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## G = C62×C12order 432 = 24·33

### Abelian group of type [6,6,12]

Aliases: C62×C12, SmallGroup(432,730)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C62×C12
 Chief series C1 — C2 — C6 — C3×C6 — C32×C6 — C32×C12 — C3×C6×C12 — C62×C12
 Lower central C1 — C62×C12
 Upper central C1 — C62×C12

Generators and relations for C62×C12
G = < a,b,c | a6=b6=c12=1, ab=ba, ac=ca, bc=cb >

Subgroups: 756, all normal (8 characteristic)
C1, C2, C2 [×6], C3 [×13], C4 [×4], C22 [×7], C6 [×91], C2×C4 [×6], C23, C32 [×13], C12 [×52], C2×C6 [×91], C22×C4, C3×C6 [×91], C2×C12 [×78], C22×C6 [×13], C33, C3×C12 [×52], C62 [×91], C22×C12 [×13], C32×C6, C32×C6 [×6], C6×C12 [×78], C2×C62 [×13], C32×C12 [×4], C3×C62 [×7], C2×C6×C12 [×13], C3×C6×C12 [×6], C63, C62×C12
Quotients: C1, C2 [×7], C3 [×13], C4 [×4], C22 [×7], C6 [×91], C2×C4 [×6], C23, C32 [×13], C12 [×52], C2×C6 [×91], C22×C4, C3×C6 [×91], C2×C12 [×78], C22×C6 [×13], C33, C3×C12 [×52], C62 [×91], C22×C12 [×13], C32×C6 [×7], C6×C12 [×78], C2×C62 [×13], C32×C12 [×4], C3×C62 [×7], C2×C6×C12 [×13], C3×C6×C12 [×6], C63, C62×C12

