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G = C2×C4×C44order 352 = 25·11

Abelian group of type [2,4,44]

direct product, abelian, monomial, 2-elementary

Aliases: C2×C4×C44, SmallGroup(352,149)

Series: Derived Chief Lower central Upper central

C1 — C2×C4×C44
C1C2C22C2×C22C2×C44C4×C44 — C2×C4×C44
C1 — C2×C4×C44
C1 — C2×C4×C44

Generators and relations for C2×C4×C44
 G = < a,b,c | a2=b4=c44=1, ab=ba, ac=ca, bc=cb >

Subgroups: 108, all normal (8 characteristic)
C1, C2 [×7], C4 [×12], C22, C22 [×6], C2×C4 [×18], C23, C11, C42 [×4], C22×C4 [×3], C22 [×7], C2×C42, C44 [×12], C2×C22, C2×C22 [×6], C2×C44 [×18], C22×C22, C4×C44 [×4], C22×C44 [×3], C2×C4×C44
Quotients: C1, C2 [×7], C4 [×12], C22 [×7], C2×C4 [×18], C23, C11, C42 [×4], C22×C4 [×3], C22 [×7], C2×C42, C44 [×12], C2×C22 [×7], C2×C44 [×18], C22×C22, C4×C44 [×4], C22×C44 [×3], C2×C4×C44

Smallest permutation representation of C2×C4×C44
Regular action on 352 points
Generators in S352
(1 164)(2 165)(3 166)(4 167)(5 168)(6 169)(7 170)(8 171)(9 172)(10 173)(11 174)(12 175)(13 176)(14 133)(15 134)(16 135)(17 136)(18 137)(19 138)(20 139)(21 140)(22 141)(23 142)(24 143)(25 144)(26 145)(27 146)(28 147)(29 148)(30 149)(31 150)(32 151)(33 152)(34 153)(35 154)(36 155)(37 156)(38 157)(39 158)(40 159)(41 160)(42 161)(43 162)(44 163)(45 178)(46 179)(47 180)(48 181)(49 182)(50 183)(51 184)(52 185)(53 186)(54 187)(55 188)(56 189)(57 190)(58 191)(59 192)(60 193)(61 194)(62 195)(63 196)(64 197)(65 198)(66 199)(67 200)(68 201)(69 202)(70 203)(71 204)(72 205)(73 206)(74 207)(75 208)(76 209)(77 210)(78 211)(79 212)(80 213)(81 214)(82 215)(83 216)(84 217)(85 218)(86 219)(87 220)(88 177)(89 250)(90 251)(91 252)(92 253)(93 254)(94 255)(95 256)(96 257)(97 258)(98 259)(99 260)(100 261)(101 262)(102 263)(103 264)(104 221)(105 222)(106 223)(107 224)(108 225)(109 226)(110 227)(111 228)(112 229)(113 230)(114 231)(115 232)(116 233)(117 234)(118 235)(119 236)(120 237)(121 