direct product, abelian, monomial, 2-elementary
Aliases: C23×C46, SmallGroup(368,42)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — 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, C22, C23, C24, C23, C46, C2×C46, C22×C46, C23×C46
Quotients: C1, C2, C22, C23, C24, C23, C46, C2×C46, C22×C46, C23×C46
►Regular action on 368 points
Generators in S368
(1 213)(2 214)(3 215)(4 216)(5 217)(6 218)(7 219)(8 220)(9 221)(10 222)(11 223)(12 224)(13 225)(14 226)(15 227)(16 228)(17 229)(18 230)(19 185)(20 186)(21 187)(22 188)(23 189)(24 190)(25 191)(26 192)(27 193)(28 194)(29 195)(30 196)(31 197)(32 198)(33 199)(34 200)(35 201)(36 202)(37 203)(38 204)(39 205)(40 206)(41 207)(42 208)(43 209)(44 210)(45 211)(46 212)(47 246)(48 247)(49 248)(50 249)(51 250)(52 251)(53 252)(54 253)(55 254)(56 255)(57 256)(58 257)(59 258)(60 259)(61 260)(62 261)(63 262)(64 263)(65 264)(66 265)(67 266)(68 267)(69 268)(70 269)(71 270)(72 271)(73 272)(74 273)(75 274)(76 275)(77 276)(78 231)(79 232)(80 233)(81 234)(82 235)(83 236)(84 237)(85 238)(86 239)(87 240)(88 241)(89 242)(90 243)(91 244)(92 245)(93 291)(94 292)(95 293)(96 294)(97 295)(98 296)(99 297)(100 298)(101 299)(102 300)(103 301)(104 302)(105 303)(106 304)(107 305)(108 306)(109 307)(110 308)(111 309)(112 310)(113 311)(114 312)(115 313)(116 314)(117 315)(118 316)(119 317)(120 318)(121 319)(122 320)(123 321)(124 322)(125 277)(126 278)(127 279)(128 280)(129 281)(130 282)(131 283)(132 284)(133 285)(134 286)(135 287)(136 288)(137 289)(138 290)(139 356)(140 357)(141 358)(142 359)(143 360)(144 361)(145 362)(146 363)(147 364)(148 365)(149 366)(150 367)(151 368)(152 323)(153 324)(154 325)(155 326)(156 327)(157 328)(158 329)(159 330)(160 331)(161 332)(162 333)(163 334)(164 335)(165 336)(166 337)(167 338)(168 339)(169 340)(170 341)(171 342)(172 343)(173 344)(174 345)(175 346)(176 347)(177 348)(178 349)(179 350)(180 351)(181 352)(182 353)(183 354)(184 355)
(1 124)(2 125)(3 126)(4 127)(5 128)(6 129)(7 130)(8 131)(9 132)(10 133)(11 134)(12 135)(13 136)(14 137)(15 138)(16 93)(17 94)(18 95)(19 96)(20 97)(21 98)(22 99)(23 100)(24 101)(25 102)(26 103)(27 104)(28 105)(29 106)(30 107)(31 108)(32 109)(33 110)(34 111)(35 112)(36 113)(37 114)(38 115)(39 116)(40 117)(41 118)(42 119)(43 120)(44 121)(45 122)(46 123)(47 145)(48 146)(49 147)(50 148)(51 149)(52 150)(53 151)(54 152)(55 153)(56 154)(57 155)(58 156)(59 157)(60 158)(61 159)(62 160)(63 161)(64 162)(65 163)(66 164)(67 165)(68 166)(69 167)(70 168)(71 169)(72 170)(73 171)(74 172)(75 173)(76 174)(77 175)(78 176)(79 177)(80 178)(81 179)(82 180)(83 181)(84 182)(85 183)(86 184)(87 139)(88 140)(89 141)(90 142)(91 143)(92 144)(185 294)(186 295)(187 296)(188 297)(189 298)(190 299)(191 300)(192 301)(193 302)(194 303)(195 304)(196 305)(197 306)(198 307)(199 308)(200 309)(201 310)(202 311)(203 312)(204 313)(205 314)(206 315)(207 316)(208 317)(209 318)(210 319)(211 320)(212 321)(213 