direct product, abelian, monomial, 3-elementary
Aliases: C32×C48, SmallGroup(432,232)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C32×C48 |
| C1 — C32×C48 |
| C1 — C32×C48 |
Generators and relations for C32×C48
G = < a,b,c | a3=b3=c48=1, ab=ba, ac=ca, bc=cb >
Subgroups: 140, all normal (10 characteristic)
C1, C2, C3, C4, C6, C8, C32, C12, C16, C3×C6, C24, C33, C3×C12, C48, C32×C6, C3×C24, C32×C12, C3×C48, C32×C24, C32×C48
Quotients: C1, C2, C3, C4, C6, C8, C32, C12, C16, C3×C6, C24, C33, C3×C12, C48, C32×C6, C3×C24, C32×C12, C3×C48, C32×C24, C32×C48
►Regular action on 432 points
Generators in S432
(1 423 233)(2 424 234)(3 425 235)(4 426 236)(5 427 237)(6 428 238)(7 429 239)(8 430 240)(9 431 193)(10 432 194)(11 385 195)(12 386 196)(13 387 197)(14 388 198)(15 389 199)(16 390 200)(17 391 201)(18 392 202)(19 393 203)(20 394 204)(21 395 205)(22 396 206)(23 397 207)(24 398 208)(25 399 209)(26 400 210)(27 401 211)(28 402 212)(29 403 213)(30 404 214)(31 405 215)(32 406 216)(33 407 217)(34 408 218)(35 409 219)(36 410 220)(37 411 221)(38 412 222)(39 413 223)(40 414 224)(41 415 225)(42 416 226)(43 417 227)(44 418 228)(45 419 229)(46 420 230)(47 421 231)(48 422 232)(49 367 246)(50 368 247)(51 369 248)(52 370 249)(53 371 250)(54 372 251)(55 373 252)(56 374 253)(57 375 254)(58 376 255)(59 377 256)(60 378 257)(61 379 258)(62 380 259)(63 381 260)(64 382 261)(65 383 262)(66 384 263)(67 337 264)(68 338 265)(69 339 266)(70 340 267)(71 341 268)(72 342 269)(73 343 270)(74 344 271)(75 345 272)(76 346 273)(77 347 274)(78 348 275)(79 349 276)(80 350 277)(81 351 278)(82 352 279)(83 353 280)(84 354 281)(85 355 282)(86 356 283)(87 357 284)(88 358 285)(89 359 286)(90 360 287)(91 361 288)(92 362 241)(93 363 242)(94 364 243)(95 365 244)(96 366 245)(97 331 181)(98 332 182)(99 333 183)(100 334 184)(101 335 185)(102 336 186)(103 289 187)(104 290 188)(105 291 189)(106 292 190)(107 293 191)(108 294 192)(109 295 145)(110 296 146)(111 297 147)(112 298 148)(113 299 149)(114 300 150)(115 301 151)(116 302 152)(117 303 153)(118 304 154)(119 305 155)(120 306 156)(121 307 157)(122 308 158)(123 309 159)(124 310 160)(125 311 161)(126 312 162)(127 313 163)(128 314 164)(129 315 165)(130 316 166)(131 317 167)(132 318 168)(133 319 169)(134 320 170)(135 321 171)(136 322 172)(137 323 173)(138 324 174)(139 325 175)(140 326 176)(141 327 177)(142 328 178)(143 329 179)(144 330 180)
(1 188 244)(2 189 245)(3 190 246)(4 191 247)(5 192 248)(6 145 249)(7 146 250)(8 147 251)(9 148 252)(10 149 253)(11 150 254)(12 151 255)(13 152 256)(14 153 257)(15 154 258)(16 155 259)(17 156 260)(18 157 261)(19 158 262)(20 159 263)(21 160 264)(22 161 265)(23 162 266)(24 163 267)(25 164 268)(26 165 269)(27 166 270)(28 167 271)(29 168 272)(30 169 273)(31 170 274)(32 171 275)(33 172 276)(34 173 277)(35 174 278)(36 175 279)(37 176 280)(38 177 281)(39 178 282)(40 179 283)(41 