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G = C23×C44order 352 = 25·11

Abelian group of type [2,2,2,44]

direct product, abelian, monomial, 2-elementary

Aliases: C23×C44, SmallGroup(352,188)

Series: Derived Chief Lower central Upper central

C1 — C23×C44
C1C2C22C44C2×C44C22×C44 — C23×C44
C1 — C23×C44
C1 — C23×C44

Generators and relations for C23×C44
 G = < a,b,c,d | a2=b2=c2=d44=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, cd=dc >

Subgroups: 236, all normal (8 characteristic)
C1, C2, C2 [×14], C4 [×8], C22 [×35], C2×C4 [×28], C23 [×15], C11, C22×C4 [×14], C24, C22, C22 [×14], C23×C4, C44 [×8], C2×C22 [×35], C2×C44 [×28], C22×C22 [×15], C22×C44 [×14], C23×C22, C23×C44
Quotients: C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], C23 [×15], C11, C22×C4 [×14], C24, C22 [×15], C23×C4, C44 [×8], C2×C22 [×35], C2×C44 [×28], C22×C22 [×15], C22×C44 [×14], C23×C22, C23×C44

Smallest permutation representation of C23×C44
Regular action on 352 points
Generators in S352
(1 242)(2 243)(3 244)(4 245)(5 246)(6 247)(7 248)(8 249)(9 250)(10 251)(11 252)(12 253)(13 254)(14 255)(15 256)(16 257)(17 258)(18 259)(19 260)(20 261)(21 262)(22 263)(23 264)(24 221)(25 222)(26 223)(27 224)(28 225)(29 226)(30 227)(31 228)(32 229)(33 230)(34 231)(35 232)(36 233)(37 234)(38 235)(39 236)(40 237)(41 238)(42 239)(43 240)(44 241)(45 158)(46 159)(47 160)(48 161)(49 162)(50 163)(51 164)(52 165)(53 166)(54 167)(55 168)(56 169)(57 170)(58 171)(59 172)(60 173)(61 174)(62 175)(63 176)(64 133)(65 134)(66 135)(67 136)(68 137)(69 138)(70 139)(71 140)(72 141)(73 142)(74 143)(75 144)(76 145)(77 146)(78 147)(79 148)(80 149)(81 150)(82 151)(83 152)(84 153)(85 154)(86 155)(87 156)(88 157)(89 343)(90 344)(91 345)(92 346)(93 347)(94 348)(95 349)(96 350)(97 351)(98 352)(99 309)(100 310)(101 311)(102 312)(103 313)(104 314)(105 315)(106 316)(107 317)(108 318)(109 319)(110 320)(111 321)(112 322)(113 323)(114 324)(115 325)(116 326)(117 327)(118 328)(119 329)(120 330)(121 331)(122 332)(123 333)(124 334)(125 335)(126 336)(127 337)(128 338)(129 339)(130 340)(131 341)(132 342)(177 267)(178 268)(179 269)(180 270)(181 271)(182 272)(183 273)(184 274)(185 275)(186 276)(187 277)(188 278)(189 279)(190 280)(191 281)(192 282)(193 283)(194 284)(195 285)(196 286)(197 287)(198 288)(199 289)(200 290)(201 291)(202 292)(203 293)(204 294)(205 295)(206 296)(207 297)(208 298)(209 299)(210 300)(211 301)(212 302)(213 303)(214 304)(215 305)(216 306)(217 307)(218 308)(219 265)(220 266)
