Copied to
clipboard

G = C23×C46order 368 = 24·23

Abelian group of type [2,2,2,46]

direct product, abelian, monomial, 2-elementary

Aliases: C23×C46, SmallGroup(368,42)

Series: Derived Chief Lower central Upper central

C1 — C23×C46
C1C23C46C2×C46C22×C46 — C23×C46
C1 — C23×C46
C1 — C23×C46

Generators and relations for C23×C46
 G = < a,b,c,d | a2=b2=c2=d46=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, cd=dc >

Subgroups: 134, all normal (4 characteristic)
C1, C2 [×15], C22 [×35], C23 [×15], C24, C23, C46 [×15], C2×C46 [×35], C22×C46 [×15], C23×C46
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], C24, C23, C46 [×15], C2×C46 [×35], C22×C46 [×15], C23×C46

Smallest permutation representation of C23×C46
Regular action on 368 points
Generators in S368
(1 227)(2 228)(3 229)(4 230)(5 185)(6 186)(7 187)(8 188)(9 189)(10 190)(11 191)(12 192)(13 193)(14 194)(15 195)(16 196)(17 197)(18 198)(19 199)(20 200)(21 201)(22 202)(23 203)(24 204)(25 205)(26 206)(27 207)(28 208)(29 209)(30 210)(31 211)(32 212)(33 213)(34 214)(35 215)(36 216)(37 217)(38 218)(39 219)(40 220)(41 221)(42 222)(43 223)(44 224)(45 225)(46 226)(47 253)(48 254)(49 255)(50 256)(51 257)(52 258)(53 259)(54 260)(55 261)(56 262)(57 263)(58 264)(59 265)(60 266)(61 267)(62 268)(63 269)(64 270)(65 271)(66 272)(67 273)(68 274)(69 275)(70 276)(71 231)(72 232)(73 233)(74 234)(75 235)(76 236)(77 237)(78 238)(79 239)(80 240)(81 241)(82 242)(83 243)(84 244)(85 245)(86 246)(87 247)(88 248)(89 249)(90 250)(91 251)(92 252)(93 319)(94 320)(95 321)(96 322)(97 277)(98 278)(99 279)(100 280)(101 281)(102 282)(103 283)(104 284)(105 285)(106 286)(107 287)(108 288)(109 289)(110 290)(111 291)(112 292)(113 293)(114 294)(115 295)(116 296)(117 297)(118 298)(119 299)(120 300)(121 301)(122 302)(123 303)(124 304)(125 305)(126 306)(127 307)(128 308)(129 309)(130 310)(131 311)(132 312)(133 313)(134 314)(135 315)(136 316)(137 317)(138 318)(139 328)(140 329)(141 330)(142 331)(143 332)(144 333)(145 334)(146 335)(147 336)(148 337)(149 338)(150 339)(151 340)(152 341)(153 342)(154 343)(155 344)(156 345)(157 346)(158 347)(159 348)(160 349)(161 350)(162 351)(163 352)(164 353)(165 354)(166 355)(167 356)(168 357)(169 358)(170 359)(171 360)(172 361)(173 362)(174 363)(175 364)(176 365)(177 366)(178 367)(179 368)(180 323)(181 324)(182 325)(183 326)(184 327)