180 284)(42 181 285)(43 182 286)(44 183 287)(45 184 288)(46 185 241)(47 186 242)(48 187 243)(49 425 106)(50 426 107)(51 427 108)(52 428 109)(53 429 110)(54 430 111)(55 431 112)(56 432 113)(57 385 114)(58 386 115)(59 387 116)(60 388 117)(61 389 118)(62 390 119)(63 391 120)(64 392 121)(65 393 122)(66 394 123)(67 395 124)(68 396 125)(69 397 126)(70 398 127)(71 399 128)(72 400 129)(73 401 130)(74 402 131)(75 403 132)(76 404 133)(77 405 134)(78 406 135)(79 407 136)(80 408 137)(81 409 138)(82 410 139)(83 411 140)(84 412 141)(85 413 142)(86 414 143)(87 415 144)(88 416 97)(89 417 98)(90 418 99)(91 419 100)(92 420 101)(93 421 102)(94 422 103)(95 423 104)(96 424 105)(193 298 373)(194 299 374)(195 300 375)(196 301 376)(197 302 377)(198 303 378)(199 304 379)(200 305 380)(201 306 381)(202 307 382)(203 308 383)(204 309 384)(205 310 337)(206 311 338)(207 312 339)(208 313 340)(209 314 341)(210 315 342)(211 316 343)(212 317 344)(213 318 345)(214 319 346)(215 320 347)(216 321 348)(217 322 349)(218 323 350)(219 324 351)(220 325 352)(221 326 353)(222 327 354)(223 328 355)(224 329 356)(225 330 357)(226 331 358)(227 332 359)(228 333 360)(229 334 361)(230 335 362)(231 336 363)(232 289 364)(233 290 365)(234 291 366)(235 292 367)(236 293 368)(237 294 369)(238 295 370)(239 296 371)(240 297 372)
(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)(337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384)(385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432)
G:=sub<Sym(432)| (1,423,233)(2,424,234)(3,425,235)(4,426,236)(5,427,237)(6,428,238)(7,429,239)(8,430,240)(9,431,193)(10,432,194)(11,385,195)(12,386,196)(13,387,197)(14,388,198)(15,389,199)(16,390,200)(17,391,201)(18,392,202)(19,393,203)(20,394,204)(21,395,205)(22,396,206)(23,397,207)(24,398,208)(25,399,209)(26,400,210)(27,401,211)(28,402,212)(29,403,213)(30,404,214)(31,405,215)(32,406,216)(33,407,217)(34,408,218)(35,409,219)(36,410,220)(37,411,221)(38,412,222)(39,413,223)(40,414,224)(41,415,225)(42,416,226)(43,417,227)(44,418,228)(45,419,229)(46,420,230)(47,421,231)(48,422,232)(49,367,246)(50,368,247)(51,369,248)(52,370,249)(53,371,250)(54,372,251)(55,373,252)(56,374,253)(57,375,254)(58,376,255)(59,377,256)(60,378,257)(61,379,258)(62,380,259)(63,381,260)(64,382,261)(65,383,262)(66,384,263)(67,337,264)(68,338,265)(69,339,266)(70,340,267)(71,341,268)(72,342,269)(73,343,270)(74,344,271)(75,345,272)(76,346,273)(77,347,274)(78,348,275)(79,349,276)(80,350,277)(81,351,278)(82,352,279)(83,353,280)(84,354,281)(85,355,282)(86,356,283)(87,357,284)(88,358,285)(89,359,286)(90,360,287)(91,361,288)(92,362,241)(93,363,242)(94,364,243)(95,365,244)(96,366,245)(97,331,181)(98,332,182)(99,333,183)(100,334,184)(101,335,185)(102,336,186)(103,289,187)(104,290,188)(105,291,189)(106,292,190)(107,293,191)(108,294,192)(109,295,145)(110,296,146)(111,297,147)(112,298,148)(113,299,149)(