C28 [×6], C22×C14, C84 [×4], C2×C42 [×7], C22×C28, C2×C84 [×6], C22×C42, C22×C84
Quotients: C1, C2 [×7], C3, C4 [×4], C22 [×7], C6 [×7], C7, C2×C4 [×6], C23, C12 [×4], C2×C6 [×7], C14 [×7], C22×C4, C21, C2×C12 [×6], C22×C6, C28 [×4], C2×C14 [×7], C42 [×7], C22×C12, C2×C28 [×6], C22×C14, C84 [×4], C2×C42 [×7], C22×C28, C2×C84 [×6], C22×C42, C22×C84

Smallest permutation representation of C22×C84
Regular action on 336 points
Generators in S336
(1 259)(2 260)(3 261)(4 262)(5 263)(6 264)(7 265)(8 266)(9 267)(10 268)(11 269)(12 270)(13 271)(14 272)(15 273)(16 274)(17 275)(18 276)(19 277)(20 278)(21 279)(22 280)(23 281)(24 282)(25 283)(26 284)(27 285)(28 286)(29 287)(30 288)(31 289)(32 290)(33 291)(34 292)(35 293)(36 294)(37 295)(38 296)(39 297)(40 298)(41 299)(42 300)(43 301)(44 302)(45 303)(46 304)(47 305)(48 306)(49 307)(50 308)(51 309)(52 310)(53 311)(54 312)(55 313)(56 314)(57 315)(58 316)(59 317)(60 318)(61 319)(62 320)(63 321)(64 322)(65 323)(66 324)(67 325)(68 326)(69 327)(70 328)(71 329)(72 330)(73 331)(74 332)(75 333)(76 334)(77 335)(78 336)(79 253)(80 254)(81 255)(82 256)(83 257)(84 258)(85 213)(86 214)(87 215)(88 216)(89 217)(90 218)(91 219)(92 220)(93 221)(94 222)(95 223)(96 224)(97 225)(98 226)(99 227)(100 228)(101 229)(102 230)(103 231)(104 232)(105 233)(106 234)(107 235)(108 236)(109 237)(110 238)(111 239)(112 240)(113 241)(114 242)(115 243)(116 244)(117 245)(118 246)(119 247)(120 248)(121 249)(122 250)(123 251)(124 252)(125 169)(126 170)(127 171)(128 172)(129 173)(130 174)(131 175)(132 176)(133 177)(134 178)(135 179)(136 180)(137 181)(138 182)(139 183)(140 184)(141 185)(142 186)(143 187)(144 188)(145 189)(146 190)(147 191)(148 192)(149 193)(150 194)(151 195)(152 196)(153 197)(154 198)(155 199)(156 200)(157 201)(158 202)(159 203)(160 204)(161 205)(162 206)(163 207)(164 208)(165 209)(166 210)(167 211)(168 212)
(1 103)(2 104)(3 105)(4 106)(5 107)(6 108)(7 109)(8 110)(9 111)(10 112)(11 113)(12 114)(13 115)(14 116)(15 117)(16 118)(17 119)(18 120)(19 121)(20 122)(21 123)(22 124)(23 125)(24 126)(25 127)(26 128)(27 129)(28 130)(29 131)(30 132)(31 133)(32 134)(33 135)(34 136)(35 137)(36 138)(37 139)(38 140)(39 141)(40 142)(41 143)(42 144)(43 145)(44 146)(45 147)(46 148)(47 149)(48 150)(49 151)(50 152)(51 153)(52 154)(53 155)(54 156)(55 157)(56 158)(57 159)(58 160)(59 161)(60 162)(61 163)(62 164)(63 165)(64 166)(65 167)(66 168)(67 85)(68 86)(69 87)(70 88)(71 89)(72 90)(73 91)(74 92)(75 93)(76 94)(77 95)(78 96)(79 97)(80 98)(81 99)(82 100)(83 101)(84 102)(169 281)(170 282)(171 283)(172 284)(173 285)(174 286)(175 287)(176 288)(177 289)(178 290)(179 291)(180 292)(181 293)(182 294)(183 295)(184 296)(185 297)(186 298)(187 299)(188 300)(189 301)(190 302)(191 303)(192 304)(193 305)(194 306)(195 307)(196 308)(197 309)(198 310)(199 311)(200 312)(201 313)(202 314)(203 315)(204 316)(205 317)(206 318)(207 319)(208 320)(209 321)(210 322)(211 323)(212 324)(213 325)(214 326)(215 327)(216 328)(217 329)(218 330)(219 331)(220 332)(221 333)(222 334)(223 335)(224 336)(225 253)(226 254)(227 255)(228 256)(229 257)(230 258)(231 259)(232 260)(233 261)(234 262)(235 263)(236 264)(237 265)(238 266)(239 267)(240 268)(241 269)(242 270)(243 271)(244 272)(245 273)(246 274)(247 275)(248 276)(249 277)(250 278)(251 279)(252 280)
(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)

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

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

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

336 conjugacy classes

class 1 2A···2G3A3B4A···4H6A···6N7A···7F12A···12P14A···14AP21A···21L28A···28AV42A···42CF84A···84CR
order12···2334···46···67···712···1214···1421···2128···2842···4284···84
size11···1111···11···11···11···11···11···11···11···11···1

336 irreducible representations

dim1111111111111111
type+++
imageC1C2C2C3C4C6C6C7C12C14C14C21C28C42C42C84
kernelC22×C84C2×C84C22×C42C22×C28C2×C42C2×C28C22×C14C22×C12C2×C14C2×C12C22×C6C22×C4C2×C6C2×C4C23C22
# reps161281226163661248721296

Matrix representation of C22×C84 in GL3(𝔽337) generated by

33600
03360
001
,
33600
03360
00336
,
14400
0260
00206
G:=sub<GL(3,GF(337))| [336,0,0,0,336,0,0,0,1],[336,0,0,0,336,0,0,0,336],[144,0,0,0,26,0,0,0,206] >;

C22×C84 in GAP, Magma, Sage, TeX

C_2^2\times C_{84}
% in TeX

G:=Group("C2^2xC84");
// GroupNames label

G:=SmallGroup(336,204);
// by ID

G=gap.SmallGroup(336,204);
# by ID

G:=PCGroup([6,-2,-2,-2,-3,-7,-2,1008]);
// Polycyclic

G:=Group<a,b,c|a^2=b^2=c^84=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations

׿
×
𝔽