238)(122 239)(123 240)(124 241)(125 242)(126 243)(127 244)(128 245)(129 246)(130 247)(131 248)(132 249)(265 320)(266 321)(267 322)(268 323)(269 324)(270 325)(271 326)(272 327)(273 328)(274 329)(275 330)(276 331)(277 332)(278 333)(279 334)(280 335)(281 336)(282 337)(283 338)(284 339)(285 340)(286 341)(287 342)(288 343)(289 344)(290 345)(291 346)(292 347)(293 348)(294 349)(295 350)(296 351)(297 352)(298 309)(299 310)(300 311)(301 312)(302 313)(303 314)(304 315)(305 316)(306 317)(307 318)(308 319)
(1 263 180 325)(2 264 181 326)(3 221 182 327)(4 222 183 328)(5 223 184 329)(6 224 185 330)(7 225 186 331)(8 226 187 332)(9 227 188 333)(10 228 189 334)(11 229 190 335)(12 230 191 336)(13 231 192 337)(14 232 193 338)(15 233 194 339)(16 234 195 340)(17 235 196 341)(18 236 197 342)(19 237 198 343)(20 238 199 344)(21 239 200 345)(22 240 201 346)(23 241 202 347)(24 242 203 348)(25 243 204 349)(26 244 205 350)(27 245 206 351)(28 246 207 352)(29 247 208 309)(30 248 209 310)(31 249 210 311)(32 250 211 312)(33 251 212 313)(34 252 213 314)(35 253 214 315)(36 254 215 316)(37 255 216 317)(38 256 217 318)(39 257 218 319)(40 258 219 320)(41 259 220 321)(42 260 177 322)(43 261 178 323)(44 262 179 324)(45 268 162 100)(46 269 163 101)(47 270 164 102)(48 271 165 103)(49 272 166 104)(50 273 167 105)(51 274 168 106)(52 275 169 107)(53 276 170 108)(54 277 171 109)(55 278 172 110)(56 279 173 111)(57 280 174 112)(58 281 175 113)(59 282 176 114)(60 283 133 115)(61 284 134 116)(62 285 135 117)(63 286 136 118)(64 287 137 119)(65 288 138 120)(66 289 139 121)(67 290 140 122)(68 291 141 123)(69 292 142 124)(70 293 143 125)(71 294 144 126)(72 295 145 127)(73 296 146 128)(74 297 147 129)(75 298 148 130)(76 299 149 131)(77 300 150 132)(78 301 151 89)(79 302 152 90)(80 303 153 91)(81 304 154 92)(82 305 155 93)(83 306 156 94)(84 307 157 95)(85 308 158 96)(86 265 159 97)(87 266 160 98)(88 267 161 99)
(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)