322)(214 277)(215 278)(216 279)(217 280)(218 281)(219 282)(220 283)(221 284)(222 285)(223 286)(224 287)(225 288)(226 289)(227 290)(228 291)(229 292)(230 293)(231 347)(232 348)(233 349)(234 350)(235 351)(236 352)(237 353)(238 354)(239 355)(240 356)(241 357)(242 358)(243 359)(244 360)(245 361)(246 362)(247 363)(248 364)(249 365)(250 366)(251 367)(252 368)(253 323)(254 324)(255 325)(256 326)(257 327)(258 328)(259 329)(260 330)(261 331)(262 332)(263 333)(264 334)(265 335)(266 336)(267 337)(268 338)(269 339)(270 340)(271 341)(272 342)(273 343)(274 344)(275 345)(276 346)
(1 78)(2 79)(3 80)(4 81)(5 82)(6 83)(7 84)(8 85)(9 86)(10 87)(11 88)(12 89)(13 90)(14 91)(15 92)(16 47)(17 48)(18 49)(19 50)(20 51)(21 52)(22 53)(23 54)(24 55)(25 56)(26 57)(27 58)(28 59)(29 60)(30 61)(31 62)(32 63)(33 64)(34 65)(35 66)(36 67)(37 68)(38 69)(39 70)(40 71)(41 72)(42 73)(43 74)(44 75)(45 76)(46 77)(93 145)(94 146)(95 147)(96 148)(97 149)(98 150)(99 151)(100 152)(101 153)(102 154)(103 155)(104 156)(105 157)(106 158)(107 159)(108 160)(109 161)(110 162)(111 163)(112 164)(113 165)(114 166)(115 167)(116 168)(117 169)(118 170)(119 171)(120 172)(121 173)(122 174)(123 175)(124 176)(125 177)(126 178)(127 179)(128 180)(129 181)(130 182)(131 183)(132 184)(133 139)(134 140)(135 141)(136 142)(137 143)(138 144)(185 249)(186 250)(187 251)(188 252)(189 253)(190 254)(191 255)(192 256)(193 257)(194 258)(195 259)(196 260)(197 261)(198 262)(199 263)(200 264)(201 265)(202 266)(203 267)(204 268)(205 269)(206 270)(207 271)(208 272)(209 273)(210 274)(211 275)(212 276)(213 231)(214 232)(215 233)(216 234)(217 235)(218 236)(219 237)(220 238)(221 239)(222 240)(223 241)(224 242)(225 243)(226 244)(227 245)(228 246)(229 247)(230 248)(277 348)(278 349)(279 350)(280 351)(281 352)(282 353)(283 354)(284 355)(285 356)(286 357)(287 358)(288 359)(289 360)(290 361)(291 362)(292 363)(293 364)(294 365)(295 366)(296 367)(297 368)(298 323)(299 324)(300 325)(301 326)(302 327)(303 328)(304 329)(305 330)(306 331)(307 332)(308 333)(309 334)(310 335)(311 336)(312 337)(313 338)(314 339)(315 340)(316 341)(317 342)(318 343)(319 344)(320 345)(321 346)(322 347)
(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)| (1,213)(2,214)(3,215)(4,216)(5,217)(6,218)(7,219)(8,220)(9,221)(10,222)(11,223)(12,224)(13,225)(14,226)(15,227)(16,228)(17,229)(18,230)(19,185)(20,186)(21,187)(22,188)(23,189)(24,190)(25,191)(26,192)(27,193)(28,194)(29,195)(30,196)(31,197)(32,198)(33,199)(34,200)(35,201)(36,202)(37,203)(38,204)(39,205)(40,206)(41,207)(42,208)(43,209)(44,210)(45,211)(46,212)(47,246)(48,247)(49,248)(50,249)(51,250)(52,251)(53,252)(54,253)(55,254)(56,255)(57,256)(58,257)(59,258)(60,259)(61,260)(62,261)(63,262)(64,263)(65,264)(66,265)(67,266)(68,267)(69,268)(70,269)(71,270)(72,271)(73,272)(74,273)(75,274)(76,275)(77,276)(78,231)(79,232)(80,233)(81,234)(82,235)(83,236)(84,237)(85,238)(86,239)(87,240)(88,241)(89,242)(90