Smallest permutation representation of C62×C12
Regular action on 432 points
Generators in S432
(1 395 243 279 129 85)(2 396 244 280 130 86)(3 385 245 281 131 87)(4 386 246 282 132 88)(5 387 247 283 121 89)(6 388 248 284 122 90)(7 389 249 285 123 91)(8 390 250 286 124 92)(9 391 251 287 125 93)(10 392 252 288 126 94)(11 393 241 277 127 95)(12 394 242 278 128 96)(13 255 213 61 97 371)(14 256 214 62 98 372)(15 257 215 63 99 361)(16 258 216 64 100 362)(17 259 205 65 101 363)(18 260 206 66 102 364)(19 261 207 67 103 365)(20 262 208 68 104 366)(21 263 209 69 105 367)(22 264 210 70 106 368)(23 253 211 71 107 369)(24 254 212 72 108 370)(25 407 335 291 141 177)(26 408 336 292 142 178)(27 397 325 293 143 179)(28 398 326 294 144 180)(29 399 327 295 133 169)(30 400 328 296 134 170)(31 401 329 297 135 171)(32 402 330 298 136 172)(33 403 331 299 137 173)(34 404 332 300 138 174)(35 405 333 289 139 175)(36 406 334 290 140 176)(37 73 347 303 231 189)(38 74 348 304 232 190)(39 75 337 305 233 191)(40 76 338 306 234 192)(41 77 339 307 235 181)(42 78 340 308 236 182)(43 79 341 309 237 183)(44 80 342 310 238 184)(45 81 343 311 239 185)(46 82 344 312 240 186)(47 83 345 301 229 187)(48 84 346 302 230 188)(49 431 359 315 165 201)(50 432 360 316 166 202)(51 421 349 317 167 203)(52 422 350 318 168 204)(53 423 351 319 157 193)(54 424 352 320 158 194)(55 425 353 321 159 195)(56 426 354 322 160 196)(57 427 355 323 161 197)(58 428 356 324 162 198)(59 429 357 313 163 199)(60 430 358 314 164 200)(109 383 419 267 221 153)(110 384 420 268 222 154)(111 373 409 269 223 155)(112 374 410 270 224 156)(113 375 411 271 225 145)(114 376 412 272 226 146)(115 377 413 273 227 147)(116 378 414 274 228 148)(117 379 415 275 217 149)(118 380 416 276 218 150)(119 381 417 265 219 151)(120 382 418 266 220 152)
(1 255 231 359 335 153)(2 256 232 360 336 154)(3 257 233 349 325 155)(4 258 234 350 326 156)(5 259 235 351 327 145)(6 260 236 352 328 146)(7 261 237 353 329 147)(8 262 238 354 330 148)(9 263 239 355 331 149)(10 264 240 356 332 150)(11 253 229 357 333 151)(12 254 230 358 334 152)(13 303 431 407 221 85)(14 304 432 408 222 86)(15 305 421 397 223 87)(16 306 422 398 224 88)(17 307 423 399 225 89)(18 308 424 400 226 90)(19 309 425 401 227 91)(20 310 426 402 228 92)(21 311 427 403 217 93)(22 312 428 404 218 94)(23 301 429 405 219 95)(24 302 430 406 220 96)(25 267 129 371 347 49)(26 268 130 372 348 50)(27 269 131 361 337 51)(28 270 132 362 338 52)(29 271 121 363 339 53)(30 272 122 364 340 54)(31 273 123 365 341 55)(32 274 124 366 342 56)(33 275 125 367 343 57)(34 276 126 368 344 58)(35 265 127 369 345 59)(36 266 128 370 346 60)(37 165 141 383 243 61)(38 166 142 384 244 62)(39 167 143 373 245 63)(40 168 144 374 246 64)(41 157 133 375 247 65)(42 158 134 376 248 66)(43 159 135 377 249 67)(44 160 136 378 250 68)(45 161 137 379 251 69)(46 162 138 380 252 70)(47 163 139 381 241 71)(48 164 140 382 242 72)(73 201 177 419 279 97)(74 202 178 420 280 98)(75 203 179 409 281 99)(76 204 180 410 282 100)(77 193 169 411 283 101)(78 194 170 412 284 102)(79 195 171 413 285 103)(80 196 172 414 286 104)(81 197 173 415 287 105)(82 198 174 416 288 106)(83 199 175 417 277 107)(84 200 176 418 278 108)(109 395 213 189 315 291)(110 396 214 190 316 292)(111 385 215 191 317 293)(112 386 216 192 318 294)(113 387 205 181 319 295)(114 388 206 182 320 296)(115 389 207 183 321 297)(116 390 208 184 322 298)(117 391 209 185 323 299)(118 392 210 186 324 300)(119 393 211 187 313 289)(120 394 212 188 314 290)