G:=sub<Sym(352)| (1,164)(2,165)(3,166)(4,167)(5,168)(6,169)(7,170)(8,171)(9,172)(10,173)(11,174)(12,175)(13,176)(14,133)(15,134)(16,135)(17,136)(18,137)(19,138)(20,139)(21,140)(22,141)(23,142)(24,143)(25,144)(26,145)(27,146)(28,147)(29,148)(30,149)(31,150)(32,151)(33,152)(34,153)(35,154)(36,155)(37,156)(38,157)(39,158)(40,159)(41,160)(42,161)(43,162)(44,163)(45,178)(46,179)(47,180)(48,181)(49,182)(50,183)(51,184)(52,185)(53,186)(54,187)(55,188)(56,189)(57,190)(58,191)(59,192)(60,193)(61,194)(62,195)(63,196)(64,197)(65,198)(66,199)(67,200)(68,201)(69,202)(70,203)(71,204)(72,205)(73,206)(74,207)(75,208)(76,209)(77,210)(78,211)(79,212)(80,213)(81,214)(82,215)(83,216)(84,217)(85,218)(86,219)(87,220)(88,177)(89,250)(90,251)(91,252)(92,253)(93,254)(94,255)(95,256)(96,257)(97,258)(98,259)(99,260)(100,261)(101,262)(102,263)(103,264)(104,221)(105,222)(106,223)(107,224)(108,225)(109,226)(110,227)(111,228)(112,229)(113,230)(114,231)(115,232)(116,233)(117,234)(118,235)(119,236)(120,237)(121,238)(122,239)(123,240)(124,241)(125,242)(126,243)(127,244)(128,245)(129,246)(130,247)(131,248)(132,249)(265,320)(266,321)(267,322)(268,323)(269,324)(270,325)(271,326)(272,327)(273,328)(274,329)(275,330)(276,331)(277,332)(278,333)(279,334)(280,335)(281,336)(282,337)(283,338)(284,339)(285,340)(286,341)(287,342)(288,343)(289,344)(290,345)(291,346)(292,347)(293,348)(294,349)(295,350)(296,351)(297,352)(298,309)(299,310)(300,311)(301,312)(302,313)(303,314)(304,315)(305,316)(306,317)(307,318)(308,319), (1,263,180,325)(2,264,181,326)(3,221,182,327)(4,222,183,328)(5,223,184,329)(6,224,185,330)(7,225,186,331)(8,226,187,332)(9,227,188,333)(10,228,189,334)(11,229,190,335)(12,230,191,336)(13,231,192,337)(14,232,193,338)(15,233,194,339)(16,234,195,340)(17,235,196,341)(18,236,197,342)(19,237,198,343)(20,238,199,344)(21,239,200,345)(22,240,201,346)(23,241,202,347)(24,242,203,348)(25,243,204,349)(26,244,205,350)(27,245,206,351)(28,246,207,352)(29,247,208,309)(30,248,209,310)(31,249,210,311)(32,250,211,312)(33,251,212,313)(34,252,213,314)(35,253,214,315)(36,254,215,316)(37,255,216,317)(38,256,217,318)(39,257,218,319)(40,258,219,320)(41,259,220,321)(42,260,177,322)(43,261,178,323)(44,262,179,324)(45,268,162,100)(46,269,163,101)(47,270,164,102)(48,271,165,103)(49,272,166,104)(50,273,167,105)(51,274,168,106)(52,275,169,107)(53,276,170,108)(54,277,171,109)(55,278,172,110)(56,279,173,111)(57,280,174,112)(58,281,175,113)(59,282,176,114)(60,283,133,115)(61,284,134,116)(62,285,135,117)(63,286,136,118)(64,287,137,119)(65,288,138,120)(66,289,139,121)(67,290,140,122)(68,291,141,123)(69,292,142,124)(70,293,143,125)(71,294,144,126)(72,295,145,127)(73,296,146,128)(74,297,147,129)(75,298,148,130)(76,299,149,131)(77,300,150,132)(78,301,151,89)(79,302,152,90)(80,303,153,91)(81,304,154,92)(82,305,155,93)(83,306,156,94)(84,307,157,95)(85,308,158,96)(86,265,159,97)(87,266,160,98)(88,267,161,99), (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)>;

