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G = C62.147D6order 432 = 24·33

31st non-split extension by C62 of D6 acting via D6/C6=C2

metabelian, supersoluble, monomial

Aliases: C62.147D6, C4⋊(C335C4), C3321(C4⋊C4), (C6×C12).33S3, (C32×C12)⋊5C4, (C3×C12)⋊7Dic3, (C3×C6).69D12, C121(C3⋊Dic3), (C3×C6).31Dic6, (C32×C6).64D4, (C32×C6).15Q8, C6.10(C12⋊S3), C32(C12⋊Dic3), C6.8(C324Q8), C2.2(C338Q8), C3212(C4⋊Dic3), C2.1(C3312D4), (C3×C62).53C22, (C3×C6×C12).4C2, C6.15(C2×C3⋊Dic3), C2.4(C2×C335C4), (C2×C12).10(C3⋊S3), (C32×C6).74(C2×C4), (C2×C335C4).6C2, (C3×C6).74(C2×Dic3), (C2×C4).3(C33⋊C2), C22.5(C2×C33⋊C2), (C2×C6).42(C2×C3⋊S3), SmallGroup(432,505)

Series: Derived Chief Lower central Upper central

C1C32×C6 — C62.147D6
C1C3C32C33C32×C6C3×C62C2×C335C4 — C62.147D6
C33C32×C6 — C62.147D6
C1C22C2×C4

Generators and relations for C62.147D6
 G = < a,b,c,d | a6=b6=1, c6=b3, d2=a3, ab=ba, ac=ca, dad-1=a-1, bc=cb, dbd-1=b-1, dcd-1=b3c5 >

Subgroups: 1512 in 364 conjugacy classes, 227 normal (13 characteristic)
C1, C2 [×3], C3 [×13], C4 [×2], C4 [×2], C22, C6 [×39], C2×C4, C2×C4 [×2], C32 [×13], Dic3 [×26], C12 [×26], C2×C6 [×13], C4⋊C4, C3×C6 [×39], C2×Dic3 [×26], C2×C12 [×13], C33, C3⋊Dic3 [×26], C3×C12 [×26], C62 [×13], C4⋊Dic3 [×13], C32×C6 [×3], C2×C3⋊Dic3 [×26], C6×C12 [×13], C335C4 [×2], C32×C12 [×2], C3×C62, C12⋊Dic3 [×13], C2×C335C4 [×2], C3×C6×C12, C62.147D6
Quotients: C1, C2 [×3], C4 [×2], C22, S3 [×13], C2×C4, D4, Q8, Dic3 [×26], D6 [×13], C4⋊C4, C3⋊S3 [×13], Dic6 [×13], D12 [×13], C2×Dic3 [×13], C3⋊Dic3 [×26], C2×C3⋊S3 [×13], C4⋊Dic3 [×13], C33⋊C2, C324Q8 [×13], C12⋊S3 [×13], C2×C3⋊Dic3 [×13], C335C4 [×2], C2×C33⋊C2, C12⋊Dic3 [×13], C338Q8, C3312D4, C2×C335C4, C62.147D6