,243)(91,244)(92,245)(93,291)(94,292)(95,293)(96,294)(97,295)(98,296)(99,297)(100,298)(101,299)(102,300)(103,301)(104,302)(105,303)(106,304)(107,305)(108,306)(109,307)(110,308)(111,309)(112,310)(113,311)(114,312)(115,313)(116,314)(117,315)(118,316)(119,317)(120,318)(121,319)(122,320)(123,321)(124,322)(125,277)(126,278)(127,279)(128,280)(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)(136,288)(137,289)(138,290)(139,356)(140,357)(141,358)(142,359)(143,360)(144,361)(145,362)(146,363)(147,364)(148,365)(149,366)(150,367)(151,368)(152,323)(153,324)(154,325)(155,326)(156,327)(157,328)(158,329)(159,330)(160,331)(161,332)(162,333)(163,334)(164,335)(165,336)(166,337)(167,338)(168,339)(169,340)(170,341)(171,342)(172,343)(173,344)(174,345)(175,346)(176,347)(177,348)(178,349)(179,350)(180,351)(181,352)(182,353)(183,354)(184,355), (1,124)(2,125)(3,126)(4,127)(5,128)(6,129)(7,130)(8,131)(9,132)(10,133)(11,134)(12,135)(13,136)(14,137)(15,138)(16,93)(17,94)(18,95)(19,96)(20,97)(21,98)(22,99)(23,100)(24,101)(25,102)(26,103)(27,104)(28,105)(29,106)(30,107)(31,108)(32,109)(33,110)(34,111)(35,112)(36,113)(37,114)(38,115)(39,116)(40,117)(41,118)(42,119)(43,120)(44,121)(45,122)(46,123)(47,145)(48,146)(49,147)(50,148)(51,149)(52,150)(53,151)(54,152)(55,153)(56,154)(57,155)(58,156)(59,157)(60,158)(61,159)(62,160)(63,161)(64,162)(65,163)(66,164)(67,165)(68,166)(69,167)(70,168)(71,169)(72,170)(73,171)(74,172)(75,173)(76,174)(77,175)(78,176)(79,177)(80,178)(81,179)(82,180)(83,181)(84,182)(85,183)(86,184)(87,139)(88,140)(89,141)(90,142)(91,143)(92,144)(185,294)(186,295)(187,296)(188,297)(189,298)(190,299)(191,300)(192,301)(193,302)(194,303)(195,304)(196,305)(197,306)(198,307)(199,308)(200,309)(201,310)(202,311)(203,312)(204,313)(205,314)(206,315)(207,316)(208,317)(209,318)(210,319)(211,320)(212,321)(213,322)(214,277)(215,278)(216,279)(217,280)(218,281)(219,282)(220,283)(221,284)(222,285)(223,286)(224,287)(225,288)(226,289)(227,290)(228,291)(229,292)(230,293)(231,347)(232,348)(233,349)(234,350)(235,351)(236,352)(237,353)(238,354)(239,355)(240,356)(241,357)(242,358)(243,359)(244,360)(245,361)(246,362)(247,363)(248,364)(249,365)(250,366)(251,367)(252,368)(253,323)(254,324)(255,325)(256,326)(257,327)(258,328)(259,329)(260,330)(261,331)(262,332)(263,333)(264,334)(265,335)(266,336)(267,337)(268,338)(269,339)(270,340)(271,341)(272,342)(273,343)(274,344)(275,345)(276,346), (1,78)(2,79)(3,80)(4,81)(5,82)(6,83)(7,84)(8,85)(9,86)(10,87)(11,88)(12,89)(13,90)(14,91)(15,92)(16,47)(17,48)(18,49)(19,50)(20,51)(21,52)(22,53)(23,54)(24,55)(25,56)(26,57)(27,58)(28,59)(29,60)(30,61)(31,62)(32,63)(33,64)(34,65)(35,66)(36,67)(37,68)(38,69)(39,70)(40,71)(41,72)(42,73)(43,74)(44,75)(45,76)(46,77)(93,145)(94,146)(95,147)(96,148)(97,149)(98,150)(99,151)(100,152)(101,153)(102,154)(103,155)(104,156)(105,157)(106,158)(107,159)(108,160)(109,161)(110,162)(111,163)(112,164)(113,165)(114