G:=Group( (1,164)(2,165)(3,166)(4,167)(5,168)(6,169)(7,170)(8,171)(9,172)(10,173)(11,174)(12,175)(13,176)(14,133)(15,134)(16,135)(17,136)(18,137)(19,138)(20,139)(21,140)(22,141)(23,142)(24,143)(25,144)(26,145)(27,146)(28,147)(29,148)(30,149)(31,150)(32,151)(33,152)(34,153)(35,154)(36,155)(37,156)(38,157)(39,158)(40,159)(41,160)(42,161)(43,162)(44,163)(45,178)(46,179)(47,180)(48,181)(49,182)(50,183)(51,184)(52,185)(53,186)(54,187)(55,188)(56,189)(57,190)(58,191)(59,192)(60,193)(61,194)(62,195)(63,196)(64,197)(65,198)(66,199)(67,200)(68,201)(69,202)(70,203)(71,204)(72,205)(73,206)(74,207)(75,208)(76,209)(77,210)(78,211)(79,212)(80,213)(81,214)(82,215)(83,216)(84,217)(85,218)(86,219)(87,220)(88,177)(89,250)(90,251)(91,252)(92,253)(93,254)(94,255)(95,256)(96,257)(97,258)(98,259)(99,260)(100,261)(101,262)(102,263)(103,264)(104,221)(105,222)(106,223)(107,224)(108,225)(109,226)(110,227)(111,228)(112,229)(113,230)(114,231)(115,232)(116,233)(117,234)(118,235)(119,236)(120,237)(121,238)(122,239)(123,240)(124,241)(125,242)(126,243)(127,244)(128,245)(129,246)(130,247)(131,248)(132,249)(265,320)(266,321)(267,322)(268,323)(269,324)(270,325)(271,326)(272,327)(273,328)(274,329)(275,330)(276,331)(277,332)(278,333)(279,334)(280,335)(281,336)(282,337)(283,338)(284,339)(285,340)(286,341)(287,342)(288,343)(289,344)(290,345)(291,346)(292,347)(293,348)(294,349)(295,350)(296,351)(297,352)(298,309)(299,310)(300,311)(301,312)(302,313)(303,314)(304,315)(305,316)(306,317)(307,318)(308,319), (1,263,180,325)(2,264,181,326)(3,221,182,327)(4,222,183,328)(5,223,184,329)(6,224,185,330)(7,225,186,331)(8,226,187,332)(9,227,188,333)(10,228,189,334)(11,229,190,335)(12,230,191,336)(13,231,192,337)(14,232,193,338)(15,233,194,339)(16,234,195,340)(17,235,196,341)(18,236,197,342)(19,237,198,343)(20,238,199,344)(21,239,200,345)(22,240,201,346)(23,241,202,347)(24,242,203,348)(25,243,204,349)(26,244,205,350)(27,245,206,351)(28,246,207,352)(29,247,208,309)(30,248,209,310)(31,249,210,311)(32,250,211,312)(33,251,212,313)(34,252,213,314)(35,253,214,315)(36,254,215,316)(37,255,216,317)(38,256,217,318)(39,257,218,319)(40,258,219,320)(41,259,220,321)(42,260,177,322)(43,261,178,323)(44,262,179,324)(45,268,162,100)(46,269,163,101)(47,270,164,102)(48,271,165,103)(49,272,166,104)(50,273,167,105)(51,274,168,106)(52,275,169,107)(53,276,170,108)(54,277,171,109)(55,278,172,110)(56,279,173,111)(57,280,174,112)(58,281,175,113)(59,282,176,114)(60,283,133,115)(61,284,134,116)(62,285,135,117)(63,286,136,118)(64,287,137,119)(65,288,138,120)(66,289,139,121)(67,290,140,122)(68,291,141,123)(69,292,142,124)(70,293,143,125)(71,294,144,126)(72,295,145,127)(73,296,146,128)(74,297,147,129)(75,298,148,130)(76,299,149,131)(77,300,150,132)(78,301,151,89)(79,302,152,90)(80,303,153,91)(81,304,154,92)(82,305,155,93)(83,306,156,94)(84,307,157,95)(85,308,158,96)(86,265,159,97)(87,266,160,98)(88,267,161,99), (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) );