(1 136)(2 137)(3 138)(4 93)(5 94)(6 95)(7 96)(8 97)(9 98)(10 99)(11 100)(12 101)(13 102)(14 103)(15 104)(16 105)(17 106)(18 107)(19 108)(20 109)(21 110)(22 111)(23 112)(24 113)(25 114)(26 115)(27 116)(28 117)(29 118)(30 119)(31 120)(32 121)(33 122)(34 123)(35 124)(36 125)(37 126)(38 127)(39 128)(40 129)(41 130)(42 131)(43 132)(44 133)(45 134)(46 135)(47 156)(48 157)(49 158)(50 159)(51 160)(52 161)(53 162)(54 163)(55 164)(56 165)(57 166)(58 167)(59 168)(60 169)(61 170)(62 171)(63 172)(64 173)(65 174)(66 175)(67 176)(68 177)(69 178)(70 179)(71 180)(72 181)(73 182)(74 183)(75 184)(76 139)(77 140)(78 141)(79 142)(80 143)(81 144)(82 145)(83 146)(84 147)(85 148)(86 149)(87 150)(88 151)(89 152)(90 153)(91 154)(92 155)(185 320)(186 321)(187 322)(188 277)(189 278)(190 279)(191 280)(192 281)(193 282)(194 283)(195 284)(196 285)(197 286)(198 287)(199 288)(200 289)(201 290)(202 291)(203 292)(204 293)(205 294)(206 295)(207 296)(208 297)(209 298)(210 299)(211 300)(212 301)(213 302)(214 303)(215 304)(216 305)(217 306)(218 307)(219 308)(220 309)(221 310)(222 311)(223 312)(224 313)(225 314)(226 315)(227 316)(228 317)(229 318)(230 319)(231 323)(232 324)(233 325)(234 326)(235 327)(236 328)(237 329)(238 330)(239 331)(240 332)(241 333)(242 334)(243 335)(244 336)(245 337)(246 338)(247 339)(248 340)(249 341)(250 342)(251 343)(252 344)(253 345)(254 346)(255 347)(256 348)(257 349)(258 350)(259 351)(260 352)(261 353)(262 354)(263 355)(264 356)(265 357)(266 358)(267 359)(268 360)(269 361)(270 362)(271 363)(272 364)(273 365)(274 366)(275 367)(276 368)
(1 71)(2 72)(3 73)(4 74)(5 75)(6 76)(7 77)(8 78)(9 79)(10 80)(11 81)(12 82)(13 83)(14 84)(15 85)(16 86)(17 87)(18 88)(19 89)(20 90)(21 91)(22 92)(23 47)(24 48)(25 49)(26 50)(27 51)(28 52)(29 53)(30 54)(31 55)(32 56)(33 57)(34 58)(35 59)(36 60)(37 61)(38 62)(39 63)(40 64)(41 65)(42 66)(43 67)(44 68)(45 69)(46 70)(93 183)(94 184)(95 139)(96 140)(97 141)(98 142)(99 143)(100 144)(101 145)(102 146)(103 147)(104 148)(105 149)(106 150)(107 151)(108 152)(109 153)(110 154)(111 155)(112 156)(113 157)(114 158)(115 159)(116 160)(117 161)(118 162)(119 163)(120 164)(121 165)(122 166)(123 167)(124 168)(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)(185 235)(186 236)(187 237)(188 238)(189 239)(190 240)(191 241)(192 242)(193 243)(194 244)(195 245)(196 246)(197 247)(198 248)(199 249)(200 250)(201 251)(202 252)(203 253)(204 254)(205 255)(206 256)(207 257)(208 258)(209 259)(210 260)(211 261)(212 262)(213 263)(214 264)(215 265)(216 266)(217 267)(218 268)(219 269)(220 270)(221 271)(222 272)(223 273)(224 274)(225 275)(226 276)(227 231)(228 232)(229 233)(230 234)(277 330)(278 331)(279 332)(280 333)(281 334)(282 335)(283 336)(284 337)(285 338)(286 339)(287 340)(288 341)(289 342)(290 343)(291 344)(292 345)(293 346)(294 347)(295 348)(296 349)(297 350)(298 351)(299 352)(300 353)(301 354)(302 355)(303 356)(304 357)(305 358)(306 359)(307 360)(308 361)(309 362)(310 363)(311 364)(312 365)(313 366)(314 367)(315 368)(316 323)(317 324)(318 325)(319 326)(320 327)(321 328)(322 329)
(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)(323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368)