(1 159)(2 160)(3 161)(4 162)(5 163)(6 164)(7 165)(8 166)(9 167)(10 168)(11 169)(12 170)(13 171)(14 172)(15 173)(16 174)(17 175)(18 176)(19 133)(20 134)(21 135)(22 136)(23 137)(24 138)(25 139)(26 140)(27 141)(28 142)(29 143)(30 144)(31 145)(32 146)(33 147)(34 148)(35 149)(36 150)(37 151)(38 152)(39 153)(40 154)(41 155)(42 156)(43 157)(44 158)(45 241)(46 242)(47 243)(48 244)(49 245)(50 246)(51 247)(52 248)(53 249)(54 250)(55 251)(56 252)(57 253)(58 254)(59 255)(60 256)(61 257)(62 258)(63 259)(64 260)(65 261)(66 262)(67 263)(68 264)(69 221)(70 222)(71 223)(72 224)(73 225)(74 226)(75 227)(76 228)(77 229)(78 230)(79 231)(80 232)(81 233)(82 234)(83 235)(84 236)(85 237)(86 238)(87 239)(88 240)(89 278)(90 279)(91 280)(92 281)(93 282)(94 283)(95 284)(96 285)(97 286)(98 287)(99 288)(100 289)(101 290)(102 291)(103 292)(104 293)(105 294)(106 295)(107 296)(108 297)(109 298)(110 299)(111 300)(112 301)(113 302)(114 303)(115 304)(116 305)(117 306)(118 307)(119 308)(120 265)(121 266)(122 267)(123 268)(124 269)(125 270)(126 271)(127 272)(128 273)(129 274)(130 275)(131 276)(132 277)(177 332)(178 333)(179 334)(180 335)(181 336)(182 337)(183 338)(184 339)(185 340)(186 341)(187 342)(188 343)(189 344)(190 345)(191 346)(192 347)(193 348)(194 349)(195 350)(196 351)(197 352)(198 309)(199 310)(200 311)(201 312)(202 313)(203 314)(204 315)(205 316)(206 317)(207 318)(208 319)(209 320)(210 321)(211 322)(212 323)(213 324)(214 325)(215 326)(216 327)(217 328)(218 329)(219 330)(220 331)
(1 179)(2 180)(3 181)(4 182)(5 183)(6 184)(7 185)(8 186)(9 187)(10 188)(11 189)(12 190)(13 191)(14 192)(15 193)(16 194)(17 195)(18 196)(19 197)(20 198)(21 199)(22 200)(23 201)(24 202)(25 203)(26 204)(27 205)(28 206)(29 207)(30 208)(31 209)(32 210)(33 211)(34 212)(35 213)(36 214)(37 215)(38 216)(39 217)(40 218)(41 219)(42 220)(43 177)(44 178)(45 123)(46 124)(47 125)(48 126)(49 127)(50 128)(51 129)(52 130)(53 131)(54 132)(55 89)(56 90)(57 91)(58 92)(59 93)(60 94)(61 95)(62 96)(63 97)(64 98)(65 99)(66 100)(67 101)(68 102)(69 103)(70 104)(71 105)(72 106)(73 107)(74 108)(75 109)(76 110)(77 111)(78 112)(79 113)(80 114)(81 115)(82 116)(83 117)(84 118)(85 119)(86 120)(87 121)(88 122)(133 352)(134 309)(135 310)(136 311)(137 312)(138 313)(139 314)(140 315)(141 316)(142 317)(143 318)(144 319)(145 320)(146 321)(147 322)(148 323)(149 324)(150 325)(151 326)(152 327)(153 328)(154 329)(155 330)(156 331)(157 332)(158 333)(159 334)(160 335)(161 336)(162 337)(163 338)(164 339)(165 340)(166 341)(167 342)(168 343)(169 344)(170 345)(171 346)(172 347)(173 348)(174 349)(175 350)(176 351)(221 292)(222 293)(223 294)(224 295)(225 296)(226 297)(227 298)(228 299)(229 300)(230 301)(231 302)(232 303)(233 304)(234 305)(235 306)(236 307)(237 308)(238 265)(239 266)(240 267)(241 268)(242 269)(243 270)(244 271)(245 272)(246 273)(247 274)(248 275)(249 276)(250 277)(251 278)(252 279)(253 280)(254 281)(255 282)(256 283)(257 284)(258 285)(259 286)(260 287)(261 288)(262 289)(263 290)(264 291)