114,300,150)(115,301,151)(116,302,152)(117,303,153)(118,304,154)(119,305,155)(120,306,156)(121,307,157)(122,308,158)(123,309,159)(124,310,160)(125,311,161)(126,312,162)(127,313,163)(128,314,164)(129,315,165)(130,316,166)(131,317,167)(132,318,168)(133,319,169)(134,320,170)(135,321,171)(136,322,172)(137,323,173)(138,324,174)(139,325,175)(140,326,176)(141,327,177)(142,328,178)(143,329,179)(144,330,180), (1,188,244)(2,189,245)(3,190,246)(4,191,247)(5,192,248)(6,145,249)(7,146,250)(8,147,251)(9,148,252)(10,149,253)(11,150,254)(12,151,255)(13,152,256)(14,153,257)(15,154,258)(16,155,259)(17,156,260)(18,157,261)(19,158,262)(20,159,263)(21,160,264)(22,161,265)(23,162,266)(24,163,267)(25,164,268)(26,165,269)(27,166,270)(28,167,271)(29,168,272)(30,169,273)(31,170,274)(32,171,275)(33,172,276)(34,173,277)(35,174,278)(36,175,279)(37,176,280)(38,177,281)(39,178,282)(40,179,283)(41,180,284)(42,181,285)(43,182,286)(44,183,287)(45,184,288)(46,185,241)(47,186,242)(48,187,243)(49,425,106)(50,426,107)(51,427,108)(52,428,109)(53,429,110)(54,430,111)(55,431,112)(56,432,113)(57,385,114)(58,386,115)(59,387,116)(60,388,117)(61,389,118)(62,390,119)(63,391,120)(64,392,121)(65,393,122)(66,394,123)(67,395,124)(68,396,125)(69,397,126)(70,398,127)(71,399,128)(72,400,129)(73,401,130)(74,402,131)(75,403,132)(76,404,133)(77,405,134)(78,406,135)(79,407,136)(80,408,137)(81,409,138)(82,410,139)(83,411,140)(84,412,141)(85,413,142)(86,414,143)(87,415,144)(88,416,97)(89,417,98)(90,418,99)(91,419,100)(92,420,101)(93,421,102)(94,422,103)(95,423,104)(96,424,105)(193,298,373)(194,299,374)(195,300,375)(196,301,376)(197,302,377)(198,303,378)(199,304,379)(200,305,380)(201,306,381)(202,307,382)(203,308,383)(204,309,384)(205,310,337)(206,311,338)(207,312,339)(208,313,340)(209,314,341)(210,315,342)(211,316,343)(212,317,344)(213,318,345)(214,319,346)(215,320,347)(216,321,348)(217,322,349)(218,323,350)(219,324,351)(220,325,352)(221,326,353)(222,327,354)(223,328,355)(224,329,356)(225,330,357)(226,331,358)(227,332,359)(228,333,360)(229,334,361)(230,335,362)(231,336,363)(232,289,364)(233,290,365)(234,291,366)(235,292,367)(236,293,368)(237,294,369)(238,295,370)(239,296,371)(240,297,372), (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)(337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384)(385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432)>;
G:=Group( (1,423,233)(2,424,234)(3,425,235)(4,426,236)(5,427,237)(6,428,238)(7,429,239)(8,430,240)(9,431,193)(10,432,194)(11,385,195)(12,386,196)(13,387,197)(14,388,198)(15,389,199)(16,390,200)(17,391,201)(18,392,202)(19,393,203)(20,394,204)(21,395,205)(22,396,206)(23,397,207)(24,398,208)(25,399,209)(26,400,210)(27,401,211)(28,402,212)(29,403,213)(30,404,214)(31,405,215)(32,406,216)(33,407,217)(34,408,218)(35,409,219)(36,410,220)(37,411,221)(38,412,222)(39,413,223)(40,414,224)(41,415,225)(42,416