(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)| (1,395,243,279,129,85)(2,396,244,280,130,86)(3,385,245,281,131,87)(4,386,246,282,132,88)(5,387,247,283,121,89)(6,388,248,284,122,90)(7,389,249,285,123,91)(8,390,250,286,124,92)(9,391,251,287,125,93)(10,392,252,288,126,94)(11,393,241,277,127,95)(12,394,242,278,128,96)(13,255,213,61,97,371)(14,256,214,62,98,372)(15,257,215,63,99,361)(16,258,216,64,100,362)(17,259,205,65,101,363)(18,260,206,66,102,364)(19,261,207,67,103,365)(20,262,208,68,104,366)(21,263,209,69,105,367)(22,264,210,70,106,368)(23,253,211,71,107,369)(24,254,212,72,108,370)(25,407,335,291,141,177)(26,408,336,292,142,178)(27,397,325,293,143,179)(28,398,326,294,144,180)(29,399,327,295,133,169)(30,400,328,296,134,170)(31,401,329,297,135,171)(32,402,330,298,136,172)(33,403,331,299,137,173)(34,404,332,300,138,174)(35,405,333,289,139,175)(36,406,334,290,140,176)(37,73,347,303,231,189)(38,74,348,304,232,190)(39,75,337,305,233,191)(40,76,338,306,234,192)(41,77,339,307,235,181)(42,78,340,308,236,182)(43,79,341,309,237,183)(44,80,342,310,238,184)(45,81,343,311,239,185)(46,82,344,312,240,186)(47,83,345,301,229,187)(48,84,346,302,230,188)(49,431,359,315,165,201)(50,432,360,316,166,202)(51,421,349,317,167,203)(52,422,350,318,168,204)(53,423,351,319,157,193)(54,424,352,320,158,194)(55,425,353,321,159,195)(56,426,354,322,160,196)(57,427,355,323,161,197)(58,428,356,324,162,198)(59,429,357,313,163,199)(60,430,358,314,164,200)(109,383,419,267,221,153)(110,384,420,268,222,154)(111,373,409,269,223,155)(112,374,410,270,224,156)(113,375,411,271,225,145)(114,376,412,272,226,146)(115,377,413,273,227,147)(116,378,414,274,228,148)(117,379,415,275,217,149)(118,380,416,276,218,150)(119,381,417,265,219,151)(120,382,418,266,220,152), (1,255,231,359,335,153)(2,256,232,360,336,154)(3,257,233,349,325,155)(4,258,234,350,326,156)(5,259,235,351,327,145)(6,260,236,352,328,146)(7,261,237,353,329,147)(8,262,238,354,330,148)(9,263,239,355,331,149)(10,264,240,356,332,150)(11,253,229,357,333,151)(12,254,230,358,334,152)(13,303,431,407,221,85)(14,304,432,408,222,86)(15,305,421,397,223,87)(16,306,422,398,224,88)(17,307,423,399,225,89)(18,308,424,400,226,90)(19,309,425,401,227,91)(20,310,426,402,228,92)(21,311,427,403,217,93)(22,312,428,404,218,94)(23,301,429,405,219,95)(24,302,430,406,220,96)(25,267,129,371,347,49)(26,268,130,372,348,50)(27,269,131,361,337,51)(28,270,132,362,338,52)(29,271,121,363,339,53)(30,272,122,364,340,54)(31,273,123,365,341,55)(32,274,124,366,342,56)(33,275,125,367,343,57)(34,276,126,368,344,58)(35,265,127,369,345,59)(36,266,128,370,346,60)(37,165,141,383,243,61)(38,166,142,384,244,62)(39,167,143,373,245,63)(40,168,144,374,246,64)(41,157,133,375,247,65)(42,158,134,376,248,66)(43,159,135,377,249,67)(44,160,136,378,250,68)(45,161,137,379,251,69)(46,162,138,380,252,70)(47,163,139,381,241,71)(48,164,140,382,242,72)(73,201,177,419,279,97)(74,202,178,420,280,98)(75,203,179,409,281,99)(76,204,180,410,282,100)(77,193,169,411,283,101)(78,194,170,412,284,102)(79,195,171,413,285,103)(80,196,172,414,286,104)(81,197,173,415,287,105)(82,198,174,416,288,106)(83,199,175,417,277,107)(84,200,176,418,278,108)(109,395,213,189,315,291)(110,396,214,190,316,292)(111,385,215,191,317,293)(112,386,216,192,318,294)(113,387,205,181,319,295)(114,388,206,182,320,296)(115,389,207,183,321,297)(116,390,208,184,322,298)(117,391,209,185,323,299)(118,392,210,186,324,300)(119,393,211,187,313,289)(120,394,212,188,314,290), (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( (1,395,243,279,129,85)(2,396,244,280,130,86)(3,385,245,281,131,87)(4,386,246,282,132,88)(5,387,247,283,121,89)(6,388,248,284,122,90)(7,389,249,285,123,91)(8,390,250,286,124,92)(9,391,251,287,125,93)(10,392,252,288,126,94)(11,393,241,277,127,95)(12,394,242,278,128,96)(13,255,213,61,97,371)(14,256,214,62,98,372)(15,257,215,63,99,361)(16,258,216,64,100,362)(17,259,205,65,101,363)(18,260,206,66,102,364)(19,261,207,67,103,365)(20,262,208,68,104,366)(21,263,209,69,105,367)(22,264,210,70,106