(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)| (1,242)(2,243)(3,244)(4,245)(5,246)(6,247)(7,248)(8,249)(9,250)(10,251)(11,252)(12,253)(13,254)(14,255)(15,256)(16,257)(17,258)(18,259)(19,260)(20,261)(21,262)(22,263)(23,264)(24,221)(25,222)(26,223)(27,224)(28,225)(29,226)(30,227)(31,228)(32,229)(33,230)(34,231)(35,232)(36,233)(37,234)(38,235)(39,236)(40,237)(41,238)(42,239)(43,240)(44,241)(45,158)(46,159)(47,160)(48,161)(49,162)(50,163)(51,164)(52,165)(53,166)(54,167)(55,168)(56,169)(57,170)(58,171)(59,172)(60,173)(61,174)(62,175)(63,176)(64,133)(65,134)(66,135)(67,136)(68,137)(69,138)(70,139)(71,140)(72,141)(73,142)(74,143)(75,144)(76,145)(77,146)(78,147)(79,148)(80,149)(81,150)(82,151)(83,152)(84,153)(85,154)(86,155)(87,156)(88,157)(89,343)(90,344)(91,345)(92,346)(93,347)(94,348)(95,349)(96,350)(97,351)(98,352)(99,309)(100,310)(101,311)(102,312)(103,313)(104,314)(105,315)(106,316)(107,317)(108,318)(109,319)(110,320)(111,321)(112,322)(113,323)(114,324)(115,325)(116,326)(117,327)(118,328)(119,329)(120,330)(121,331)(122,332)(123,333)(124,334)(125,335)(126,336)(127,337)(128,338)(129,339)(130,340)(131,341)(132,342)(177,267)(178,268)(179,269)(180,270)(181,271)(182,272)(183,273)(184,274)(185,275)(186,276)(187,277)(188,278)(189,279)(190,280)(191,281)(192,282)(193,283)(194,284)(195,285)(196,286)(197,287)(198,288)(199,289)(200,290)(201,291)(202,292)(203,293)(204,294)(205,295)(206,296)(207,297)(208,298)(209,299)(210,300)(211,301)(212,302)(213,303)(214,304)(215,305)(216,306)(217,307)(218,308)(219,265)(220,266), (1,159)(2,160)(3,161)(4,162)(5,163)(6,164)(7,165)(8,166)(9,167)(10,168)(11,169)(12,170)(13,171)(14,172)(15,173)(16,174)(17,175)(18,176)(19,133)(20,134)(21,135)(22,136)(23,137)(24,138)(25,139)(26,140)(27,141)(28,142)(29,143)(30,144)(31,145)(32,146)(33,147)(34,148)(35,149)(36,150)(37,151)(38,152)(39,153)(40,154)(41,155)(42,156)(43,157)(44,158)(45,241)(46,242)(47,243)(48,244)(49,245)(50,246)(51,247)(52,248)(53,249)(54,250)(55,251)(56,252)(57,253)(58,254)(59,255)(60,256)(61,257)(62,258)(63,259)(64,260)(65,261)(66,262)(67,263)(68,264)(69,221)(70,222)(71,223)(72,224)(73,225)(74,226)(75,227)(76,228)(77,229)(78,230)(79,231)(80,232)(81,233)(82,234)(83,235)(84,236)(85,237)(86,238)(87,239)(88,240)(89,278)(90,279)(91,280)(92,281)(93,282)(94,283)(95,284)(96,285)(97,286)(98,287)(99,288)(100,289)(101,290)(102,291)(103,292)(104,293)(105,294)(106,295)(107,296)(108,297)(109,298)(110,299)(111,300)(112,301)(113,302)(114,303)(115,304)(116,305)(117,306)(118,307)(119,308)(120,265)(121,266)(122,267)(123,268)(124,269)(125,270)(126,271)(127,272)(128,273)(129,274)(130,275)(131,276)(132,277)(177,332)(178,333)(179,334)(180,335)(181,336)(182,337)(183,338)(184,339)(185,340)(186,341)(187,342)(188,343)(189,344)(190,345)(191,346)(192,347)(193,348)(194,349)(195,350)(196,351)(197,352)(198,309)(199,310)(200,311)(201,312)(202,313)(203,314)(204,315)(205,316)(206,317)(207,318)(208,319)(209,320)(210,321)(211,322)(212,323)(213,324)(214,325)(215,326)(216,327)(217,328)(218,329)(219,330)(220,331), (1,179)(2,180)(3,181)(4,182)(5,183)(6,184)(7,185)(8,186)(9,187)(10,188)(11,189)(12,190)(13,191)(14,192)(15,193)(16,194)(17,195)(18,196)(19,197)(20,198)(21,199)(22,200)(23,201)(24,202)(25,203)(26,204)(27,205)(28,206)(29,207)(30,208)(31,209)(32,210)(33,211)(34,212)(35,213)(36,214)(37,215)(38,216