,226)(43,417,227)(44,418,228)(45,419,229)(46,420,230)(47,421,231)(48,422,232)(49,367,246)(50,368,247)(51,369,248)(52,370,249)(53,371,250)(54,372,251)(55,373,252)(56,374,253)(57,375,254)(58,376,255)(59,377,256)(60,378,257)(61,379,258)(62,380,259)(63,381,260)(64,382,261)(65,383,262)(66,384,263)(67,337,264)(68,338,265)(69,339,266)(70,340,267)(71,341,268)(72,342,269)(73,343,270)(74,344,271)(75,345,272)(76,346,273)(77,347,274)(78,348,275)(79,349,276)(80,350,277)(81,351,278)(82,352,279)(83,353,280)(84,354,281)(85,355,282)(86,356,283)(87,357,284)(88,358,285)(89,359,286)(90,360,287)(91,361,288)(92,362,241)(93,363,242)(94,364,243)(95,365,244)(96,366,245)(97,331,181)(98,332,182)(99,333,183)(100,334,184)(101,335,185)(102,336,186)(103,289,187)(104,290,188)(105,291,189)(106,292,190)(107,293,191)(108,294,192)(109,295,145)(110,296,146)(111,297,147)(112,298,148)(113,299,149)(114,300,150)(115,301,151)(116,302,152)(117,303,153)(118,304,154)(119,305,155)(120,306,156)(121,307,157)(122,308,158)(123,309,159)(124,310,160)(125,311,161)(126,312,162)(127,313,163)(128,314,164)(129,315,165)(130,316,166)(131,317,167)(132,318,168)(133,319,169)(134,320,170)(135,321,171)(136,322,172)(137,323,173)(138,324,174)(139,325,175)(140,326,176)(141,327,177)(142,328,178)(143,329,179)(144,330,180), (1,188,244)(2,189,245)(3,190,246)(4,191,247)(5,192,248)(6,145,249)(7,146,250)(8,147,251)(9,148,252)(10,149,253)(11,150,254)(12,151,255)(13,152,256)(14,153,257)(15,154,258)(16,155,259)(17,156,260)(18,157,261)(19,158,262)(20,159,263)(21,160,264)(22,161,265)(23,162,266)(24,163,267)(25,164,268)(26,165,269)(27,166,270)(28,167,271)(29,168,272)(30,169,273)(31,170,274)(32,171,275)(33,172,276)(34,173,277)(35,174,278)(36,175,279)(37,176,280)(38,177,281)(39,178,282)(40,179,283)(41,180,284)(42,181,285)(43,182,286)(44,183,287)(45,184,288)(46,185,241)(47,186,242)(48,187,243)(49,425,106)(50,426,107)(51,427,108)(52,428,109)(53,429,110)(54,430,111)(55,431,112)(56,432,113)(57,385,114)(58,386,115)(59,387,116)(60,388,117)(61,389,118)(62,390,119)(63,391,120)(64,392,121)(65,393,122)(66,394,123)(67,395,124)(68,396,125)(69,397,126)(70,398,127)(71,399,128)(72,400,129)(73,401,130)(74,402,131)(75,403,132)(76,404,133)(77,405,134)(78,406,135)(79,407,136)(80,408,137)(81,409,138)(82,410,139)(83,411,140)(84,412,141)(85,413,142)(86,414,143)(87,415,144)(88,416,97)(89,417,98)(90,418,99)(91,419,100)(92,420,101)(93,421,102)(94,422,103)(95,423,104)(96,424,105)(193,298,373)(194,299,374)(195,300,375)(196,301,376)(197,302,377)(198,303,378)(199,304,379)(200,305,380)(201,306,381)(202,307,382)(203,308,383)(204,309,384)(205,310,337)(206,311,338)(207,312,339)(208,313,340)(209,314,341)(210,315,342)(211,316,343)(212,317,344)(213,318,345)(214,319,346)(215,320,347)(216,321,348)(217,322,349)(218,323,350)(219,324,351)(220,325,352)(221,326,353)(222,327,354)(223,328,355)(224,329,356)(225,330,357)(226,331,358)(227,332,359)(228,333,360)(229,334,361)(230,335,362)(231,336,363)(232,289,364)(233,290,365)(234,291,366)(235,292,367)(236,293,368)(237,294,369)(238,295,370)(239,296,371)(240,297,372), (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)(337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384)(385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432) );
