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G = C2×C63order 432 = 24·33

Abelian group of type [2,6,6,6]

direct product, abelian, monomial

Aliases: C2×C63, SmallGroup(432,775)

Series: Derived Chief Lower central Upper central

C1 — C2×C63
C1C3C32C33C32×C6C3×C62C63 — C2×C63
C1 — C2×C63
C1 — C2×C63

Generators and relations for C2×C63
 G = < a,b,c,d | a2=b6=c6=d6=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, cd=dc >

Subgroups: 1876, all normal (4 characteristic)
C1, C2 [×15], C3 [×13], C22 [×35], C6 [×195], C23 [×15], C32 [×13], C2×C6 [×455], C24, C3×C6 [×195], C22×C6 [×195], C33, C62 [×455], C23×C6 [×13], C32×C6 [×15], C2×C62 [×195], C3×C62 [×35], C22×C62 [×13], C63 [×15], C2×C63
Quotients: C1, C2 [×15], C3 [×13], C22 [×35], C6 [×195], C23 [×15], C32 [×13], C2×C6 [×455], C24, C3×C6 [×195], C22×C6 [×195], C33, C62 [×455], C23×C6 [×13], C32×C6 [×15], C2×C62 [×195], C3×C62 [×35], C22×C62 [×13], C63 [×15], C2×C63

