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G = C32×C48order 432 = 24·33

Abelian group of type [3,3,48]

direct product, abelian, monomial, 3-elementary

Aliases: C32×C48, SmallGroup(432,232)

Series: Derived Chief Lower central Upper central

C1 — C32×C48
C1C2C4C8C24C3×C24C32×C24 — 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 [×13], C4, C6 [×13], C8, C32 [×13], C12 [×13], C16, C3×C6 [×13], C24 [×13], C33, C3×C12 [×13], C48 [×13], C32×C6, C3×C24 [×13], C32×C12, C3×C48 [×13], C32×C24, C32×C48
Quotients: C1, C2, C3 [×13], C4, C6 [×13], C8, C32 [×13], C12 [×13], C16, C3×C6 [×13], C24 [×13], C33, C3×C12 [×13], C48 [×13], C32×C6, C3×C24 [×13], C32×C12, C3×C48 [×13], C32×C24, C32×C48

Smallest permutation representation of C32×C48
Regular action on 432 points
Generators in S432
(1 315 172)(2 316 173)(3 317 174)(4 318 175)(5 319 176)(6 320 177)(7 321 178)(8 322 179)(9 323 180)(10 324 181)(11 325 182)(12 326 183)(13 327 184)(14 328 185)(15 329 186)(16 330 187)(17 331 188)(18 332 189)(19 333 190)(20 334 191)(21 335 192)(22 336 145)(23 289 146)(24 290 147)(25 291 148)(26 292 149)(27 293 150)(28 294 151)(29 295 152)(30 296 153)(31 297 154)(32 298 155)(33 299 156)(34 300 157)(35 301 158)(36 302 159)(37 303 160)(38 304 161)(39 305 162)(40 306 163)(41 307 164)(42 308 165)(43 309 166)(44 310 167)(45 311 168)(46 312 169)(47 313 170)(48 314 171)(49 287 142)(50 288 143)(51 241 144)(52 242 97)(53 243 98)(54 244 99)(55 245 100)(56 246 101)(57 247 102)(58 248 103)(59 249 104)(60 250 105)(61 251 106)(62 252 107)(63 253 108)(64 254 109)(65 255 110)(66 256 111)(67 257 112)(68 258 113)(69 259 114)(70 260 115)(71 261 116)(72 262 117)(73 263 118)(74 264 119)(75 265 120)(76 266 121)(77 267 122)(78 268 123)(79 269 124)(80 270 125)(81 271 126)(82 272 127)(83 273 128)(84 274 129)(85 275 130)(86 276 131)(87 277 132)(88 278 133)(89 279 134)(90 280 135)(91 281 136)(92 282 137)(93 283 138)(94 284 139)(95 285 140)(96 286 141)(193 364 432)(194 365 385)(195 366 386)(196 367 387)(197 368 388)(198 369 389)(199 370 390)(200 371 391)(201 372 392)(202 373 393)(203 374 394)(204 375 395)(205 376 396)(206 377 397)(207 378 398)(208 379 399)(209 380 400)(210 381 401)(211 382 402)(212 383 403)(213 384 404)(214 337 405)(215 338 406)(216 339 407)(217 340 408)(218 341 409)(219 342 410)(220 343 411)(221 344 412)(222 345 413)(223 346 414)(224 347 415)(225 348 416)(226 349 417)(227 350 418)(228 351 419)(229 352 420)(230 353 421)(231 354 422)(232 355 423)(233 356 424)(234 357 425)(235 358 426)(236 359 427)(237 360 428)(238 361 429)(239 362 430)(240 363 431)
(1 213 278)(2 214 279)(3 215 280)(4 216 281)(5 217 282)(6 218 283)(7 219 284)(8 220 285)(9 221 286)(10 222 287)(11 223 288)(12 224 241)(13 225 242)(14 226 243)(15 227 244)(16 228 245)(17 229 246)(18 230 247)(19 231 248)(20 232 249)(21 233 250)(22 234 251)(23 235 252)(24 236 253)(25 237 254)(26 238 255)(27 239 256)(28 240 257)(29 193 258)(30 194 259)(31 195 260)(32 196 261)(33 197 262)(34 198 263)(35 199 264)(36 200 265)(37 201 266)(38 202 267)(39 203 268)(40 204 269)(41 205 270)(42 206 271)(43 207 272)(44 208 273)(45 209 274)(46 210 275)(47 211 276)(48 212 277)(49 181 413)(50 182 414)(51 183 415)(52 184 416)(53 185 417)(54 186 418)(55 187 419)(56 188 420)(57 189 421)(58 190 422)(59 191 423)(60 192 424)(61 