)(39,217)(40,218)(41,219)(42,220)(43,177)(44,178)(45,123)(46,124)(47,125)(48,126)(49,127)(50,128)(51,129)(52,130)(53,131)(54,132)(55,89)(56,90)(57,91)(58,92)(59,93)(60,94)(61,95)(62,96)(63,97)(64,98)(65,99)(66,100)(67,101)(68,102)(69,103)(70,104)(71,105)(72,106)(73,107)(74,108)(75,109)(76,110)(77,111)(78,112)(79,113)(80,114)(81,115)(82,116)(83,117)(84,118)(85,119)(86,120)(87,121)(88,122)(133,352)(134,309)(135,310)(136,311)(137,312)(138,313)(139,314)(140,315)(141,316)(142,317)(143,318)(144,319)(145,320)(146,321)(147,322)(148,323)(149,324)(150,325)(151,326)(152,327)(153,328)(154,329)(155,330)(156,331)(157,332)(158,333)(159,334)(160,335)(161,336)(162,337)(163,338)(164,339)(165,340)(166,341)(167,342)(168,343)(169,344)(170,345)(171,346)(172,347)(173,348)(174,349)(175,350)(176,351)(221,292)(222,293)(223,294)(224,295)(225,296)(226,297)(227,298)(228,299)(229,300)(230,301)(231,302)(232,303)(233,304)(234,305)(235,306)(236,307)(237,308)(238,265)(239,266)(240,267)(241,268)(242,269)(243,270)(244,271)(245,272)(246,273)(247,274)(248,275)(249,276)(250,277)(251,278)(252,279)(253,280)(254,281)(255,282)(256,283)(257,284)(258,285)(259,286)(260,287)(261,288)(262,289)(263,290)(264,291), (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( (1,242)(2,243)(3,244)(4,245)(5,246)(6,247)(7,248)(8,249)(9,250)(10,251)(11,252)(12,253)(13,254)(14,255)(15,256)(16,257)(17,258)(18,259)(19,260)(20,261)(21,262)(22,263)(23,264)(24,221)(25,222)(26,223)(27,224)(28,225)(29,226)(30,227)(31,228)(32,229)(33,230)(34,231)(35,232)(36,233)(37,234)(38,235)(39,236)(40,237)(41,238)(42,239)(43,240)(44,241)(45,158)(46,159)(47,160)(48,161)(49,162)(50,163)(51,164)(52,165)(53,166)(54,167)(55,168)(56,169)(57,170)(58,171)(59,172)(60,173)(61,174)(62,175)(63,176)(64,133)(65,134)(66,135)(67,136)(68,137)(69,138)(70,139)(71,140)(72,141)(73,142)(74,143)(75,144)(76,145)(77,146)(78,147)(79,148)(80,149)(81,150)(82,151)(83,152)(84,153)(85,154)(86,155)(87,156)(88,157)(89,343)(90,344)(91,345)(92,346)(93,347)(94,348)(95,349)(96,350)(97,351)(98,352)(99,309)(100,310)(101,311)(102,312)(103,313)(104,314)(105,315)(106,316)(107,317)(108,318)(109,319)(110,320)(111,321)(112,322)(113,323)(114,324)(115,325)(116,326)(117,327)(118,328)(119,329)(120,330)(121,331)(122,332)(123,333)(124,334)(125,335)(126,336)(127,337)(128,338)(129,339)(130,340)(131,341)(132,342)(177,267)(178,268)(179,269)(180,270)(181,271)(182,272)(183,273)(184,274)(185,275)(186,276)(187,277)(188,278)(189,279)(190,280)(191,281)(192,282)(193,283)(194,284)(195,285)(196,286)(197,287)(198,288)(199,289)(200,290)(201,291)(202,292)(203,293)(204,294)(205,295)(206,296)(207,297)(208,298)(209,299)(210,300)(211,301)(212,302)(213,303)(214,304)(215,305)(216,306)(217,307)(218,308)(219,265)(220,266), (1,159)(2,160)(3,161)(4,162)(5,163)(6,164)(7,165)(8,166)(9,167)(10,168)(11,169)(12,170)(13,171)(14,172)(15,173)(16,174)(17,175)(18,176)(19,133)(20,134)(21,135)(22,136)(23,137)(24,138)(25,139)(26