Smallest permutation representation of C2×C63
Regular action on 432 points
Generators in S432
(1 347)(2 348)(3 343)(4 344)(5 345)(6 346)(7 336)(8 331)(9 332)(10 333)(11 334)(12 335)(13 220)(14 221)(15 222)(16 217)(17 218)(18 219)(19 330)(20 325)(21 326)(22 327)(23 328)(24 329)(25 241)(26 242)(27 243)(28 244)(29 245)(30 246)(31 247)(32 248)(33 249)(34 250)(35 251)(36 252)(37 253)(38 254)(39 255)(40 256)(41 257)(42 258)(43 259)(44 260)(45 261)(46 262)(47 263)(48 264)(49 265)(50 266)(51 267)(52 268)(53 269)(54 270)(55 271)(56 272)(57 273)(58 274)(59 275)(60 276)(61 277)(62 278)(63 279)(64 280)(65 281)(66 282)(67 283)(68 284)(69 285)(70 286)(71 287)(72 288)(73 289)(74 290)(75 291)(76 292)(77 293)(78 294)(79 295)(80 296)(81 297)(82 298)(83 299)(84 300)(85 301)(86 302)(87 303)(88 304)(89 305)(90 306)(91 307)(92 308)(93 309)(94 310)(95 311)(96 312)(97 313)(98 314)(99 315)(100 316)(101 317)(102 318)(103 319)(104 320)(105 321)(106 322)(107 323)(108 324)(109 231)(110 232)(111 233)(112 234)(113 229)(114 230)(115 237)(116 238)(117 239)(118 240)(119 235)(120 236)(121 338)(122 339)(123 340)(124 341)(125 342)(126 337)(127 225)(128 226)(129 227)(130 228)(131 223)(132 224)(133 349)(134 350)(135 351)(136 352)(137 353)(138 354)(139 355)(140 356)(141 357)(142 358)(143 359)(144 360)(145 361)(146 362)(147 363)(148 364)(149 365)(150 366)(151 367)(152 368)(153 369)(154 370)(155 371)(156 372)(157 373)(158 374)(159 375)(160 376)(161 377)(162 378)(163 379)(164 380)(165 381)(166 382)(167 383)(168 384)(169 385)(170 386)(171 387)(172 388)(173 389)(174 390)(175 391)(176 392)(177 393)(178 394)(179 395)(180 396)(181 397)(182 398)(183 399)(184 400)(185 401)(186 402)(187 403)(188 404)(189 405)(190 406)(191 407)(192 408)(193 409)(194 410)(195 411)(196 412)(197 413)(198 414)(199 415)(200 416)(201 417)(202 418)(203 419)(204 420)(205 421)(206 422)(207 423)(208 424)(209 425)(210 426)(211 427)(212 428)(213 429)(214 430)(215 431)(216 432)
(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)
(1 156 38 35 18 161)(2 151 39 36 13 162)(3 152 40 31 14 157)(4 153 41 32 15 158)(5 154 42 33 16 159)(6 155 37 34 17 160)(7 405 282 420 130 351)(8 406 277 415 131 352)(9 407 278 416 132 353)(10 408 279 417 127 354)(11 403 280 418 128 349)(12 404 281 419 129 350)(19 298 118 315 113 414)(20 299 119 316 114 409)(21 300 120 317 109 410)(22 295 115 318 110 411)(23 296 116 313 111 412)(24 297 117 314 112 413)(25 77 48 70 143 165)(26 78 43 71 144 166)(27 73 44 72 139 167)(28 74 45 67 140 168)(29 75 46 68 141 163)(30 76 47 69 142 164)(49 150 103 123 174 178)(50 145 104 124 169 179)(51 146 105 125 170 180)(52 147 106 126 171 175)(53 148 107 121 172 176)(54 149 108 122 173 177)(55 213 181 208 96 85)(56 214 182 209 91 86)(57 215 183 210 92 87)(58 216 184 205 93 88)(59 211 185 206 94 89)(60 212 186 207 95 90)(61 199 223 136 331 190)(62 200 224 137 332 191)(63 201 225 138 333 192)(64 202 226 133 334 187)(65 203 227 134 335 188)(66 204 228 135 336 189)(79 237 102 232 195 327)(80 238 97 233 196 328)(81 239 98 234 197 329)(82 240 99 229 198 330)(83 235 100 230 193 325)(84 236 101 231 194 326)(217 375 345 370 258 249)(218 376 346 371 253 250)(219 377 347 372 254 251)(220 378 348 367 255 252)(221 373 343 368 256 247)(222 374 344 369 257 248)(241 293 264 286 359 381)(242 294 259 287 360 382)(243 289 260 288 355 383)(244 290 261 283 356 384)(245 291 262 284 357 379)(246 292 263 285 358 380)(265 366 319 340 390 394)(266 361 320 341 385 395)(267 362 321 342 386 396)(268 363 322 337 387 391)(269 364 323 338 388 392)(270 365 324 339 389 393)(271 429 397 424 312 301)(272 430 398 425 307 302)(273 431 399 426 308 303)(274 432 400 421 309 304)(275 427 401 422 310 305)(276 428 402 423 311 306)
(1 191 59 139 148 100)(2 192 60 140 149 101)(3 187 55 141 150 102)(4 188 56 142 145 97)(5 189 57 143 146 98)(6 190 58 144 147 99)(7 303 286 267 117 375)(8 304 287 268 118 376)(9 305 288 269 119 377)(10 306 283 270 120 378)(11 301 284 265 115 373)(12 302 285 266 116 374)(13 138 95 45 177 84)(14 133 96 46 178 79)(15 134 91 47 179 80)(16 135 92 48 180 81)(17 136 93 43 175 82)(18 137 94 44 176 83)(19 250 131 421 294 387)(20 251 132 422 289 388)(21 252 127 423 290 389)(22 247 128 424 291 390)(23 248 129 425 292 385)(24 249 130 426 293 386)(25 125 197 42 204 183)(26 126 198 37 199 184)(27 121 193 38 200 185)(28 122 194 39 201 186)(29 123 195 40 202 181)(30 124 196 41 203 182)(31 226 208 75 174 327)(32 227 209 76 169 328)(33 228 210 77 170 329)(34 223 205 78 171 330)(35 224 206 73 172 325)(36 225 207 74 173 326)(49 237 157 334 85 68)(50 238 158 335 86 69)(51 239 159 336 87 70)(52 240 160 331 88 71)(53 235 161 332 89 72)(54 236 162 333 90 67)(61 216 166 106 229 155)(62 211 167 107 230 156)(63 212 168 108 231 151)(64 213 163 103 232 152)(65 214 164 104 233 153)(66 215 165 105 234 154)(109 367 279 428 384 324)(110 368 280 429 379 319)(111 369 281 430 380 320)(112 370 282 431 381 321)(113 371 277 432 382 322)(114 372 278 427 383 323)(217 351 308 264 396 297)(218 352 309 259 391 298)(219 353 310 260 392 299)(220 354 311 261 393 300)(221 349 312 262 394 295)(222 350 307 263 395 296)(241 342 413 258 420 399)(242 337 414 253 415 400)(243 338 409 254 416 401)(244 339 410 255 417 402)(245 340 411 256 418 397)(246 341 412 257 419 398)(271 357 366 318 343 403)(272 358 361 313 344 404)(273 359 362 314 345 405)(274 360 363 315 346 406)(275 355 364 316 347 407)(276 356 365 317 348 408)

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

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

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

432 conjugacy classes

class 1 2A···2O3A···3Z6A···6NZ
order12···23···36···6
size11···11···11···1

432 irreducible representations

dim1111
type++
imageC1C2C3C6
kernelC2×C63C63C22×C62C2×C62
# reps11526390

Matrix representation of C2×C63 in GL4(𝔽7) generated by

6000
0600
0060
0001
,
6000
0600
0040
0004
,
6000
0500
0020
0005
,
3000
0200
0060
0005
G:=sub<GL(4,GF(7))| [6,0,0,0,0,6,0,0,0,0,6,0,0,0,0,1],[6,0,0,0,0,6,0,0,0,0,4,0,0,0,0,4],[6,0,0,0,0,5,0,0,0,0,2,0,0,0,0,5],[3,0,0,0,0,2,0,0,0,0,6,0,0,0,0,5] >;

C2×C63 in GAP, Magma, Sage, TeX

C_2\times C_6^3
% in TeX

G:=Group("C2xC6^3");
// GroupNames label

G:=SmallGroup(432,775);
// by ID

G=gap.SmallGroup(432,775);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^6=c^6=d^6=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