G:=sub<Sym(368)| (1,227)(2,228)(3,229)(4,230)(5,185)(6,186)(7,187)(8,188)(9,189)(10,190)(11,191)(12,192)(13,193)(14,194)(15,195)(16,196)(17,197)(18,198)(19,199)(20,200)(21,201)(22,202)(23,203)(24,204)(25,205)(26,206)(27,207)(28,208)(29,209)(30,210)(31,211)(32,212)(33,213)(34,214)(35,215)(36,216)(37,217)(38,218)(39,219)(40,220)(41,221)(42,222)(43,223)(44,224)(45,225)(46,226)(47,253)(48,254)(49,255)(50,256)(51,257)(52,258)(53,259)(54,260)(55,261)(56,262)(57,263)(58,264)(59,265)(60,266)(61,267)(62,268)(63,269)(64,270)(65,271)(66,272)(67,273)(68,274)(69,275)(70,276)(71,231)(72,232)(73,233)(74,234)(75,235)(76,236)(77,237)(78,238)(79,239)(80,240)(81,241)(82,242)(83,243)(84,244)(85,245)(86,246)(87,247)(88,248)(89,249)(90,250)(91,251)(92,252)(93,319)(94,320)(95,321)(96,322)(97,277)(98,278)(99,279)(100,280)(101,281)(102,282)(103,283)(104,284)(105,285)(106,286)(107,287)(108,288)(109,289)(110,290)(111,291)(112,292)(113,293)(114,294)(115,295)(116,296)(117,297)(118,298)(119,299)(120,300)(121,301)(122,302)(123,303)(124,304)(125,305)(126,306)(127,307)(128,308)(129,309)(130,310)(131,311)(132,312)(133,313)(134,314)(135,315)(136,316)(137,317)(138,318)(139,328)(140,329)(141,330)(142,331)(143,332)(144,333)(145,334)(146,335)(147,336)(148,337)(149,338)(150,339)(151,340)(152,341)(153,342)(154,343)(155,344)(156,345)(157,346)(158,347)(159,348)(160,349)(161,350)(162,351)(163,352)(164,353)(165,354)(166,355)(167,356)(168,357)(169,358)(170,359)(171,360)(172,361)(173,362)(174,363)(175,364)(176,365)(177,366)(178,367)(179,368)(180,323)(181,324)(182,325)(183,326)(184,327), (1,136)(2,137)(3,138)(4,93)(5,94)(6,95)(7,96)(8,97)(9,98)(10,99)(11,100)(12,101)(13,102)(14,103)(15,104)(16,105)(17,106)(18,107)(19,108)(20,109)(21,110)(22,111)(23,112)(24,113)(25,114)(26,115)(27,116)(28,117)(29,118)(30,119)(31,120)(32,121)(33,122)(34,123)(35,124)(36,125)(37,126)(38,127)(39,128)(40,129)(41,130)(42,131)(43,132)(44,133)(45,134)(46,135)(47,156)(48,157)(49,158)(50,159)(51,160)(52,161)(53,162)(54,163)(55,164)(56,165)(57,166)(58,167)(59,168)(60,169)(61,170)(62,171)(63,172)(64,173)(65,174)(66,175)(67,176)(68,177)(69,178)(70,179)(71,180)(72,181)(73,182)(74,183)(75,184)(76,139)(77,140)(78,141)(79,142)(80,143)(81,144)(82,145)(83,146)(84,147)(85,148)(86,149)(87,150)(88,151)(89,152)(90,153)(91,154)(92,155)(185,320)(186,321)(187,322)(188,277)(189,278)(190,279)(191,280)(192,