,140)(27,141)(28,142)(29,143)(30,144)(31,145)(32,146)(33,147)(34,148)(35,149)(36,150)(37,151)(38,152)(39,153)(40,154)(41,155)(42,156)(43,157)(44,158)(45,241)(46,242)(47,243)(48,244)(49,245)(50,246)(51,247)(52,248)(53,249)(54,250)(55,251)(56,252)(57,253)(58,254)(59,255)(60,256)(61,257)(62,258)(63,259)(64,260)(65,261)(66,262)(67,263)(68,264)(69,221)(70,222)(71,223)(72,224)(73,225)(74,226)(75,227)(76,228)(77,229)(78,230)(79,231)(80,232)(81,233)(82,234)(83,235)(84,236)(85,237)(86,238)(87,239)(88,240)(89,278)(90,279)(91,280)(92,281)(93,282)(94,283)(95,284)(96,285)(97,286)(98,287)(99,288)(100,289)(101,290)(102,291)(103,292)(104,293)(105,294)(106,295)(107,296)(108,297)(109,298)(110,299)(111,300)(112,301)(113,302)(114,303)(115,304)(116,305)(117,306)(118,307)(119,308)(120,265)(121,266)(122,267)(123,268)(124,269)(125,270)(126,271)(127,272)(128,273)(129,274)(130,275)(131,276)(132,277)(177,332)(178,333)(179,334)(180,335)(181,336)(182,337)(183,338)(184,339)(185,340)(186,341)(187,342)(188,343)(189,344)(190,345)(191,346)(192,347)(193,348)(194,349)(195,350)(196,351)(197,352)(198,309)(199,310)(200,311)(201,312)(202,313)(203,314)(204,315)(205,316)(206,317)(207,318)(208,319)(209,320)(210,321)(211,322)(212,323)(213,324)(214,325)(215,326)(216,327)(217,328)(218,329)(219,330)(220,331), (1,179)(2,180)(3,181)(4,182)(5,183)(6,184)(7,185)(8,186)(9,187)(10,188)(11,189)(12,190)(13,191)(14,192)(15,193)(16,194)(17,195)(18,196)(19,197)(20,198)(21,199)(22,200)(23,201)(24,202)(25,203)(26,204)(27,205)(28,206)(29,207)(30,208)(31,209)(32,210)(33,211)(34,212)(35,213)(36,214)(37,215)(38,216)(39,217)(40,218)(41,219)(42,220)(43,177)(44,178)(45,123)(46,124)(47,125)(48,126)(49,127)(50,128)(51,129)(52,130)(53,131)(54,132)(55,89)(56,90)(57,91)(58,92)(59,93)(60,94)(61,95)(62,96)(63,97)(64,98)(65,99)(66,100)(67,101)(68,102)(69,103)(70,104)(71,105)(72,106)(73,107)(74,108)(75,109)(76,110)(77,111)(78,112)(79,113)(80,114)(81,115)(82,116)(83,117)(84,118)(85,119)(86,120)(87,121)(88,122)(133,352)(134,309)(135,310)(136,311)(137,312)(138,313)(139,314)(140,315)(141,316)(142,317)(143,318)(144,319)(145,320)(146,321)(147,322)(148,323)(149,324)(150,325)(151,326)(152,327)(153,328)(154,329)(155,330)(156,331)(157,332)(158,333)(159,334)(160,335)(161,336)(162,337)(163,338)(164,339)(165,340)(166,341)(167,342)(168,343)(169,344)(170,345)(171,346)(172,347)(173,348)(174,349)(175,350)(176,351)(221,292)(222,293)(223,294)(224,295)(225,296)(226,297)(227,298)(228,299)(229,300)(230,301)(231,302)(232,303)(233,304)(234,305)(235,306)(236,307)(237,308)(238,265)(239,266)(240,267)(241,268)(242,269)(243,270)(244,271)(245,272)(246,273)(247,274)(248,275)(249,276)(250,277)(251,278)(252,279)(253,280)(254,281)(255,282)(256,283)(257,284)(258,285)(259,286)(260,287)(261,288)(262,289)(263,290)(264,291), (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([(1,242),(2,243),(3,244),(4,245),(5,246),(6,247),(7,248),(8,249),(9,250),(10,251),(11,252),(12,253