,368)(23,253,211,71,107,369)(24,254,212,72,108,370)(25,407,335,291,141,177)(26,408,336,292,142,178)(27,397,325,293,143,179)(28,398,326,294,144,180)(29,399,327,295,133,169)(30,400,328,296,134,170)(31,401,329,297,135,171)(32,402,330,298,136,172)(33,403,331,299,137,173)(34,404,332,300,138,174)(35,405,333,289,139,175)(36,406,334,290,140,176)(37,73,347,303,231,189)(38,74,348,304,232,190)(39,75,337,305,233,191)(40,76,338,306,234,192)(41,77,339,307,235,181)(42,78,340,308,236,182)(43,79,341,309,237,183)(44,80,342,310,238,184)(45,81,343,311,239,185)(46,82,344,312,240,186)(47,83,345,301,229,187)(48,84,346,302,230,188)(49,431,359,315,165,201)(50,432,360,316,166,202)(51,421,349,317,167,203)(52,422,350,318,168,204)(53,423,351,319,157,193)(54,424,352,320,158,194)(55,425,353,321,159,195)(56,426,354,322,160,196)(57,427,355,323,161,197)(58,428,356,324,162,198)(59,429,357,313,163,199)(60,430,358,314,164,200)(109,383,419,267,221,153)(110,384,420,268,222,154)(111,373,409,269,223,155)(112,374,410,270,224,156)(113,375,411,271,225,145)(114,376,412,272,226,146)(115,377,413,273,227,147)(116,378,414,274,228,148)(117,379,415,275,217,149)(118,380,416,276,218,150)(119,381,417,265,219,151)(120,382,418,266,220,152), (1,255,231,359,335,153)(2,256,232,360,336,154)(3,257,233,349,325,155)(4,258,234,350,326,156)(5,259,235,351,327,145)(6,260,236,352,328,146)(7,261,237,353,329,147)(8,262,238,354,330,148)(9,263,239,355,331,149)(10,264,240,356,332,150)(11,253,229,357,333,151)(12,254,230,358,334,152)(13,303,431,407,221,85)(14,304,432,408,222,86)(15,305,421,397,223,87)(16,306,422,398,224,88)(17,307,423,399,225,89)(18,308,424,400,226,90)(19,309,425,401,227,91)(20,310,426,402,228,92)(21,311,427,403,217,93)(22,312,428,404,218,94)(23,301,429,405,219,95)(24,302,430,406,220,96)(25,267,129,371,347,49)(26,268,130,372,348,50)(27,269,131,361,337,51)(28,270,132,362,338,52)(29,271,121,363,339,53)(30,272,122,364,340,54)(31,273,123,365,341,55)(32,274,124,366,342,56)(33,275,125,367,343,57)(34,276,126,368,344,58)(35,265,127,369,345,59)(36,266,128,370,346,60)(37,165,141,383,243,61)(38,166,142,384,244,62)(39,167,143,373,245,63)(40,168,144,374,246,64)(41,157,133,375,247,65)(42,158,134,376,248,66)(43,159,135,377,249,67)(44,160,136,378,250,68)(45,161,137,379,251,69)(46,162,138,380,252,70)(47,163,139,381,241,71)(48,164,140,382,242,72)(73,201,177,419,279,97)(74,202,178,420,280,98)(75,203,179,409,281,99)(76,204,180,410,282,100)(77,193,169,411,283,101)(78,194,170,412,284,102)(79,195,171,413,285,103)(80,196,172,414,286,104)(81,197,173,415,287,105)(82,198,174,416,288,106)(83,199,175,417,277,107)(84,200,176,418,278,108)(109,395,213,189,315,291)(110,396,214,190,316,292)(111,385,215,191,317,293)(112,386,216,192,318,294)(113,387,205,181,319,295)(114,388,206,182,320,296)(115,389,207,183,321,297)(116,390,208,184,322,298)(117,391,209,185,323,299)(118,392,210,186,324,300)(119,393,211,187,313,289)(120,394,212,188,314,290), (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([(1,395,243,279,129,85),(2,396,244,280,130,86),(3,385,245,281,131,87),(4,386,246,282,132,88),(5,387,247,283,121,89),(6,388,248,284,122,90),(7,389,249,285,123,91),(8,390,250,286,124,92),(9,391,251,287,125,93),(10,392,252,288,126,94),(11,393,241,277,127,95),(12,394,242,278,128,96),(13,255,213,61,97,371),(14,256,214,62,98,372),(15,257,215,63,99,361),(16,258,216,64,100,362),(17,259,205,65,101,363),(18,260,206,66,102,364),(19,261,207,67,103,365),(20,262,208,68,104,366),(21,263,209,69,105,367),(22,264,210,70,106,368),(23,253,211,71,107,369),(24,254,212,72,108,370),(25,407,335,291,141,177),(26,408,336,292,142,178),(27,397,325,293,143,179),(28,398,326,294,144,180),(29,399,327,295,133,169),(30,400,328,296,134,170),(31,401,329,297,135,171),(32,402,330,298,136,172),(33,403,331,299,