281)(193,282)(194,283)(195,284)(196,285)(197,286)(198,287)(199,288)(200,289)(201,290)(202,291)(203,292)(204,293)(205,294)(206,295)(207,296)(208,297)(209,298)(210,299)(211,300)(212,301)(213,302)(214,303)(215,304)(216,305)(217,306)(218,307)(219,308)(220,309)(221,310)(222,311)(223,312)(224,313)(225,314)(226,315)(227,316)(228,317)(229,318)(230,319)(231,323)(232,324)(233,325)(234,326)(235,327)(236,328)(237,329)(238,330)(239,331)(240,332)(241,333)(242,334)(243,335)(244,336)(245,337)(246,338)(247,339)(248,340)(249,341)(250,342)(251,343)(252,344)(253,345)(254,346)(255,347)(256,348)(257,349)(258,350)(259,351)(260,352)(261,353)(262,354)(263,355)(264,356)(265,357)(266,358)(267,359)(268,360)(269,361)(270,362)(271,363)(272,364)(273,365)(274,366)(275,367)(276,368), (1,71)(2,72)(3,73)(4,74)(5,75)(6,76)(7,77)(8,78)(9,79)(10,80)(11,81)(12,82)(13,83)(14,84)(15,85)(16,86)(17,87)(18,88)(19,89)(20,90)(21,91)(22,92)(23,47)(24,48)(25,49)(26,50)(27,51)(28,52)(29,53)(30,54)(31,55)(32,56)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,65)(42,66)(43,67)(44,68)(45,69)(46,70)(93,183)(94,184)(95,139)(96,140)(97,141)(98,142)(99,143)(100,144)(101,145)(102,146)(103,147)(104,148)(105,149)(106,150)(107,151)(108,152)(109,153)(110,154)(111,155)(112,156)(113,157)(114,158)(115,159)(116,160)(117,161)(118,162)(119,163)(120,164)(121,165)(122,166)(123,167)(124,168)(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)(185,235)(186,236)(187,237)(188,238)(189,239)(190,240)(191,241)(192,242)(193,243)(194,244)(195,245)(196,246)(197,247)(198,248)(199,249)(200,250)(201,251)(202,252)(203,253)(204,254)(205,255)(206,256)(207,257)(208,258)(209,259)(210,260)(211,261)(212,262)(213,263)(214,264)(215,265)(216,266)(217,267)(218,268)(219,269)(220,270)(221,271)(222,272)(223,273)(224,274)(225,275)(226,276)(227,231)(228,232)(229,233)(230,234)(277,330)(278,331)(279,332)(280,333)(281,334)(282,335)(283,336)(284,337)(285,338)(286,339)(287,340)(288,341)(289,342)(290,343)(291,344)(292,345)(293,346)(294,347)(295,348)(296,349)(297,350)(298,351)(299,352)(300,353)(301,354)(302,355)(303,356)(304,357)(305,358)(306,359)(307,360)(308,361)(309,362)(310,363)(311,364)(312,365)(313,366)(314,367)(315,368)(316,323)(317,324)(318,325)(319,326)(320,327)(321,328)(322,329), (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)(323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368)>;