),(13,254),(14,255),(15,256),(16,257),(17,258),(18,259),(19,260),(20,261),(21,262),(22,263),(23,264),(24,221),(25,222),(26,223),(27,224),(28,225),(29,226),(30,227),(31,228),(32,229),(33,230),(34,231),(35,232),(36,233),(37,234),(38,235),(39,236),(40,237),(41,238),(42,239),(43,240),(44,241),(45,158),(46,159),(47,160),(48,161),(49,162),(50,163),(51,164),(52,165),(53,166),(54,167),(55,168),(56,169),(57,170),(58,171),(59,172),(60,173),(61,174),(62,175),(63,176),(64,133),(65,134),(66,135),(67,136),(68,137),(69,138),(70,139),(71,140),(72,141),(73,142),(74,143),(75,144),(76,145),(77,146),(78,147),(79,148),(80,149),(81,150),(82,151),(83,152),(84,153),(85,154),(86,155),(87,156),(88,157),(89,343),(90,344),(91,345),(92,346),(93,347),(94,348),(95,349),(96,350),(97,351),(98,352),(99,309),(100,310),(101,311),(102,312),(103,313),(104,314),(105,315),(106,316),(107,317),(108,318),(109,319),(110,320),(111,321),(112,322),(113,323),(114,324),(115,325),(116,326),(117,327),(118,328),(119,329),(120,330),(121,331),(122,332),(123,333),(124,334),(125,335),(126,336),(127,337),(128,338),(129,339),(130,340),(131,341),(132,342),(177,267),(178,268),(179,269),(180,270),(181,271),(182,272),(183,273),(184,274),(185,275),(186,276),(187,277),(188,278),(189,279),(190,280),(191,281),(192,282),(193,283),(194,284),(195,285),(196,286),(197,287),(198,288),(199,289),(200,290),(201,291),(202,292),(203,293),(204,294),(205,295),(206,296),(207,297),(208,298),(209,299),(210,300),(211,301),(212,302),(213,303),(214,304),(215,305),(216,306),(217,307),(218,308),(219,265),(220,266)], [(1,159),(2,160),(3,161),(4,162),(5,163),(6,164),(7,165),(8,166),(9,167),(10,168),(11,169),(12,170),(13,171),(14,172),(15,173),(16,174),(17,175),(18,176),(19,133),(20,134),(21,135),(22,136),(23,137),(24,138),(25,139),(26,140),(27,141),(28,142),(29,143),(30,144),(31,145),(32,146),(33,147),(34,148),(35,149),(36,150),(37,151),(38,152),(39,153),(40,154),(41,155),(42,156),(43,157),(44,158),(45,241),(46,242),(47,243),(48,244),(49,245),(50,246),(51,247),(52,248),(53,249),(54,250),(55,251),(56,252),(57,253),(58,254),(59,255),(60,256),(61,257),(62,258),(63,259),(64,260),(65,261),(66,262),(67,263),(68,264),(69,221),(70,222),(71,223),(72,224),(73,225),(74,226),(75,227),(76,228),(77,229),(78,230),(79,231),(80,232),(81,233),(82,234),(83,235),(84,236),(85,237),(86,238),(87,239),(88,240),(89,278),(90,279),(91,280),(92,281),(93,282),(94,283),(95,284),(96,285),(97,286),(98,287),(99,288),(100,289),(101,290),(102,291),(103,292),(104,293),(105,294),(106,295),(107,296),(108,297),(109,298),(110,299),(111,300),(112,301),(113,302),(114,303),(115,304),(116,305),(117,306),(118,307),(119,308),(120,265),(121,266),(122,267),(123,268),(124,269),(125,270),(126,271),(127,272),(128,273),(129,274),(130,275),(131,276),(132,277),(177,332),(178,333),(179,334),(180,335),(181,336),(182,337),(183,338),(184,339),(185,340),(186,341),(187,342),(188,343),(189,344),(190,345),(191