145 425)(62 146 426)(63 147 427)(64 148 428)(65 149 429)(66 150 430)(67 151 431)(68 152 432)(69 153 385)(70 154 386)(71 155 387)(72 156 388)(73 157 389)(74 158 390)(75 159 391)(76 160 392)(77 161 393)(78 162 394)(79 163 395)(80 164 396)(81 165 397)(82 166 398)(83 167 399)(84 168 400)(85 169 401)(86 170 402)(87 171 403)(88 172 404)(89 173 405)(90 174 406)(91 175 407)(92 176 408)(93 177 409)(94 178 410)(95 179 411)(96 180 412)(97 327 348)(98 328 349)(99 329 350)(100 330 351)(101 331 352)(102 332 353)(103 333 354)(104 334 355)(105 335 356)(106 336 357)(107 289 358)(108 290 359)(109 291 360)(110 292 361)(111 293 362)(112 294 363)(113 295 364)(114 296 365)(115 297 366)(116 298 367)(117 299 368)(118 300 369)(119 301 370)(120 302 371)(121 303 372)(122 304 373)(123 305 374)(124 306 375)(125 307 376)(126 308 377)(127 309 378)(128 310 379)(129 311 380)(130 312 381)(131 313 382)(132 314 383)(133 315 384)(134 316 337)(135 317 338)(136 318 339)(137 319 340)(138 320 341)(139 321 342)(140 322 343)(141 323 344)(142 324 345)(143 325 346)(144 326 347)
(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)(337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384)(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)| (1,315,172)(2,316,173)(3,317,174)(4,318,175)(5,319,176)(6,320,177)(7,321,178)(8,322,179)(9,323,180)(10,324,181)(11,325,182)(12,326,183)(13,327,184)(14,328,185)(15,329,186)(16,330,187)(17,331,188)(18,332,189)(19,333,190)(20,334,191)(21,335,192)(22,336,145)(23,289,146)(24,290,147)(25,291,148)(26,292,149)(27,293,150)(28,294,151)(29,295,152)(30,296,153)(31,297,154)(32,298,155)(33,299,156)(34,300,157)(35,301,158)(36,302,159)(37,303,160)(38,304,161)(39,305,162)(40,306,163)(41,307,164)(42,308,165)(43,309,166)(44,310,167)(45,311,168)(46,312,169)(47,313,170)(48,314,171)(49,287,142)(50,288,143)(51,241,144)(52,242,97)(53,243,98)(54,244,99)(55,245,100)(56,246,101)(57,247,102)(58,248,103)(59,249,104)(60,250,105)(61,251,106)(62,252,107)(63,253,108)(64,254,109)(65,255,110)(66,256,111)(67,257,112)(68,258,113)(69,259,114)(70,260,115)(71,261,116)(72,262,117)(73,263,118)(74,264,119)(75,265,120)(76,266,121)(77,267,122)(78,268,123)(79,269,124)(80,270,125)(81,271,126)(82,272,127)(83,273,128)(84,274,129)(85,275,130)(86,276,131)(87,277,132)(88,278,133)(89,279,134)(90,280,135)(91,281,136)(92,282,137)(93,283,138)(94,284,139)(95,285,140)(96,286,141)(193,364,432)(194,365,385)(195,366,386)(196,367,387)(197,368,388)(198,369,389)(199,370,390)(200,371,391)(201,372,392)(202,373,393)(203,374,394)(204,375,395)(205,376,396)(206,377,397)(207,378,398)(208,379,399)(209,380,400)(210,381,401)(211,382,402)(212,383,403)(213,384,404)(214,337,405)(215,338,406)(216,339,407)(217,340,408)(218,341,409)(219,342,410)(220,343,411)(221,344,412)(222,345,413)(223,346,414)(224,347,415)(225,348,416)(226,349,417)(227,350,418)(228,351,419)(229,352,420)(230,353,421)(231,354,422)(232,355,423)(233,356,424)(234,357,425)(235,358,426)(236,359,427)(237,360,428)(238,361,429)(239,362,430)(240,363,431), (1,213,278)(2,214,279)(3,215,280)(4,216,281)(5,217,282)(6,218,283)(7,219,284)(8,220,285)(9,221,286)(10,222,287)(11,223,288)(12,224,241)(13,225,242)(14,226,243)(15,227,244)(16,228,245)(17,229,246)(18,230,247)(19,231,248)(20,232,249)(21,233,250)(22,234,251)(23,235,252)(24,236,253)(25,237,254