G:=Group( (1,227)(2,228)(3,229)(4,230)(5,185)(6,186)(7,187)(8,188)(9,189)(10,190)(11,191)(12,192)(13,193)(14,194)(15,195)(16,196)(17,197)(18,198)(19,199)(20,200)(21,201)(22,202)(23,203)(24,204)(25,205)(26,206)(27,207)(28,208)(29,209)(30,210)(31,211)(32,212)(33,213)(34,214)(35,215)(36,216)(37,217)(38,218)(39,219)(40,220)(41,221)(42,222)(43,223)(44,224)(45,225)(46,226)(47,253)(48,254)(49,255)(50,256)(51,257)(52,258)(53,259)(54,260)(55,261)(56,262)(57,263)(58,264)(59,265)(60,266)(61,267)(62,268)(63,269)(64,270)(65,271)(66,272)(67,273)(68,274)(69,275)(70,276)(71,231)(72,232)(73,233)(74,234)(75,235)(76,236)(77,237)(78,238)(79,239)(80,240)(81,241)(82,242)(83,243)(84,244)(85,245)(86,246)(87,247)(88,248)(89,249)(90,250)(91,251)(92,252)(93,319)(94,320)(95,321)(96,322)(97,277)(98,278)(99,279)(100,280)(101,281)(102,282)(103,283)(104,284)(105,285)(106,286)(107,287)(108,288)(109,289)(110,290)(111,291)(112,292)(113,293)(114,294)(115,295)(116,296)(117,297)(118,298)(119,299)(120,300)(121,301)(122,302)(123,303)(124,304)(125,305)(126,306)(127,307)(128,308)(129,309)(130,310)(131,311)(132,312)(133,313)(134,314)(135,315)(136,316)(137,317)(138,318)(139,328)(140,329)(141,330)(142,331)(143,332)(144,333)(145,334)(146,335)(147,336)(148,337)(149,338)(150,339)(151,340)(152,341)(153,342)(154,343)(155,344)(156,345)(157,346)(158,347)(159,348)(160,349)(161,350)(162,351)(163,352)(164,353)(165,354)(166,355)(167,356)(168,357)(169,358)(170,359)(171,360)(172,361)(173,362)(174,363)(175,364)(176,365)(177,366)(178,367)(179,368)(180,323)(181,324)(182,325)(183,326)(184,327), (1,136)(2,137)(3,138)(4,93)(5,94)(6,95)(7,96)(8,97)(9,98)(10,99)(11,100)(12,101)(13,102)(14,103)(15,104)(16,105)(17,106)(18,107)(19,108)(20,109)(21,110)(22,111)(23,112)(24,113)(25,114)(26,115)(27,116)(28,117)(29,118)(30,119)(31,120)(32,121)(33,122)(34,123)(35,124)(36,125)(37,126)(38,127)(39,128)(40,129)(41,130)(42,131)(43,132)(44,133)(45,134)(46,135)(47,156)(48,157)(49,158)(50,159)(51,160)(52,161)(53,162)(54,163)(55,164)(56,165)(57,166)(58,167)(59,168)(60,169)(61,170)(62,171)(63,172)(64,173)(65,174)(66,175)(67,176)(68,177)(69,178)(70,179)(71,180)(72,181)(73,182)(74,183)(75,184)(76,139)(77,140)(78,141)(79,142)(80,143)(81,144)(82,145)(83,146)(84,147)(85,148)(86,149)(87,150)(88,151)(89,152)(90,153)(91,154)(92,155)(185,320)(186,321)(187,322)(188,277)(189,278)(190,279)(191,280)(192,281)(193,282)(194,283)(195,284)(196,285)(197,286)(198,287)(199,288)(200,289)(201,290)(202,291)(203,292)(204,293)(205,294)(206,295)(207,296)(208,297)(209,298)(210,299)(211,300)(212,301)(213,302)(214,303)(215,304)(216,305)(217,306)(218,307)(219,308)(220,309)(221,310)(222,311)(223,312)(224,313)(225,314)(226,315)(227,316)(228,317)(229,318)(230,319)(231,323)(232,324)(233,325)(234,326)(235,327)(236,328)(237,329)(238,330)(239,331)(240,332)(241,333)(242,334)(243,335)(244,336)(245,337)(246,338)(247,339)(248,340)(249,341)(250,342)(251,343)(252,344)(253,345)(254,346)(255,347)(256,348)(257,349)(258,350)(259,351)(260,352)(261,353)(262,354)(263,355)(264,356)(265,357)(266,358)(267,359)(268,360)(269,361)(270,362)(271,363)(272,364)(273,365)(274,366)(275,367)(276,368), (1,71)(2,72)(3,73)(4,74)(5,75)(6,76)(7,77)(8,78)(9,79)(10,80)(11,81)(12,82)(13,83)(14,84)(15,85)(16,86)(17,87)(18,88)(19,89)(20,90)(21,91)(22,92)(23,47)(24,48)(25,49)(26,50)(27,51)(28,52)(29,53)(30,54)(31,55)(32,56)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,65)(42,66)(43,67)(44,68)(45,69)(46,70)(93,183)(94,184)(95,139)(96,140)(97,141)(98,142)(99,143)(100,144)(101,145)(102,146)(103,147)(104,148)(105,149)(106,150)(107,151)(108,152)(109,153)(110,154)(111,155)(112,156)(113,157)(114,158)(115,159)(116,160)(117,161)(118,162)(119,163)(120,164)(121,165)(122,166)(123,167)(124,168)(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)(185,235)(186,236)(187,237)(188,238)(189,239)(190,240)(191,241)(192,242)(193,243)(194,244)(195,245)(196,246)(197,247)(198,248)(199,249)(200,250)(201,251)(202,252)(203,253)(204,254)(205,255)(206,256)(207,257)(208,258)(209,259)(210,260)(211,261)(212,262)(213,263)(214,264)(215,265)(216,266)(217,267)(218,268)(219,269)(220,270)(221,271)(222,272)(223,273)(224,274)(225,275)(226,276)(227,231)(228,232)(229,233)(230,234)(277,330)(278,331)(279,332)(280,333)(281,334)(282,335)(283,336)(284,337)(285,338)(286,339)(287,340)(288,341)(289,342)(290,343)(291,344)(292,345)(293,346)(294,347)(295,348)(296,349)(297,350)(298,351)(299,352)(300,353)(301,354)(302,355)(303,356)(304,357)(305,358)(306,359)(307,360)(308,361)(309,362)(310,363)(311,364)(312,365)(313,366)(314,367)(315,368)(316,323)(317,324)(318,325)(319,326)(320,327)(321,328)(322,329), (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)(323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368) );