137,173),(34,404,332,300,138,174),(35,405,333,289,139,175),(36,406,334,290,140,176),(37,73,347,303,231,189),(38,74,348,304,232,190),(39,75,337,305,233,191),(40,76,338,306,234,192),(41,77,339,307,235,181),(42,78,340,308,236,182),(43,79,341,309,237,183),(44,80,342,310,238,184),(45,81,343,311,239,185),(46,82,344,312,240,186),(47,83,345,301,229,187),(48,84,346,302,230,188),(49,431,359,315,165,201),(50,432,360,316,166,202),(51,421,349,317,167,203),(52,422,350,318,168,204),(53,423,351,319,157,193),(54,424,352,320,158,194),(55,425,353,321,159,195),(56,426,354,322,160,196),(57,427,355,323,161,197),(58,428,356,324,162,198),(59,429,357,313,163,199),(60,430,358,314,164,200),(109,383,419,267,221,153),(110,384,420,268,222,154),(111,373,409,269,223,155),(112,374,410,270,224,156),(113,375,411,271,225,145),(114,376,412,272,226,146),(115,377,413,273,227,147),(116,378,414,274,228,148),(117,379,415,275,217,149),(118,380,416,276,218,150),(119,381,417,265,219,151),(120,382,418,266,220,152)], [(1,255,231,359,335,153),(2,256,232,360,336,154),(3,257,233,349,325,155),(4,258,234,350,326,156),(5,259,235,351,327,145),(6,260,236,352,328,146),(7,261,237,353,329,147),(8,262,238,354,330,148),(9,263,239,355,331,149),(10,264,240,356,332,150),(11,253,229,357,333,151),(12,254,230,358,334,152),(13,303,431,407,221,85),(14,304,432,408,222,86),(15,305,421,397,223,87),(16,306,422,398,224,88),(17,307,423,399,225,89),(18,308,424,400,226,90),(19,309,425,401,227,91),(20,310,426,402,228,92),(21,311,427,403,217,93),(22,312,428,404,218,94),(23,301,429,405,219,95),(24,302,430,406,220,96),(25,267,129,371,347,49),(26,268,130,372,348,50),(27,269,131,361,337,51),(28,270,132,362,338,52),(29,271,121,363,339,53),(30,272,122,364,340,54),(31,273,123,365,341,55),(32,274,124,366,342,56),(33,275,125,367,343,57),(34,276,126,368,344,58),(35,265,127,369,345,59),(36,266,128,370,346,60),(37,165,141,383,243,61),(38,166,142,384,244,62),(39,167,143,373,245,63),(40,168,144,374,246,64),(41,157,133,375,247,65),(42,158,134,376,248,66),(43,159,135,377,249,67),(44,160,136,378,250,68),(45,161,137,379,251,69),(46,162,138,380,252,70),(47,163,139,381,241,71),(48,164,140,382,242,72),(73,201,177,419,279,97),(74,202,178,420,280,98),(75,203,179,409,281,99),(76,204,180,410,282,100),(77,193,169,411,283,101),(78,194,170,412,284,102),(79,195,171,413,285,103),(80,196,172,414,286,104),(81,197,173,415,287,105),(82,198,174,416,288,106),(83,199,175,417,277,107),(84,200,176,418,278,108),(109,395,213,189,315,291),(110,396,214,190,316,292),(111,385,215,191,317,293),(112,386,216,192,318,294),(113,387,205,181,319,295),(114,388,206,182,320,296),(115,389,207,183,321,297),(116,390,208,184,322,298),(117,391,209,185,323,299),(118,392,210,186,324,300),(119,393,211,187,313,289),(120,394,212,188,314,290)], [(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 2A ··· 2G 3A ··· 3Z 4A ··· 4H 6A ··· 6FZ 12A ··· 12GZ order 1 2 ··· 2 3 ··· 3 4 ··· 4 6 ··· 6 12 ··· 12 size 1 1 ··· 1 1 ··· 1 1 ··· 1 1 ··· 1 1 ··· 1

432 irreducible representations

 dim 1 1 1 1 1 1 1 1 type + + + image C1 C2 C2 C3 C4 C6 C6 C12 kernel C62×C12 C3×C6×C12 C63 C2×C6×C12 C3×C62 C6×C12 C2×C62 C62 # reps 1 6 1 26 8 156 26 208

Matrix representation of C62×C12 in GL3(𝔽13) generated by

 4 0 0 0 4 0 0 0 9
,
 12 0 0 0 1 0 0 0 4
,
 11 0 0 0 9 0 0 0 3
G:=sub<GL(3,GF(13))| [4,0,0,0,4,0,0,0,9],[12,0,0,0,1,0,0,0,4],[11,0,0,0,9,0,0,0,3] >;

C62×C12 in GAP, Magma, Sage, TeX

C_6^2\times C_{12}
% in TeX

G:=Group("C6^2xC12");
// GroupNames label

G:=SmallGroup(432,730);
// by ID

G=gap.SmallGroup(432,730);
# by ID

G:=PCGroup([7,-2,-2,-2,-3,-3,-3,-2,1512]);
// Polycyclic

G:=Group<a,b,c|a^6=b^6=c^12=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations

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