)(26,238,255)(27,239,256)(28,240,257)(29,193,258)(30,194,259)(31,195,260)(32,196,261)(33,197,262)(34,198,263)(35,199,264)(36,200,265)(37,201,266)(38,202,267)(39,203,268)(40,204,269)(41,205,270)(42,206,271)(43,207,272)(44,208,273)(45,209,274)(46,210,275)(47,211,276)(48,212,277)(49,181,413)(50,182,414)(51,183,415)(52,184,416)(53,185,417)(54,186,418)(55,187,419)(56,188,420)(57,189,421)(58,190,422)(59,191,423)(60,192,424)(61,145,425)(62,146,426)(63,147,427)(64,148,428)(65,149,429)(66,150,430)(67,151,431)(68,152,432)(69,153,385)(70,154,386)(71,155,387)(72,156,388)(73,157,389)(74,158,390)(75,159,391)(76,160,392)(77,161,393)(78,162,394)(79,163,395)(80,164,396)(81,165,397)(82,166,398)(83,167,399)(84,168,400)(85,169,401)(86,170,402)(87,171,403)(88,172,404)(89,173,405)(90,174,406)(91,175,407)(92,176,408)(93,177,409)(94,178,410)(95,179,411)(96,180,412)(97,327,348)(98,328,349)(99,329,350)(100,330,351)(101,331,352)(102,332,353)(103,333,354)(104,334,355)(105,335,356)(106,336,357)(107,289,358)(108,290,359)(109,291,360)(110,292,361)(111,293,362)(112,294,363)(113,295,364)(114,296,365)(115,297,366)(116,298,367)(117,299,368)(118,300,369)(119,301,370)(120,302,371)(121,303,372)(122,304,373)(123,305,374)(124,306,375)(125,307,376)(126,308,377)(127,309,378)(128,310,379)(129,311,380)(130,312,381)(131,313,382)(132,314,383)(133,315,384)(134,316,337)(135,317,338)(136,318,339)(137,319,340)(138,320,341)(139,321,342)(140,322,343)(141,323,344)(142,324,345)(143,325,346)(144,326,347), (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)(337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384)(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( (1,315,172)(2,316,173)(3,317,174)(4,318,175)(5,319,176)(6,320,177)(7,321,178)(8,322,179)(9,323,180)(10,324,181)(11,325,182)(12,326,183)(13,327,184)(14,328,185)(15,329,186)(16,330,187)(17,331,188)(18,332,189)(19,333,190)(20,334,191)(21,335,192)(22,336,145)(23,289,146)(24,290,147)(25,291,148)(26,292,149)(27,293,150)(28,294,151)(29,295,152)(30,296,153)(31,297,154)(32,298,155)(33,299,156)(34,300,157)(35,301,158)(36,302,159)(37,303,160)(38,304,161)(39,305,162)(40,306,163)(41,307,164)(42,308,165)(43,309,166)(44,310,167)(45,311,168)(46,312,169)(47,313,170)(48,314,171)(49,287,142)(50,288,143)(51,241,144)(52,242,97)(53,243,98)(54,244,99)(55,245,100)(56,246,101)(57,247,102)(58,248,103)(59,249,104)(60,250,105)(61,251,106)(62,252,107)(63,253,108)(64,254,109)(65,255,110)(66,256,111)(67,257,112)(68,258,113)(69,259,114)(70,260,115)(71,261,116)(72,262,117)(73,263,118)(74,264,119)(75,265,120)(76,266,121)(77,267,122)(78,268,123)(79,269,124)(80,270,125)(81,271,126)(82,272,127)(83,273,128)(84,274,129)(85,275,130)(86,276,131)(87,277,132)(88,278,133)(89,279,134)(90,280,135)(91,281,136)(92,282,137)(93,283,138)(94,284,139)(95,285,140)(96,286,141)(193,364,432)(194,365,385)(195,366,386)(196,367,387)(197,368,388)(198,369,389)(199,370,390)(200,371,391)(201,372,392)(202,373,393)(203,374,394)(204,375,395)(205,376,396)(206,377,397)(207,378,398)(208,379,399)(209,380,400)(210,381,401)(211,382,402)(212,383,403)(213,384,404)(214,337,405)(215,338,406)(216,339,407)(217,340,408)(218,341,409)(219,342,410)(220,343,411)(221,344,412)(222,345,413)(223,346,414)(224,347,415)(225,348,416)(226,349,417)(227,350,418)(228,351,419)(229,352,420)(230,353,421