,166)(115,167)(116,168)(117,169)(118,170)(119,171)(120,172)(121,173)(122,174)(123,175)(124,176)(125,177)(126,178)(127,179)(128,180)(129,181)(130,182)(131,183)(132,184)(133,139)(134,140)(135,141)(136,142)(137,143)(138,144)(185,249)(186,250)(187,251)(188,252)(189,253)(190,254)(191,255)(192,256)(193,257)(194,258)(195,259)(196,260)(197,261)(198,262)(199,263)(200,264)(201,265)(202,266)(203,267)(204,268)(205,269)(206,270)(207,271)(208,272)(209,273)(210,274)(211,275)(212,276)(213,231)(214,232)(215,233)(216,234)(217,235)(218,236)(219,237)(220,238)(221,239)(222,240)(223,241)(224,242)(225,243)(226,244)(227,245)(228,246)(229,247)(230,248)(277,348)(278,349)(279,350)(280,351)(281,352)(282,353)(283,354)(284,355)(285,356)(286,357)(287,358)(288,359)(289,360)(290,361)(291,362)(292,363)(293,364)(294,365)(295,366)(296,367)(297,368)(298,323)(299,324)(300,325)(301,326)(302,327)(303,328)(304,329)(305,330)(306,331)(307,332)(308,333)(309,334)(310,335)(311,336)(312,337)(313,338)(314,339)(315,340)(316,341)(317,342)(318,343)(319,344)(320,345)(321,346)(322,347), (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( (1,213)(2,214)(3,215)(4,216)(5,217)(6,218)(7,219)(8,220)(9,221)(10,222)(11,223)(12,224)(13,225)(14,226)(15,227)(16,228)(17,229)(18,230)(19,185)(20,186)(21,187)(22,188)(23,189)(24,190)(25,191)(26,192)(27,193)(28,194)(29,195)(30,196)(31,197)(32,198)(33,199)(34,200)(35,201)(36,202)(37,203)(38,204)(39,205)(40,206)(41,207)(42,208)(43,209)(44,210)(45,211)(46,212)(47,246)(48,247)(49,248)(50,249)(51,250)(52,251)(53,252)(54,253)(55,254)(56,255)(57,256)(58,257)(59,258)(60,259)(61,260)(62,261)(63,262)(64,263)(65,264)(66,265)(67,266)(68,267)(69,268)(70,269)(71,270)(72,271)(73,272)(74,273)(75,274)(76,275)(77,276)(78,231)(79,232)(80,233)(81,234)(82,235)(83,236)(84,237)(85,238)(86,239)(87,240)(88,241)(89,242)(90,243)(91,244)(92,245)(93,291)(94,292)(95,293)(96,294)(97,295)(98,296)(99,297)(100,298)(101,299)(102,300)(103,301)(104,302)(105,303)(106,304)(107,305)(108,306)(109,307)(110,308)(111,309)(112,310)(113,311)(114,312)(115,313)(116,314)(117,315)(118,316)(119,317)(120,318)(121,319)(122,320)(123,321)(124,322)(125,277)(126,278)(127,279)(128,280)(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)(136,288)(137,289)(138,290)(139,356)(140,357)(141,358)(142,359)(143,360)(144,361)(145,362)(146,363)(147,364)(148,365)(149,366)(150,367)(151,368)(152,323)(153,324)(154,325)(155,326)(156,327)(157,328)(158,329)(159,330)(160,331)(161,332)(162,333)(163,334)(164,335)(165,336)(166,337)(167,338)(168,339)(169,340)(170,341)(171,342)(172,343)(173,344)(174,345)(175,346)(176,347)(177,348)(178,349)(179,350)(180,351)(181,352)(182,353)(183,354)(184,355), (1,124)(2,125)(3,126)(4,127)(5,128)(6,129)(7,130)(8,131)(9,132)(10,133)(11,134)(12,135)(13,136)(14,137)(15,138)(16,93)(17,94)(18,95)(19,96)(20,97)(21,98)(22,99)(23,100)(24,101)(25,102)(26,103)(27,104)(28,105)(29,106)(30,107)(31,108)(32,