Smallest permutation representation of C62.147D6
Regular action on 432 points
Generators in S432
(1 122 119 361 91 108)(2 123 120 362 92 97)(3 124 109 363 93 98)(4 125 110 364 94 99)(5 126 111 365 95 100)(6 127 112 366 96 101)(7 128 113 367 85 102)(8 129 114 368 86 103)(9 130 115 369 87 104)(10 131 116 370 88 105)(11 132 117 371 89 106)(12 121 118 372 90 107)(13 292 270 166 28 188)(14 293 271 167 29 189)(15 294 272 168 30 190)(16 295 273 157 31 191)(17 296 274 158 32 192)(18 297 275 159 33 181)(19 298 276 160 34 182)(20 299 265 161 35 183)(21 300 266 162 36 184)(22 289 267 163 25 185)(23 290 268 164 26 186)(24 291 269 165 27 187)(37 223 355 262 310 146)(38 224 356 263 311 147)(39 225 357 264 312 148)(40 226 358 253 301 149)(41 227 359 254 302 150)(42 228 360 255 303 151)(43 217 349 256 304 152)(44 218 350 257 305 153)(45 219 351 258 306 154)(46 220 352 259 307 155)(47 221 353 260 308 156)(48 222 354 261 309 145)(49 392 234 203 339 142)(50 393 235 204 340 143)(51 394 236 193 341 144)(52 395 237 194 342 133)(53 396 238 195 343 134)(54 385 239 196 344 135)(55 386 240 197 345 136)(56 387 229 198 346 137)(57 388 230 199 347 138)(58 389 231 200 348 139)(59 390 232 201 337 140)(60 391 233 202 338 141)(61 378 74 214 406 250)(62 379 75 215 407 251)(63 380 76 216 408 252)(64 381 77 205 397 241)(65 382 78 206 398 242)(66 383 79 207 399 243)(67 384 80 208 400 244)(68 373 81 209 401 245)(69 374 82 210 402 246)(70 375 83 211 403 247)(71 376 84 212 404 248)(72 377 73 213 405 249)(169 328 313 424 415 277)(170 329 314 425 416 278)(171 330 315 426 417 279)(172 331 316 427 418 280)(173 332 317 428 419 281)(174 333 318 429 420 282)(175 334 319 430 409 283)(176 335 320 431 410 284)(177 336 321 432 411 285)(178 325 322 421 412 286)(179 326 323 422 413 287)(180 327 324 423 414 288)
(1 221 17 7 227 23)(2 222 18 8 228 24)(3 223 19 9 217 13)(4 224 20 10 218 14)(5 225 21 11 219 15)(6 226 22 12 220 16)(25 90 155 31 96 149)(26 91 156 32 85 150)(27 92 145 33 86 151)(28 93 146 34 87 152)(29 94 147 35 88 153)(30 95 148 36 89 154)(37 182 104 43 188 98)(38 183 105 44 189 99)(39 184 106 45 190 100)(40 185 107 46 191 101)(41 186 108 47 192 102)(42 187 97 48 181 103)(49 424 81 55 430 75)(50 425 82 56 431 76)(51 426 83 57 432 77)(52 427 84 58 421 78)(53 428 73 59 422 79)(54 429 74 60 423 80)(61 338 327 67 344 333)(62 339 328 68 345 334)(63 340 329 69 346 335)(64 341 330 70 347 336)(65 342 331 71 348 325)(66 343 332 72 337 326)(109 262 276 115 256 270)(110 263 265 116 257 271)(111 264 266 117 258 272)(112 253 267 118 259 273)(113 254 268 119 260 274)(114 255 269 120 261 275)(121 352 295 127 358 289)(122 353 296 128 359 290)(123 354 297 129 360 291)(124 355 298 130 349 292)(125 356 299 131 350 293)(126 357 300 132 351 294)(133 316 376 139 322 382)(134 317 377 140 323 383)(135 318 378 141 324 384)(136 319 379 142 313 373)(137 320 380 143 314 374)(138 321 381 144 315 375)(157 366 301 163 372 307)(158 367 302 164 361 308)(159 368 303 165 362 309)(160 369 304 166 363 310)(161 370 305 167 364 311)(162 371 306 168 365 312)(169 245 197 175 251 203)(170 246 198 176 252 204)(171 247 199 177 241 193)(172 248 200 178 242 194)(173 249 201 179 243 195)(174 250 202 180 244 196)(205 394 417 211 388 411)(206 395 418 212 389 412)(207 396 419 213 390 413)(208 385 420 214 391 414)(209 386 409 215 392 415)(210 387 410 216 393 416)(229 284 408 235 278 402)(230 285 397 236 279 403)(231 286 398 237 280 404)(232 287 399 238 281 405)(233 288 400 239 282 406)(234 277 401 240 283 407)
(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)
(1 140 361 232)(2 139 362 231)(3 138 363 230)(4 137 364 229)(5 136 365 240)(6 135 366 239)(7 134 367 238)(8 133 368 237)(9 144 369 236)(10 143 370 235)(11 142 371 234)(12 141 372 233)(13 321 166 285)(14 320 167 284)(15 319 168 283)(16 318 157 282)(17 317 158 281)(18 316 159 280)(19 315 160 279)(20 314 161 278)(21 313 162 277)(22 324 163 288)(23 323 164 287)(24 322 165 286)(25 414 289 327)(26 413 290 326)(27 412 291 325)(28 411 292 336)(29 410 293 335)(30 409 294 334)(31 420 295 333)(32 419 296 332)(33 418 297 331)(34 417 298 330)(35 416 299 329)(36 415 300 328)(37 83 262 247)(38 82 263 246)(39 81 264 245)(40 80 253 244)(41 79 254 243)(42 78 255 242)(43 77 256 241)(44 76 257 252)(45 75 258 251)(46 74 259 250)(47 73 260 249)(48 84 261 248)(49 117 203 106)(50 116 204 105)(51 115 193 104)(52 114 194 103)(53 113 195 102)(54 112 196 101)(55 111 197 100)(56 110 198 99)(57 109 199 98)(58 120 200 97)(59 119 201 108)(60 118 202 107)(61 155 214 352)(62 154 215 351)(63 153 216 350)(64 152 205 349)(65 151 206 360)(66 150 207 359)(67 149 208 358)(68 148 209 357)(69 147 210 356)(70 146 211 355)(71 145 212 354)(72 156 213 353)(85 396 128 343)(86 395 129 342)(87 394 130 341)(88 393 131 340)(89 392 132 339)(90 391 121 338)(91 390 122 337)(92 389 123 348)(93 388 124 347)(94 387 125 346)(95 386 126 345)(96 385 127 344)(169 184 424 266)(170 183 425 265)(171 182 426 276)(172 181 427 275)(173 192 428 274)(174 191 429 273)(175 190 430 272)(176 189 431 271)(177 188 432 270)(178 187 421 269)(179 186 422 268)(180 185 423 267)(217 381 304 397)(218 380 305 408)(219 379 306 407)(220 378 307 406)(221 377 308 405)(222 376 309 404)(223 375 310 403)(224 374 311 402)(225 373 312 401)(226 384 301 400)(227 383 302 399)(228 382 303 398)