)(231,354,422)(232,355,423)(233,356,424)(234,357,425)(235,358,426)(236,359,427)(237,360,428)(238,361,429)(239,362,430)(240,363,431), (1,213,278)(2,214,279)(3,215,280)(4,216,281)(5,217,282)(6,218,283)(7,219,284)(8,220,285)(9,221,286)(10,222,287)(11,223,288)(12,224,241)(13,225,242)(14,226,243)(15,227,244)(16,228,245)(17,229,246)(18,230,247)(19,231,248)(20,232,249)(21,233,250)(22,234,251)(23,235,252)(24,236,253)(25,237,254)(26,238,255)(27,239,256)(28,240,257)(29,193,258)(30,194,259)(31,195,260)(32,196,261)(33,197,262)(34,198,263)(35,199,264)(36,200,265)(37,201,266)(38,202,267)(39,203,268)(40,204,269)(41,205,270)(42,206,271)(43,207,272)(44,208,273)(45,209,274)(46,210,275)(47,211,276)(48,212,277)(49,181,413)(50,182,414)(51,183,415)(52,184,416)(53,185,417)(54,186,418)(55,187,419)(56,188,420)(57,189,421)(58,190,422)(59,191,423)(60,192,424)(61,145,425)(62,146,426)(63,147,427)(64,148,428)(65,149,429)(66,150,430)(67,151,431)(68,152,432)(69,153,385)(70,154,386)(71,155,387)(72,156,388)(73,157,389)(74,158,390)(75,159,391)(76,160,392)(77,161,393)(78,162,394)(79,163,395)(80,164,396)(81,165,397)(82,166,398)(83,167,399)(84,168,400)(85,169,401)(86,170,402)(87,171,403)(88,172,404)(89,173,405)(90,174,406)(91,175,407)(92,176,408)(93,177,409)(94,178,410)(95,179,411)(96,180,412)(97,327,348)(98,328,349)(99,329,350)(100,330,351)(101,331,352)(102,332,353)(103,333,354)(104,334,355)(105,335,356)(106,336,357)(107,289,358)(108,290,359)(109,291,360)(110,292,361)(111,293,362)(112,294,363)(113,295,364)(114,296,365)(115,297,366)(116,298,367)(117,299,368)(118,300,369)(119,301,370)(120,302,371)(121,303,372)(122,304,373)(123,305,374)(124,306,375)(125,307,376)(126,308,377)(127,309,378)(128,310,379)(129,311,380)(130,312,381)(131,313,382)(132,314,383)(133,315,384)(134,316,337)(135,317,338)(136,318,339)(137,319,340)(138,320,341)(139,321,342)(140,322,343)(141,323,344)(142,324,345)(143,325,346)(144,326,347), (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)(337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384)(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([(1,315,172),(2,316,173),(3,317,174),(4,318,175),(5,319,176),(6,320,177),(7,321,178),(8,322,179),(9,323,180),(10,324,181),(11,325,182),(12,326,183),(13,327,184),(14,328,185),(15,329,186),(16,330,187),(17,331,188),(18,332,189),(19,333,190),(20,334,191),(21,335,192),(22,336,145),(23,289,146),(24,290,147),(25,291,148),(26,292,149),(27,293,150),(28,294,151),(29,295,152),(30,296,153),(31,297,154),(32,298,155),(33,299,156),(34,300,157),(35,301,158),(36,302,159),(37,303,160),(38,304,161),(39,305,162),(40,306,163),(41,307,164),(42,308,165),(43,309,166),(44,310,167),(45,311,168),(46,312,169),(47,313,170),(48,314,171),(49,287,142),(50,288,143),(51,241,144),(52,242,97),(53,243,98),(54,244,99),(55,245,100),(56,246,101),(57,247,102),(58,248,103),(59,249,104),(60,250,105),(61,251,106),(62,252,107),(63,253,108),(64,254,109),(65,255,110),(66,256,111),(67,257,112),(68,258,113),(69,259,114),(70,260,115),(71,261,116),(72,262,117),(73,263,118),(74,264,119),(75,265,120),(76,266,121),(77,267,122),(78,268,123),(79,269,124),(80,270,125),(81,271,126),(82,272,127),(83,273,128),(84,274,129),(85,275,130),(86,276,131),(87,277,132),(88,278,133),(89,279,134),(90,280,135),(91,281,136),(92,282,137),(93,283,138),(94,284,139),