109)(33,110)(34,111)(35,112)(36,113)(37,114)(38,115)(39,116)(40,117)(41,118)(42,119)(43,120)(44,121)(45,122)(46,123)(47,145)(48,146)(49,147)(50,148)(51,149)(52,150)(53,151)(54,152)(55,153)(56,154)(57,155)(58,156)(59,157)(60,158)(61,159)(62,160)(63,161)(64,162)(65,163)(66,164)(67,165)(68,166)(69,167)(70,168)(71,169)(72,170)(73,171)(74,172)(75,173)(76,174)(77,175)(78,176)(79,177)(80,178)(81,179)(82,180)(83,181)(84,182)(85,183)(86,184)(87,139)(88,140)(89,141)(90,142)(91,143)(92,144)(185,294)(186,295)(187,296)(188,297)(189,298)(190,299)(191,300)(192,301)(193,302)(194,303)(195,304)(196,305)(197,306)(198,307)(199,308)(200,309)(201,310)(202,311)(203,312)(204,313)(205,314)(206,315)(207,316)(208,317)(209,318)(210,319)(211,320)(212,321)(213,322)(214,277)(215,278)(216,279)(217,280)(218,281)(219,282)(220,283)(221,284)(222,285)(223,286)(224,287)(225,288)(226,289)(227,290)(228,291)(229,292)(230,293)(231,347)(232,348)(233,349)(234,350)(235,351)(236,352)(237,353)(238,354)(239,355)(240,356)(241,357)(242,358)(243,359)(244,360)(245,361)(246,362)(247,363)(248,364)(249,365)(250,366)(251,367)(252,368)(253,323)(254,324)(255,325)(256,326)(257,327)(258,328)(259,329)(260,330)(261,331)(262,332)(263,333)(264,334)(265,335)(266,336)(267,337)(268,338)(269,339)(270,340)(271,341)(272,342)(273,343)(274,344)(275,345)(276,346), (1,78)(2,79)(3,80)(4,81)(5,82)(6,83)(7,84)(8,85)(9,86)(10,87)(11,88)(12,89)(13,90)(14,91)(15,92)(16,47)(17,48)(18,49)(19,50)(20,51)(21,52)(22,53)(23,54)(24,55)(25,56)(26,57)(27,58)(28,59)(29,60)(30,61)(31,62)(32,63)(33,64)(34,65)(35,66)(36,67)(37,68)(38,69)(39,70)(40,71)(41,72)(42,73)(43,74)(44,75)(45,76)(46,77)(93,145)(94,146)(95,147)(96,148)(97,149)(98,150)(99,151)(100,152)(101,153)(102,154)(103,155)(104,156)(105,157)(106,158)(107,159)(108,160)(109,161)(110,162)(111,163)(112,164)(113,165)(114,166)(115,167)(116,168)(117,169)(118,170)(119,171)(120,172)(121,173)(122,174)(123,175)(124,176)(125,177)(126,178)(127,179)(128,180)(129,181)(130,182)(131,183)(132,184)(133,139)(134,140)(135,141)(136,142)(137,143)(138,144)(185,249)(186,250)(187,251)(188,252)(189,253)(190,254)(191,255)(192,256)(193,257)(194,258)(195,259)(196,260)(197,261)(198,262)(199,263)(200,264)(201,265)(202,266)(203,267)(204,268)(205,269)(206,270)(207,271)(208,272)(209,273)(210,274)(211,275)(212,276)(213,231)(214,232)(215,233)(216,234)(217,235)(218,236)(219,237)(220,238)(221,239)(222,240)(223,241)(224,242)(225,243)(226,244)(227,245)(228,246)(229,247)(230,248)(277,348)(278,349)(279,350)(280,351)(281,352)(282,353)(283,354)(284,355)(285,356)(286,357)(287,358)(288,359)(289,360)(290,361)(291,362)(292,363)(293,364)(294,365)(295,366)(296,367)(297,368)(298,323)(299,324)(300,325)(301,326)(302,327)(303,328)(304,329)(305,330)(306,331)(307,332)(308,333)(309,334)(310,335)(311,336)(312,337)(313,338)(314,339)(315,340)(316,341)(317,342)(318,343)(319,344)(320,345)(321,346)(322,347), (