G=PermutationGroup([(1,227),(2,228),(3,229),(4,230),(5,185),(6,186),(7,187),(8,188),(9,189),(10,190),(11,191),(12,192),(13,193),(14,194),(15,195),(16,196),(17,197),(18,198),(19,199),(20,200),(21,201),(22,202),(23,203),(24,204),(25,205),(26,206),(27,207),(28,208),(29,209),(30,210),(31,211),(32,212),(33,213),(34,214),(35,215),(36,216),(37,217),(38,218),(39,219),(40,220),(41,221),(42,222),(43,223),(44,224),(45,225),(46,226),(47,253),(48,254),(49,255),(50,256),(51,257),(52,258),(53,259),(54,260),(55,261),(56,262),(57,263),(58,264),(59,265),(60,266),(61,267),(62,268),(63,269),(64,270),(65,271),(66,272),(67,273),(68,274),(69,275),(70,276),(71,231),(72,232),(73,233),(74,234),(75,235),(76,236),(77,237),(78,238),(79,239),(80,240),(81,241),(82,242),(83,243),(84,244),(85,245),(86,246),(87,247),(88,248),(89,249),(90,250),(91,251),(92,252),(93,319),(94,320),(95,321),(96,322),(97,277),(98,278),(99,279),(100,280),(101,281),(102,282),(103,283),(104,284),(105,285),(106,286),(107,287),(108,288),(109,289),(110,290),(111,291),(112,292),(113,293),(114,294),(115,295),(116,296),(117,297),(118,298),(119,299),(120,300),(121,301),(122,302),(123,303),(124,304),(125,305),(126,306),(127,307),(128,308),(129,309),(130,310),(131,311),(132,312),(133,313),(134,314),(135,315),(136,316),(137,317),(138,318),(139,328),(140,329),(141,330),(142,331),(143,332),(144,333),(145,334),(146,335),(147,336),(148,337),(149,338),(150,339),(151,340),(152,341),(153,342),(154,343),(155,344),(156,345),(157,346),(158,347),(159,348),(160,349),(161,350),(162,351),(163,352),(164,353),(165,354),(166,355),(167,356),(168,357),(169,358),(170,359),(171,360),(172,361),(173,362),(174,363),(175,364),(176,365),(177,366),(178,367),(179,368),(180,323),(181,324),(182,325),(183,326),(184,327)], [(1,136),(2,137),(3,138),(4,93),(5,94),(6,95),(7,96),(8,97),(9,98),(10,99),(11,100),(12,101),(13,102),(14,103),(15,104),(16,105),(17,106),(18,107),(19,108),(20,109),(21,110),(22,111),(23,112),(24,113),(25,114),(26,115),(27,116),(28,117),(29,118),(30,119),(31,120),(32,121),(33,122),(34,123),(35,124),(36,125),(37,126),(38,127),(39,128),(40,129),(41,130),(42,131),(43,132),(44,133),(45,134),(46,135),(47,156),(48,157),(49,158),(50,159),(51,160),(52,161),(53,162),(54,163),(55,164),(56,165),(57,166),(58,167),(59,168),(60,169),(61,170),(62,171),(63,172),(64,173),(65,174),(66,175),(67,176),(68,177),(69,178),(70,179),(71,180),(72,181),(73,182),(74,183),(75,184),(76,139),(77,140),(78,141),(79,142),(80,143),(81,144),(82,145),(83,146),(84,147),(85,148),(86,149),(87,150),(88,151),(89,152),(90,153),(91,154),(92,155),(185,320),(186,321),(187,322),(188,277),(189,278),(190,279),(191,280),(192,281),(193,282),(194,283),(195,284),(196,285),(197,286),(198,287),(199,288),(200,289),(201,290),(202,291),(203,292),(204,293),(205,294),(206,295),(207,296),(208,297),(209,298),(210,299),(211,300),(212,301),(213,302),(214,303),(215,304),(216,305),(217,306),(218,307),(219,308),(220,309),(221,310),(222,311),(223,312),(224,313),(225,314),(226,315),(227,316),(228,317),(229,318),(230,319),(231,323),(232,324),(233,325),(234