G=PermutationGroup([[(1,423,233),(2,424,234),(3,425,235),(4,426,236),(5,427,237),(6,428,238),(7,429,239),(8,430,240),(9,431,193),(10,432,194),(11,385,195),(12,386,196),(13,387,197),(14,388,198),(15,389,199),(16,390,200),(17,391,201),(18,392,202),(19,393,203),(20,394,204),(21,395,205),(22,396,206),(23,397,207),(24,398,208),(25,399,209),(26,400,210),(27,401,211),(28,402,212),(29,403,213),(30,404,214),(31,405,215),(32,406,216),(33,407,217),(34,408,218),(35,409,219),(36,410,220),(37,411,221),(38,412,222),(39,413,223),(40,414,224),(41,415,225),(42,416,226),(43,417,227),(44,418,228),(45,419,229),(46,420,230),(47,421,231),(48,422,232),(49,367,246),(50,368,247),(51,369,248),(52,370,249),(53,371,250),(54,372,251),(55,373,252),(56,374,253),(57,375,254),(58,376,255),(59,377,256),(60,378,257),(61,379,258),(62,380,259),(63,381,260),(64,382,261),(65,383,262),(66,384,263),(67,337,264),(68,338,265),(69,339,266),(70,340,267),(71,341,268),(72,342,269),(73,343,270),(74,344,271),(75,345,272),(76,346,273),(77,347,274),(78,348,275),(79,349,276),(80,350,277),(81,351,278),(82,352,279),(83,353,280),(84,354,281),(85,355,282),(86,356,283),(87,357,284),(88,358,285),(89,359,286),(90,360,287),(91,361,288),(92,362,241),(93,363,242),(94,364,243),(95,365,244),(96,366,245),(97,331,181),(98,332,182),(99,333,183),(100,334,184),(101,335,185),(102,336,186),(103,289,187),(104,290,188),(105,291,189),(106,292,190),(107,293,191),(108,294,192),(109,295,145),(110,296,146),(111,297,147),(112,298,148),(113,299,149),(114,300,150),(115,301,151),(116,302,152),(117,303,153),(118,304,154),(119,305,155),(120,306,156),(121,307,157),(122,308,158),(123,309,159),(124,310,160),(125,311,161),(126,312,162),(127,313,163),(128,314,164),(129,315,165),(130,316,166),(131,317,167),(132,318,168),(133,319,169),(134,320,170),(135,321,171),(136,322,172),(137,323,173),(138,324,174),(139,325,175),(140,326,176),(141,327,177),(142,328,178),(143,329,179),(144,330,180)], [(1,188,244),(2,189,245),(3,190,246),(4,191,247),(5,192,248),(6,145,249),(7,146,250),(8,147,251),(9,148,252),(10,149,253),(11,150,254),(12,151,255),(13,152,256),(14,153,257),(15,154,258),(16,155,259),(17,156,260),(18,157,261),(19,158,262),(20,159,263),(21,160,264),(22,161,265),(23,162,266),(24,163,267),(25,164,268),(26,165,269),(27,166,270),(28,167,271),(29,168,272),(30,169,273),(31,170,274),(32,171,275),(33,172,276),(34,173,277),(35,174,278),(36,175,279),(37,176,280),(38,177,281),(39,178,282),(40,179,283),(41,180,284),(42,181,285),(43,182,