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([[(1,213),(2,214),(3,215),(4,216),(5,217),(6,218),(7,219),(8,220),(9,221),(10,222),(11,223),(12,224),(13,225),(14,226),(15,227),(16,228),(17,229),(18,230),(19,185),(20,186),(21,187),(22,188),(23,189),(24,190),(25,191),(26,192),(27,193),(28,194),(29,195),(30,196),(31,197),(32,198),(33,199),(34,200),(35,201),(36,202),(37,203),(38,204),(39,205),(40,206),(41,207),(42,208),(43,209),(44,210),(45,211),(46,212),(47,246),(48,247),(49,248),(50,249),(51,250),(52,251),(53,252),(54,253),(55,254),(56,255),(57,256),(58,257),(59,258),(60,259),(61,260),(62,261),(63,262),(64,263),(65,264),(66,265),(67,266),(68,267),(69,268),(70,269),(71,270),(72,271),(73,272),(74,273),(75,274),(76,275),(77,276),(78,231),(79,232),(80,233),(81,234),(82,235),(83,236),(84,237),(85,238),(86,239),(87,240),(88,241),(89,242),(90,243),(91,244),(92,245),(93,291),(94,292),(95,293),(96,294),(97,295),(98,296),(99,297),(100,298),(101,299),(102,300),(103,301),(104,302),(105,303),(106,304),(107,305),(108,306),(109,307),(110,308),(111,309),(112,310),(113,311),(114,312),(115,313),(116,314),(117,315),(118,316),(119,317),(120,318),(121,319),(122,320),(123,321),(124,322),(125,277),(126,278),(127,279),(128,280),(129,281),(130,282),(131,283),(132,284),(133,285),(134,286),(135,287),(136,288),(137,289),(138,290),(139,356),(140,357),(141,358),(142,359),(143,360),(144,361),(145,362),(146,363),(147,364),(148,365),(149,366),(150,367),(151,368),(152,323),(153,324),(154,325),(155,326),(156,327),(157,328),(158,329),(159,330),(160,331),(161,332),(162,333),(163,334),(164,335),(165,336),(166,337),(167,338),(168,339),(169,340),(170,341),(171,342),(172,343),(173,344),(174,345),(175,346),(176,347),(177,348),(178,349),(179,350),(180,351),(181,352),(182,353),(183,354),(184,355)], [(1,124),(2,125),(3,126),(4,127),(5,128),(6,129),(7,130),(8,131),(9,132),(10,133),(11,134),(12,135),(13,136),(14,137),(15,138),(16,93),(17,94),(18,95),(19,96),(20,97),(21,98),(22,99),(23,100),(24,101),(25,102),(26,103),(27,104),(28,105),(29,106),(30,107),(31,108),(32,109),(33,110),(34,111),(35,112),(36,113),(37,114),(38,115),(39,116),(40,117),(41,118),(42,119),(43,120),(44,121),(45,122),(46,123),(47,145),(48,146),(49,147),(50,148),(51,149),(52,150),(53,151),(54,152),(55,153),(56,154),(57,155),(58,156),(59,157),(60,158),(61,159),(62,160),(63,161),(64,162),(65,163),(66,164),(67,165),(68,166),(69,167),(70,168),(71,169),(72,170),(73,171),(74,172),(75,173),(76,174),(77,175),(78,176),(79,177),(80,178),(81,179),(82,180),(83,181),(84,182),(85,183),(86,184),(87,139),(88,140),(89,141),(90,142),(91,143),(92,144),(185,294),(186,295),(187,296),(188,297),(189,298),(190,299),(191,300),(192,301),(193,302),(194,303),(195,304),(196,305),(197,306),(198,307),(199,308),(200,309),(201,310),(202,311),(203,312),(204,313),(205,314),(206,315),(207,316),(208,317),(209,318),(210,319),(211,320),(212,321),(213,322),(214,277),(215