,326),(235,327),(236,328),(237,329),(238,330),(239,331),(240,332),(241,333),(242,334),(243,335),(244,336),(245,337),(246,338),(247,339),(248,340),(249,341),(250,342),(251,343),(252,344),(253,345),(254,346),(255,347),(256,348),(257,349),(258,350),(259,351),(260,352),(261,353),(262,354),(263,355),(264,356),(265,357),(266,358),(267,359),(268,360),(269,361),(270,362),(271,363),(272,364),(273,365),(274,366),(275,367),(276,368)], [(1,71),(2,72),(3,73),(4,74),(5,75),(6,76),(7,77),(8,78),(9,79),(10,80),(11,81),(12,82),(13,83),(14,84),(15,85),(16,86),(17,87),(18,88),(19,89),(20,90),(21,91),(22,92),(23,47),(24,48),(25,49),(26,50),(27,51),(28,52),(29,53),(30,54),(31,55),(32,56),(33,57),(34,58),(35,59),(36,60),(37,61),(38,62),(39,63),(40,64),(41,65),(42,66),(43,67),(44,68),(45,69),(46,70),(93,183),(94,184),(95,139),(96,140),(97,141),(98,142),(99,143),(100,144),(101,145),(102,146),(103,147),(104,148),(105,149),(106,150),(107,151),(108,152),(109,153),(110,154),(111,155),(112,156),(113,157),(114,158),(115,159),(116,160),(117,161),(118,162),(119,163),(120,164),(121,165),(122,166),(123,167),(124,168),(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),(185,235),(186,236),(187,237),(188,238),(189,239),(190,240),(191,241),(192,242),(193,243),(194,244),(195,245),(196,246),(197,247),(198,248),(199,249),(200,250),(201,251),(202,252),(203,253),(204,254),(205,255),(206,256),(207,257),(208,258),(209,259),(210,260),(211,261),(212,262),(213,263),(214,264),(215,265),(216,266),(217,267),(218,268),(219,269),(220,270),(221,271),(222,272),(223,273),(224,274),(225,275),(226,276),(227,231),(228,232),(229,233),(230,234),(277,330),(278,331),(279,332),(280,333),(281,334),(282,335),(283,336),(284,337),(285,338),(286,339),(287,340),(288,341),(289,342),(290,343),(291,344),(292,345),(293,346),(294,347),(295,348),(296,349),(297,350),(298,351),(299,352),(300,353),(301,354),(302,355),(303,356),(304,357),(305,358),(306,359),(307,360),(308,361),(309,362),(310,363),(311,364),(312,365),(313,366),(314,367),(315,368),(316,323),(317,324),(318,325),(319,326),(320,327),(321,328),(322,329)], [(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),(323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368)])

368 conjugacy classes

class 1 2A···2O23A···23V46A···46LR
order12···223···2346···46
size11···11···11···1

368 irreducible representations

dim1111
type++
imageC1C2C23C46
kernelC23×C46C22×C46C24C23
# reps11522330

Matrix representation of C23×C46 in GL4(𝔽47) generated by

1000
04600
00460
0001
,
46000
0100
0010
0001
,
1000
0100
00460
0001
,
24000
03400
00350
00035
G:=sub<GL(4,GF(47))| [1,0,0,0,0,46,0,0,0,0,46,0,0,0,0,1],[46,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,46,0,0,0,0,1],[24,0,0,0,0,34,0,0,0,0,35,0,0,0,0,35] >;

C23×C46 in GAP, Magma, Sage, TeX

C_2^3\times C_{46}
% in TeX

G:=Group("C2^3xC46");
// GroupNames label

G:=SmallGroup(368,42);
// by ID

G=gap.SmallGroup(368,42);
# by ID

G:=PCGroup([5,-2,-2,-2,-2,-23]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^2=c^2=d^46=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