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

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

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

114 conjugacy classes

class 1 2A2B2C3A···3M4A4B4C4D4E4F6A···6AM12A···12AZ
order12223···34444446···612···12
size11112···222545454542···22···2

114 irreducible representations

dim11112222222
type+++++--+-+
imageC1C2C2C4S3D4Q8Dic3D6Dic6D12
kernelC62.147D6C2×C335C4C3×C6×C12C32×C12C6×C12C32×C6C32×C6C3×C12C62C3×C6C3×C6
# reps1214131126132626

Matrix representation of C62.147D6 in GL7(𝔽13)

12000000
012120000
0100000
00001200
00011200
0000010
0000001
,
1000000
01200000
00120000
00001200
00011200
0000001
000001212
,
12000000
0360000
07100000
0000100
00012100
0000011
00000120
,
8000000
0010000
0100000
00011200
00001200
0000063
00000107

G:=sub<GL(7,GF(13))| [12,0,0,0,0,0,0,0,12,1,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,12,12,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,1,12],[12,0,0,0,0,0,0,0,3,7,0,0,0,0,0,6,10,0,0,0,0,0,0,0,0,12,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,12,0,0,0,0,0,1,0],[8,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,6,10,0,0,0,0,0,3,7] >;

C62.147D6 in GAP, Magma, Sage, TeX

C_6^2._{147}D_6
% in TeX

G:=Group("C6^2.147D6");
// GroupNames label

G:=SmallGroup(432,505);
// by ID

G=gap.SmallGroup(432,505);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,28,141,64,1124,4037,14118]);
// Polycyclic

G:=Group<a,b,c,d|a^6=b^6=1,c^6=b^3,d^2=a^3,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=b^3*c^5>;
// generators/relations

׿
×
𝔽