,346),(192,347),(193,348),(194,349),(195,350),(196,351),(197,352),(198,309),(199,310),(200,311),(201,312),(202,313),(203,314),(204,315),(205,316),(206,317),(207,318),(208,319),(209,320),(210,321),(211,322),(212,323),(213,324),(214,325),(215,326),(216,327),(217,328),(218,329),(219,330),(220,331)], [(1,179),(2,180),(3,181),(4,182),(5,183),(6,184),(7,185),(8,186),(9,187),(10,188),(11,189),(12,190),(13,191),(14,192),(15,193),(16,194),(17,195),(18,196),(19,197),(20,198),(21,199),(22,200),(23,201),(24,202),(25,203),(26,204),(27,205),(28,206),(29,207),(30,208),(31,209),(32,210),(33,211),(34,212),(35,213),(36,214),(37,215),(38,216),(39,217),(40,218),(41,219),(42,220),(43,177),(44,178),(45,123),(46,124),(47,125),(48,126),(49,127),(50,128),(51,129),(52,130),(53,131),(54,132),(55,89),(56,90),(57,91),(58,92),(59,93),(60,94),(61,95),(62,96),(63,97),(64,98),(65,99),(66,100),(67,101),(68,102),(69,103),(70,104),(71,105),(72,106),(73,107),(74,108),(75,109),(76,110),(77,111),(78,112),(79,113),(80,114),(81,115),(82,116),(83,117),(84,118),(85,119),(86,120),(87,121),(88,122),(133,352),(134,309),(135,310),(136,311),(137,312),(138,313),(139,314),(140,315),(141,316),(142,317),(143,318),(144,319),(145,320),(146,321),(147,322),(148,323),(149,324),(150,325),(151,326),(152,327),(153,328),(154,329),(155,330),(156,331),(157,332),(158,333),(159,334),(160,335),(161,336),(162,337),(163,338),(164,339),(165,340),(166,341),(167,342),(168,343),(169,344),(170,345),(171,346),(172,347),(173,348),(174,349),(175,350),(176,351),(221,292),(222,293),(223,294),(224,295),(225,296),(226,297),(227,298),(228,299),(229,300),(230,301),(231,302),(232,303),(233,304),(234,305),(235,306),(236,307),(237,308),(238,265),(239,266),(240,267),(241,268),(242,269),(243,270),(244,271),(245,272),(246,273),(247,274),(248,275),(249,276),(250,277),(251,278),(252,279),(253,280),(254,281),(255,282),(256,283),(257,284),(258,285),(259,286),(260,287),(261,288),(262,289),(263,290),(264,291)], [(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···2O4A···4P11A···11J22A···22ET44A···44FD
order12···24···411···1122···2244···44
size11···11···11···11···11···1

352 irreducible representations

dim11111111
type+++
imageC1C2C2C4C11C22C22C44
kernelC23×C44C22×C44C23×C22C22×C22C23×C4C22×C4C24C23
# reps1141161014010160

Matrix representation of C23×C44 in GL4(𝔽89) generated by

88000
08800
00880
00088
,
1000
08800
00880
0001
,
1000
08800
0010
00088
,
81000
0100
00500
00010
G:=sub<GL(4,GF(89))| [88,0,0,0,0,88,0,0,0,0,88,0,0,0,0,88],[1,0,0,0,0,88,0,0,0,0,88,0,0,0,0,1],[1,0,0,0,0,88,0,0,0,0,1,0,0,0,0,88],[81,0,0,0,0,1,0,0,0,0,50,0,0,0,0,10] >;

C23×C44 in GAP, Magma, Sage, TeX

C_2^3\times C_{44}
% in TeX

G:=Group("C2^3xC44");
// GroupNames label

G:=SmallGroup(352,188);
// by ID

G=gap.SmallGroup(352,188);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-11,-2,1056]);
// Polycyclic

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

׿
×
𝔽