(95,285,140),(96,286,141),(193,364,432),(194,365,385),(195,366,386),(196,367,387),(197,368,388),(198,369,389),(199,370,390),(200,371,391),(201,372,392),(202,373,393),(203,374,394),(204,375,395),(205,376,396),(206,377,397),(207,378,398),(208,379,399),(209,380,400),(210,381,401),(211,382,402),(212,383,403),(213,384,404),(214,337,405),(215,338,406),(216,339,407),(217,340,408),(218,341,409),(219,342,410),(220,343,411),(221,344,412),(222,345,413),(223,346,414),(224,347,415),(225,348,416),(226,349,417),(227,350,418),(228,351,419),(229,352,420),(230,353,421),(231,354,422),(232,355,423),(233,356,424),(234,357,425),(235,358,426),(236,359,427),(237,360,428),(238,361,429),(239,362,430),(240,363,431)], [(1,213,278),(2,214,279),(3,215,280),(4,216,281),(5,217,282),(6,218,283),(7,219,284),(8,220,285),(9,221,286),(10,222,287),(11,223,288),(12,224,241),(13,225,242),(14,226,243),(15,227,244),(16,228,245),(17,229,246),(18,230,247),(19,231,248),(20,232,249),(21,233,250),(22,234,251),(23,235,252),(24,236,253),(25,237,254),(26,238,255),(27,239,256),(28,240,257),(29,193,258),(30,194,259),(31,195,260),(32,196,261),(33,197,262),(34,198,263),(35,199,264),(36,200,265),(37,201,266),(38,202,267),(39,203,268),(40,204,269),(41,205,270),(42,206,271),(43,207,272),(44,208,273),(45,209,274),(46,210,275),(47,211,276),(48,212,277),(49,181,413),(50,182,414),(51,183,415),(52,184,416),(53,185,417),(54,186,418),(55,187,419),(56,188,420),(57,189,421),(58,190,422),(59,191,423),(60,192,424),(61,145,425),(62,146,426),(63,147,427),(64,148,428),(65,149,429),(66,150,430),(67,151,431),(68,152,432),(69,153,385),(70,154,386),(71,155,387),(72,156,388),(73,157,389),(74,158,390),(75,159,391),(76,160,392),(77,161,393),(78,162,394),(79,163,395),(80,164,396),(81,165,397),(82,166,398),(83,167,399),(84,168,400),(85,169,401),(86,170,402),(87,171,403),(88,172,404),(89,173,405),(90,174,406),(91,175,407),(92,176,408),(93,177,409),(94,178,410),(95,179,411),(96,180,412),(97,327,348),(98,328,349),(99,329,350),(100,330,351),(101,331,352),(102,332,353),(103,333,354),(104,334,355),(105,335,356),(106,336,357),(107,289,358),(108,290,359),(109,291,360),(110,292,361),(111,293,362),(112,294,363),(113,295,364),(114,296,365),(115,297,366),(116,298,367),(117,299,368),(118,300,369),(119,301,370),(120,302,371),(121,303,372),(122,304,373),(123,305,374),(124,306,375),(125,307,376),(126,308,377),(127,309,378),(128,310,379),(129,311,380),(130,312,381),(131,313,382),(132,314,383),(133,315,384),(134,316,337),(135,317,338),(136,318,339),(137,319,340),(138,320,341),(139,321,342),(140,322,343),(141,323,344),(142,324,345),(143,325,346),(144,326,347)], [(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),(337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384),(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···3Z4A4B6A···6Z8A8B8C8D12A···12AZ16A···16H24A···24CZ48A···48GZ
order123···3446···6888812···1216···1624···2448···48
size111···1111···111111···11···11···11···1

432 irreducible representations

dim1111111111
type++
imageC1C2C3C4C6C8C12C16C24C48
kernelC32×C48C32×C24C3×C48C32×C12C3×C24C32×C6C3×C12C33C3×C6C32
# reps11262264528104208

Matrix representation of C32×C48 in GL3(𝔽97) generated by

100
0350
0061
,
100
0350
0035
,
3100
060
002
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

׿
×
𝔽