G=PermutationGroup([(1,164),(2,165),(3,166),(4,167),(5,168),(6,169),(7,170),(8,171),(9,172),(10,173),(11,174),(12,175),(13,176),(14,133),(15,134),(16,135),(17,136),(18,137),(19,138),(20,139),(21,140),(22,141),(23,142),(24,143),(25,144),(26,145),(27,146),(28,147),(29,148),(30,149),(31,150),(32,151),(33,152),(34,153),(35,154),(36,155),(37,156),(38,157),(39,158),(40,159),(41,160),(42,161),(43,162),(44,163),(45,178),(46,179),(47,180),(48,181),(49,182),(50,183),(51,184),(52,185),(53,186),(54,187),(55,188),(56,189),(57,190),(58,191),(59,192),(60,193),(61,194),(62,195),(63,196),(64,197),(65,198),(66,199),(67,200),(68,201),(69,202),(70,203),(71,204),(72,205),(73,206),(74,207),(75,208),(76,209),(77,210),(78,211),(79,212),(80,213),(81,214),(82,215),(83,216),(84,217),(85,218),(86,219),(87,220),(88,177),(89,250),(90,251),(91,252),(92,253),(93,254),(94,255),(95,256),(96,257),(97,258),(98,259),(99,260),(100,261),(101,262),(102,263),(103,264),(104,221),(105,222),(106,223),(107,224),(108,225),(109,226),(110,227),(111,228),(112,229),(113,230),(114,231),(115,232),(116,233),(117,234),(118,235),(119,236),(120,237),(121,238),(122,239),(123,240),(124,241),(125,242),(126,243),(127,244),(128,245),(129,246),(130,247),(131,248),(132,249),(265,320),(266,321),(267,322),(268,323),(269,324),(270,325),(271,326),(272,327),(273,328),(274,329),(275,330),(276,331),(277,332),(278,333),(279,334),(280,335),(281,336),(282,337),(283,338),(284,339),(285,340),(286,341),(287,342),(288,343),(289,344),(290,345),(291,346),(292,347),(293,348),(294,349),(295,350),(296,351),(297,352),(298,309),(299,310),(300,311),(301,312),(302,313),(303,314),(304,315),(305,316),(306,317),(307,318),(308,319)], [(1,263,180,325),(2,264,181,326),(3,221,182,327),(4,222,183,328),(5,223,184,329),(6,224,185,330),(7,225,186,331),(8,226,187,332),(9,227,188,333),(10,228,189,334),(11,229,190,335),(12,230,191,336),(13,231,192,337),(14,232,193,338),(15,233,194,339),(16,234,195,340),(17,235,196,341),(18,236,197,342),(19,237,198,343),(20,238,199,344),(21,239,200,345),(22,240,201,346),(23,241,202,347),(24,242,203,348),(25,243,204,349),(26,244,205,350),(27,245,206,351),(28,246,207,352),(29,247,208,309),(30,248,209,310),(31,249,210,311),(32,250,211,312),(33,251,212,313),(34,252,213,314),(35,253,214,315),(36,254,215,316),(37,255,216,317),(38,256,217,318),(39,257,218,319),(40,258,219,320),(41,259,220,321),(42,260,177,322),(43,261,178,323),(44,262,179,324),(45,268,162,100),(46,269,163,101),(47,270,164,102),(48,271,165,103),(49,272,166,104),(50,273,167,105),(51,274,168,106),(52,275,169,107),(53,276,170,108),(54,277,171,109),(55,278,172,110),(56,279,173,111),(57,280,174,112),(58,281,175,113),(59,282,176,114),(60,283,133,115),(61,284,134,116),(62,285,135,117),(63,286,136,118),(64,287,137,119),(65,288,138,120),(66,289,139,121),(67,290,140,122),(68,291,141,123),(69,292,142,124),(70,293,143,125),(71,294,144,126),(72,295,145,127),(73,296,146,128),(74,297,147,129),(75,298,148,130),(76,299,149,131),(77,300,150,132),(78,301,151,89),(79,302,152,90),(80,303,153,91),(81,304,154,92),(82,305,155,93),(83,306,156,94),(84,307,157,95),(85,308,158,96),(86,265,159,97),(87,266,160,98),(88,267,161,99)], [(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)])

352 conjugacy classes

class 1 2A···2G4A···4X11A···11J22A···22BR44A···44IF
order12···24···411···1122···2244···44
size11···11···11···11···11···1

352 irreducible representations

dim11111111
type+++
imageC1C2C2C4C11C22C22C44
kernelC2×C4×C44C4×C44C22×C44C2×C44C2×C42C42C22×C4C2×C4
# reps14324104030240

Matrix representation of C2×C4×C44 in GL3(𝔽89) generated by

100
010
0088
,
5500
0550
0055
,
4400
0180
0080
G:=sub<GL(3,GF(89))| [1,0,0,0,1,0,0,0,88],[55,0,0,0,55,0,0,0,55],[44,0,0,0,18,0,0,0,80] >;

C2×C4×C44 in GAP, Magma, Sage, TeX

C_2\times C_4\times C_{44}
% in TeX

G:=Group("C2xC4xC44");
// GroupNames label

G:=SmallGroup(352,149);
// by ID

G=gap.SmallGroup(352,149);
# by ID

G:=PCGroup([6,-2,-2,-2,-11,-2,-2,528,1063]);
// Polycyclic

G:=Group<a,b,c|a^2=b^4=c^44=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations

׿
×
𝔽