,278),(216,279),(217,280),(218,281),(219,282),(220,283),(221,284),(222,285),(223,286),(224,287),(225,288),(226,289),(227,290),(228,291),(229,292),(230,293),(231,347),(232,348),(233,349),(234,350),(235,351),(236,352),(237,353),(238,354),(239,355),(240,356),(241,357),(242,358),(243,359),(244,360),(245,361),(246,362),(247,363),(248,364),(249,365),(250,366),(251,367),(252,368),(253,323),(254,324),(255,325),(256,326),(257,327),(258,328),(259,329),(260,330),(261,331),(262,332),(263,333),(264,334),(265,335),(266,336),(267,337),(268,338),(269,339),(270,340),(271,341),(272,342),(273,343),(274,344),(275,345),(276,346)], [(1,78),(2,79),(3,80),(4,81),(5,82),(6,83),(7,84),(8,85),(9,86),(10,87),(11,88),(12,89),(13,90),(14,91),(15,92),(16,47),(17,48),(18,49),(19,50),(20,51),(21,52),(22,53),(23,54),(24,55),(25,56),(26,57),(27,58),(28,59),(29,60),(30,61),(31,62),(32,63),(33,64),(34,65),(35,66),(36,67),(37,68),(38,69),(39,70),(40,71),(41,72),(42,73),(43,74),(44,75),(45,76),(46,77),(93,145),(94,146),(95,147),(96,148),(97,149),(98,150),(99,151),(100,152),(101,153),(102,154),(103,155),(104,156),(105,157),(106,158),(107,159),(108,160),(109,161),(110,162),(111,163),(112,164),(113,165),(114,166),(115,167),(116,168),(117,169),(118,170),(119,171),(120,172),(121,173),(122,174),(123,175),(124,176),(125,177),(126,178),(127,179),(128,180),(129,181),(130,182),(131,183),(132,184),(133,139),(134,140),(135,141),(136,142),(137,143),(138,144),(185,249),(186,250),(187,251),(188,252),(189,253),(190,254),(191,255),(192,256),(193,257),(194,258),(195,259),(196,260),(197,261),(198,262),(199,263),(200,264),(201,265),(202,266),(203,267),(204,268),(205,269),(206,270),(207,271),(208,272),(209,273),(210,274),(211,275),(212,276),(213,231),(214,232),(215,233),(216,234),(217,235),(218,236),(219,237),(220,238),(221,239),(222,240),(223,241),(224,242),(225,243),(226,244),(227,245),(228,246),(229,247),(230,248),(277,348),(278,349),(279,350),(280,351),(281,352),(282,353),(283,354),(284,355),(285,356),(286,357),(287,358),(288,359),(289,360),(290,361),(291,362),(292,363),(293,364),(294,365),(295,366),(296,367),(297,368),(298,323),(299,324),(300,325),(301,326),(302,327),(303,328),(304,329),(305,330),(306,331),(307,332),(308,333),(309,334),(310,335),(311,336),(312,337),(313,338),(314,339),(315,340),(316,341),(317,342),(318,343),(319,344),(320,345),(321,346),(322,347)], [(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 | ··· | 2O | 23A | ··· | 23V | 46A | ··· | 46LR |
| order | 1 | 2 | ··· | 2 | 23 | ··· | 23 | 46 | ··· | 46 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
368 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C23 | C46 |
| kernel | C23×C46 | C22×C46 | C24 | C23 |
| # reps | 1 | 15 | 22 | 330 |
Matrix representation of C23×C46 ►in GL4(𝔽47) generated by
| 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 |
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