286),(44,183,287),(45,184,288),(46,185,241),(47,186,242),(48,187,243),(49,425,106),(50,426,107),(51,427,108),(52,428,109),(53,429,110),(54,430,111),(55,431,112),(56,432,113),(57,385,114),(58,386,115),(59,387,116),(60,388,117),(61,389,118),(62,390,119),(63,391,120),(64,392,121),(65,393,122),(66,394,123),(67,395,124),(68,396,125),(69,397,126),(70,398,127),(71,399,128),(72,400,129),(73,401,130),(74,402,131),(75,403,132),(76,404,133),(77,405,134),(78,406,135),(79,407,136),(80,408,137),(81,409,138),(82,410,139),(83,411,140),(84,412,141),(85,413,142),(86,414,143),(87,415,144),(88,416,97),(89,417,98),(90,418,99),(91,419,100),(92,420,101),(93,421,102),(94,422,103),(95,423,104),(96,424,105),(193,298,373),(194,299,374),(195,300,375),(196,301,376),(197,302,377),(198,303,378),(199,304,379),(200,305,380),(201,306,381),(202,307,382),(203,308,383),(204,309,384),(205,310,337),(206,311,338),(207,312,339),(208,313,340),(209,314,341),(210,315,342),(211,316,343),(212,317,344),(213,318,345),(214,319,346),(215,320,347),(216,321,348),(217,322,349),(218,323,350),(219,324,351),(220,325,352),(221,326,353),(222,327,354),(223,328,355),(224,329,356),(225,330,357),(226,331,358),(227,332,359),(228,333,360),(229,334,361),(230,335,362),(231,336,363),(232,289,364),(233,290,365),(234,291,366),(235,292,367),(236,293,368),(237,294,369),(238,295,370),(239,296,371),(240,297,372)], [(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),(337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384),(385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432)]])
432 conjugacy classes
| class | 1 | 2 | 3A | ··· | 3Z | 4A | 4B | 6A | ··· | 6Z | 8A | 8B | 8C | 8D | 12A | ··· | 12AZ | 16A | ··· | 16H | 24A | ··· | 24CZ | 48A | ··· | 48GZ |
| order | 1 | 2 | 3 | ··· | 3 | 4 | 4 | 6 | ··· | 6 | 8 | 8 | 8 | 8 | 12 | ··· | 12 | 16 | ··· | 16 | 24 | ··· | 24 | 48 | ··· | 48 |
| size | 1 | 1 | 1 | ··· | 1 | 1 | 1 | 1 | ··· | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
432 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | ||||||||
| image | C1 | C2 | C3 | C4 | C6 | C8 | C12 | C16 | C24 | C48 |
| kernel | C32×C48 | C32×C24 | C3×C48 | C32×C12 | C3×C24 | C32×C6 | C3×C12 | C33 | C3×C6 | C32 |
| # reps | 1 | 1 | 26 | 2 | 26 | 4 | 52 | 8 | 104 | 208 |
Matrix representation of C32×C48 ►in GL3(𝔽97) generated by
| 1 | 0 | 0 |
| 0 | 35 | 0 |
| 0 | 0 | 61 |
| 1 | 0 | 0 |
| 0 | 35 | 0 |
| 0 | 0 | 35 |
| 31 | 0 | 0 |
| 0 | 6 | 0 |
| 0 | 0 | 2 |
G:=sub<GL(3,GF(97))| [1,0,0,0,35,0,0,0,61],[1,0,0,0,35,0,0,0,35],[31,0,0,0,6,0,0,0,2] >;
C32×C48 in GAP, Magma, Sage, TeX
C_3^2\times C_{48} % in TeX
G:=Group("C3^2xC48"); // GroupNames label
G:=SmallGroup(432,232);
// by ID
G=gap.SmallGroup(432,232);
# by ID
G:=PCGroup([7,-2,-3,-3,-3,-2,-2,-2,378,102,124]);
// Polycyclic
G:=Group<a,b,c|a^3=b^3=c^48=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations