direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C10×Dic6, C30.84C24, C60.273C23, C30⋊7(C2×Q8), C6⋊1(Q8×C10), (C2×C30)⋊14Q8, C15⋊8(C22×Q8), (C2×C20).441D6, C6.1(C23×C10), C23.38(S3×C10), (C22×C12).8C10, (C22×C20).22S3, C10.69(S3×C23), (C22×C60).24C2, (C2×C30).441C23, (C2×C60).533C22, C20.237(C22×S3), C12.34(C22×C10), (C22×C10).152D6, Dic3.1(C22×C10), (C5×Dic3).37C23, (C22×Dic3).6C10, (C22×C30).181C22, (C10×Dic3).234C22, C3⋊1(Q8×C2×C10), (C2×C6)⋊4(C5×Q8), C4.34(S3×C2×C10), C2.3(S3×C22×C10), (C2×C4).88(S3×C10), C22.28(S3×C2×C10), (C22×C4).10(C5×S3), (Dic3×C2×C10).14C2, (C2×C12).100(C2×C10), (C22×C6).43(C2×C10), (C2×C6).62(C22×C10), (C2×C10).375(C22×S3), (C2×Dic3).43(C2×C10), SmallGroup(480,1150)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 516 in 312 conjugacy classes, 210 normal (18 characteristic)
C1, C2, C2 [×6], C3, C4 [×4], C4 [×8], C22 [×7], C5, C6, C6 [×6], C2×C4 [×6], C2×C4 [×12], Q8 [×16], C23, C10, C10 [×6], Dic3 [×8], C12 [×4], C2×C6 [×7], C15, C22×C4, C22×C4 [×2], C2×Q8 [×12], C20 [×4], C20 [×8], C2×C10 [×7], Dic6 [×16], C2×Dic3 [×12], C2×C12 [×6], C22×C6, C30, C30 [×6], C22×Q8, C2×C20 [×6], C2×C20 [×12], C5×Q8 [×16], C22×C10, C2×Dic6 [×12], C22×Dic3 [×2], C22×C12, C5×Dic3 [×8], C60 [×4], C2×C30 [×7], C22×C20, C22×C20 [×2], Q8×C10 [×12], C22×Dic6, C5×Dic6 [×16], C10×Dic3 [×12], C2×C60 [×6], C22×C30, Q8×C2×C10, C10×Dic6 [×12], Dic3×C2×C10 [×2], C22×C60, C2×C10×Dic6
Quotients:
C1, C2 [×15], C22 [×35], C5, S3, Q8 [×4], C23 [×15], C10 [×15], D6 [×7], C2×Q8 [×6], C24, C2×C10 [×35], Dic6 [×4], C22×S3 [×7], C5×S3, C22×Q8, C5×Q8 [×4], C22×C10 [×15], C2×Dic6 [×6], S3×C23, S3×C10 [×7], Q8×C10 [×6], C23×C10, C22×Dic6, C5×Dic6 [×4], S3×C2×C10 [×7], Q8×C2×C10, C10×Dic6 [×6], S3×C22×C10, C2×C10×Dic6
Generators and relations
G = < a,b,c,d | a2=b10=c12=1, d2=c6, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >
►Regular action on 480 points
Generators in S480
(1 279)(2 280)(3 281)(4 282)(5 283)(6 284)(7 285)(8 286)(9 287)(10 288)(11 277)(12 278)(13 160)(14 161)(15 162)(16 163)(17 164)(18 165)(19 166)(20 167)(21 168)(22 157)(23 158)(24 159)(25 195)(26 196)(27 197)(28 198)(29 199)(30 200)(31 201)(32 202)(33 203)(34 204)(35 193)(36 194)(37 62)(38 63)(39 64)(40 65)(41 66)(42 67)(43 68)(44 69)(45 70)(46 71)(47 72)(48 61)(49 384)(50 373)(51 374)(52 375)(53 376)(54 377)(55 378)(56 379)(57 380)(58 381)(59 382)(60 383)(73 175)(74 176)(75 177)(76 178)(77 179)(78 180)(79 169)(80 170)(81 171)(82 172)(83 173)(84 174)(85 319)(86 320)(87 321)(88 322)(89 323)(90 324)(91 313)(92 314)(93 315)(94 316)(95 317)(96 318)(97 334)(98 335)(99 336)(100 325)(101 326)(102 327)(103 328)(104 329)(105 330)(106 331)(107 332)(108 333)(109 451)(110 452)(111 453)(112 454)(113 455)(114 456)(115 445)(116 446)(117 447)(118 448)(119 449)(120 450)(121 386)(122 387)(123 388)(124 389)(125 390)(126 391)(127 392)(128 393)(129 394)(130 395)(131 396)(132 385)(133 214)(134 215)(135 216)(136 205)(137 206)(138 207)(139 208)(140 209)(141 210)(142 211)(143 212)(144 213)(145 425)(146 426)(147 427)(148 428)(149 429)(150 430)(151 431)(152 432)(153 421)(154 422)(155 423)(156 424)(181 260)(182 261)(183 262)(184 263)(185 264)(186 253)(187 254)(188 255)(189 256)(190 257)(191 258)(192 259)(217 247)(218 248)(219 249)(220 250)(221 251)(222 252)(223 241)(224 242)(225 243)(226 244)(227 245)(228 246)(229 364)(230 365)(231 366)(232 367)(233 368)(234 369)(235 370)(236 371)(237 372)(238 361)(239 362)(240 363)(265 407)(266 408)(267 397)(268 398)(269 399)(270 400)(271 401)(272 402)(273 403)(274 404)(275 405)(276 406)(289 471)(290 472)(291 473)(292 474)(293 475)(294 476)(295 477)(296 478)(297 479)(298 480)(299 469)(300 470)(301 410)(302 411)(303 412)(304 413)(305 414)(306 415)(307 416)(308 417)(309 418)(310 419)(311 420)(312 409)(337 441)(338 442)(339 443)(340 444)(341 433)(342 434)(343 435)(344 436)(345 437)(346 438)(347 439)(348 440)(349 457)(350 458)(351 459)(352 460)(353 461)(354 462)(355 463)(356 464)(357 465)(358 466)(359 467)(360 468)
(1 295 272 309 339 80 208 257 72 425)(2 296 273 310 340 81 209 258 61 426)(3 297 274 311 341 82 210 259 62 427)(4 298 275 312 342 83 211 260 63 428)(5 299 276 301 343 84 212 261 64 429)(6 300 265 302 344 73 213 262 65 430)(7 289 266 303 345 74 214 263 66 431)(8 290 267 304 346 75 215 264 67 432)(9 291 268 305 347 76 216 253 68 421)(10 292 269 306 348 77 205 254 69 422)(11 293 270 307 337 78 206 255 70 423)(12 294 271 308 338 79 207 256 71 424)(13 236 111 336 374 355 394 314 217 200)(14 237 112 325 375 356 395 315 218 201)(15 238 113 326 376 357 396 316 219 202)(16 239 114 327 377 358 385 317 220 203)(17 240 115 328 378 359 386 318 221 204)(18 229 116 329 379 360 387 319 222 193)(19 230 117 330 380 349 388 320 223 194)(20 231 118 331 381 350 389 321 224 195)(21 232 119 332 382 351 390 322 225 196)(22 233 120 333 383 352 391 323 226 197)(23 234 109 334 384 353 392 324 227 198)(24 235 110 335 373 354 393 313 228 199)(25 167 366 448 106 58 458 124 87 242)(26 168 367 449 107 59 459 125 88 243)(27 157 368 450 108 60 460 126 89 244)(28 158 369 451 97 49 461 127 90 245)(29 159 370 452 98 50 462 128 91 246)(30 160 371 453 99 51 463 129 92 247)(31 161 372 454 100 52 464 130 93 248)(32 162 361 455 101 53 465 131 94 249)(33 163 362 456 102 54 466 132 95 250)(34 164 363 445 103 55 467 121 96 251)(35 165 364 446 104 56 468 122 85 252)(36 166 365 447 105 57 457 123 86 241)(37 147 281 479 404 420 433 172 141 192)(38 148 282 480 405 409 434 173 142 181)(39 149 283 469 406 410 435 174 143 182)(40 150 284 470 407 411 436 175 144 183)(41 151 285 471 408 412 437 176 133 184)(42 152 286 472 397 413 438 177 134 185)(43 153 287 473 398 414 439 178 135 186)(44 154 288 474 399 415 440 179 136 187)(45 155 277 475 400 416 441 180 137 188)(46 156 278 476 401 417 442 169 138 189)(47 145 279 477 402 418 443 170 139 190)(48 146 280 478 403 419 444 171 140 191)
(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)(433 434 435 436 437 438 439 440 441 442 443 444)(445 446 447 448 449 450 451 452 453 454 455 456)(457 458 459 460 461 462 463 464 465 466 467 468)(469 470 471 472 473 474 475 476 477 478 479 480)
(1 360 7 354)(2 359 8 353)(3 358 9 352)(4 357 10 351)(5 356 11 350)(6 355 12 349)(13 79 19 73)(14 78 20 84)(15 77 21 83)(16 76 22 82)(17 75 23 81)(18 74 24 80)(25 435 31 441)(26 434 32 440)(27 433 33 439)(28 444 34 438)(29 443 35 437)(30 442 36 436)(37 102 43 108)(38 101 44 107)(39 100 45 106)(40 99 46 105)(41 98 47 104)(42 97 48 103)(49 146 55 152)(50 145 56 151)(51 156 57 150)(52 155 58 149)(53 154 59 148)(54 153 60 147)(61 328 67 334)(62 327 68 333)(63 326 69 332)(64 325 70 331)(65 336 71 330)(66 335 72 329)(85 408 91 402)(86 407 92 401)(87 406 93 400)(88 405 94 399)(89 404 95 398)(90 403 96 397)(109 258 115 264)(110 257 116 263)(111 256 117 262)(112 255 118 261)(113 254 119 260)(114 253 120 259)(121 472 127 478)(122 471 128 477)(123 470 129 476)(124 469 130 475)(125 480 131 474)(126 479 132 473)(133 370 139 364)(134 369 140 363)(135 368 141 362)(136 367 142 361)(137 366 143 372)(138 365 144 371)(157 172 163 178)(158 171 164 177)(159 170 165 176)(160 169 166 175)(161 180 167 174)(162 179 168 173)(181 455 187 449)(182 454 188 448)(183 453 189 447)(184 452 190 446)(185 451 191 445)(186 450 192 456)(193 345 199 339)(194 344 200 338)(195 343 201 337)(196 342 202 348)(197 341 203 347)(198 340 204 346)(205 232 211 238)(206 231 212 237)(207 230 213 236)(208 229 214 235)(209 240 215 234)(210 239 216 233)(217 308 223 302)(218 307 224 301)(219 306 225 312)(220 305 226 311)(221 304 227 310)(222 303 228 309)(241 411 247 417)(242 410 248 416)(243 409 249 415)(244 420 250 414)(245 419 251 413)(246 418 252 412)(265 314 271 320)(266 313 272 319)(267 324 273 318)(268 323 274 317)(269 322 275 316)(270 321 276 315)(277 458 283 464)(278 457 284 463)(279 468 285 462)(280 467 286 461)(281 466 287 460)(282 465 288 459)(289 393 295 387)(290 392 296 386)(291 391 297 385)(292 390 298 396)(293 389 299 395)(294 388 300 394)(373 425 379 431)(374 424 380 430)(375 423 381 429)(376 422 382 428)(377 421 383 427)(378 432 384 426)
G:=sub<Sym(480)| (1,279)(2,280)(3,281)(4,282)(5,283)(6,284)(7,285)(8,286)(9,287)(10,288)(11,277)(12,278)(13,160)(14,161)(15,162)(16,163)(17,164)(18,165)(19,166)(20,167)(21,168)(22,157)(23,158)(24,159)(25,195)(26,196)(27,197)(28,198)(29,199)(30,200)(31,201)(32,202)(33,203)(34,204)(35,193)(36,194)(37,62)(38,63)(39,64)(40,65)(41,66)(42,67)(43,68)(44,69)(45,70)(46,71)(47,72)(48,61)(49,384)(50,373)(51,374)(52,375)(53,376)(54,377)(55,378)(56,379)(57,380)(58,381)(59,382)(60,383)(73,175)(74,176)(75,177)(76,178)(77,179)(78,180)(79,169)(80,170)(81,171)(82,172)(83,173)(84,174)(85,319)(86,320)(87,321)(88,322)(89,323)(90,324)(91,313)(92,314)(93,315)(94,316)(95,317)(96,318)(97,334)(98,335)(99,336)(100,325)(101,326)(102,327)(103,328)(104,329)(105,330)(106,331)(107,332)(108,333)(109,451)(110,452)(111,453)(112,454)(113,455)(114,456)(115,445)(116,446)(117,447)(118,448)(119,449)(120,450)(121,386)(122,387)(123,388)(124,389)(125,390)(126,391)(127,392)(128,393)(129,394)(130,395)(131,396)(132,385)(133,214)(134,215)(135,216)(136,205)(137,206)(138,207)(139,208)(140,209)(141,210)(142,211)(143,212)(144,213)(145,425)(146,426)(147,427)(148,428)(149,429)(150,430)(151,431)(152,432)(153,421)(154,422)(155,423)(156,424)(181,260)(182,261)(183,262)(184,263)(185,264)(186,253)(187,254)(188,255)(189,256)(190,257)(191,258)(192,259)(217,247)(218,248)(219,249)(220,250)(221,251)(222,252)(223,241)(224,242)(225,243)(226,244)(227,245)(228,246)(229,364)(230,365)(231,366)(232,367)(233,368)(234,369)(235,370)(236,371)(237,372)(238,361)(239,362)(240,363)(265,407)(266,408)(267,397)(268,398)(269,399)(270,400)(271,401)(272,402)(273,403)(274,404)(275,405)(276,406)(289,471)(290,472)(291,473)(292,474)(293,475)(294,476)(295,477)(296,478)(297,479)(298,480)(299,469)(300,470)(301,410)(302,411)(303,412)(304,413)(305,414)(306,415)(307,416)(308,417)(309,418)(310,419)(311,420)(312,409)(337,441)(338,442)(339,443)(340,444)(341,433)(342,434)(343,435)(344,436)(345,437)(346,438)(347,439)(348,440)(349,457)(350,458)(351,459)(352,460)(353,461)(354,462)(355,463)(356,464)(357,465)(358,466)(359,467)(360,468), (1,295,272,309,339,80,208,257,72,425)(2,296,273,310,340,81,209,258,61,426)(3,297,274,311,341,82,210,259,62,427)(4,298,275,312,342,83,211,260,63,428)(5,299,276,301,343,84,212,261,64,429)(6,300,265,302,344,73,213,262,65,430)(7,289,266,303,345,74,214,263,66,431)(8,290,267,304,346,75,215,264,67,432)(9,291,268,305,347,76,216,253,68,421)(10,292,269,306,348,77,205,254,69,422)(11,293,270,307,337,78,206,255,70,423)(12,294,271,308,338,79,207,256,71,424)(13,236,111,336,374,355,394,314,217,200)(14,237,112,325,375,356,395,315,218,201)(15,238,113,326,376,357,396,316,219,202)(16,239,114,327,377,358,385,317,220,203)(17,240,115,328,378,359,386,318,221,204)(18,229,116,329,379,360,387,319,222,193)(19,230,117,330,380,349,388,320,223,194)(20,231,118,331,381,350,389,321,224,195)(21,232,119,332,382,351,390,322,225,196)(22,233,120,333,383,352,391,323,226,197)(23,234,109,334,384,353,392,324,227,198)(24,235,110,335,373,354,393,313,228,199)(25,167,366,448,106,58,458,124,87,242)(26,168,367,449,107,59,459,125,88,243)(27,157,368,450,108,60,460,126,89,244)(28,158,369,451,97,49,461,127,90,245)(29,159,370,452,98,50,462,128,91,246)(30,160,371,453,99,51,463,129,92,247)(31,161,372,454,100,52,464,130,93,248)(32,162,361,455,101,53,465,131,94,249)(33,163,362,456,102,54,466,132,95,250)(34,164,363,445,103,55,467,121,96,251)(35,165,364,446,104,56,468,122,85,252)(36,166,365,447,105,57,457,123,86,241)(37,147,281,479,404,420,433,172,141,192)(38,148,282,480,405,409,434,173,142,181)(39,149,283,469,406,410,435,174,143,182)(40,150,284,470,407,411,436,175,144,183)(41,151,285,471,408,412,437,176,133,184)(42,152,286,472,397,413,438,177,134,185)(43,153,287,473,398,414,439,178,135,186)(44,154,288,474,399,415,440,179,136,187)(45,155,277,475,400,416,441,180,137,188)(46,156,278,476,401,417,442,169,138,189)(47,145,279,477,402,418,443,170,139,190)(48,146,280,478,403,419,444,171,140,191), (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)(433,434,435,436,437,438,439,440,441,442,443,444)(445,446,447,448,449,450,451,452,453,454,455,456)(457,458,459,460,461,462,463,464,465,466,467,468)(469,470,471,472,473,474,475,476,477,478,479,480), (1,360,7,354)(2,359,8,353)(3,358,9,352)(4,357,10,351)(5,356,11,350)(6,355,12,349)(13,79,19,73)(14,78,20,84)(15,77,21,83)(16,76,22,82)(17,75,23,81)(18,74,24,80)(25,435,31,441)(26,434,32,440)(27,433,33,439)(28,444,34,438)(29,443,35,437)(30,442,36,436)(37,102,43,108)(38,101,44,107)(39,100,45,106)(40,99,46,105)(41,98,47,104)(42,97,48,103)(49,146,55,152)(50,145,56,151)(51,156,57,150)(52,155,58,149)(53,154,59,148)(54,153,60,147)(61,328,67,334)(62,327,68,333)(63,326,69,332)(64,325,70,331)(65,336,71,330)(66,335,72,329)(85,408,91,402)(86,407,92,401)(87,406,93,400)(88,405,94,399)(89,404,95,398)(90,403,96,397)(109,258,115,264)(110,257,116,263)(111,256,117,262)(112,255,118,261)(113,254,119,260)(114,253,120,259)(121,472,127,478)(122,471,128,477)(123,470,129,476)(124,469,130,475)(125,480,131,474)(126,479,132,473)(133,370,139,364)(134,369,140,363)(135,368,141,362)(136,367,142,361)(137,366,143,372)(138,365,144,371)(157,172,163,178)(158,171,164,177)(159,170,165,176)(160,169,166,175)(161,180,167,174)(162,179,168,173)(181,455,187,449)(182,454,188,448)(183,453,189,447)(184,452,190,446)(185,451,191,445)(186,450,192,456)(193,345,199,339)(194,344,200,338)(195,343,201,337)(196,342,202,348)(197,341,203,347)(198,340,204,346)(205,232,211,238)(206,231,212,237)(207,230,213,236)(208,229,214,235)(209,240,215,234)(210,239,216,233)(217,308,223,302)(218,307,224,301)(219,306,225,312)(220,305,226,311)(221,304,227,310)(222,303,228,309)(241,411,247,417)(242,410,248,416)(243,409,249,415)(244,420,250,414)(245,419,251,413)(246,418,252,412)(265,314,271,320)(266,313,272,319)(267,324,273,318)(268,323,274,317)(269,322,275,316)(270,321,276,315)(277,458,283,464)(278,457,284,463)(279,468,285,462)(280,467,286,461)(281,466,287,460)(282,465,288,459)(289,393,295,387)(290,392,296,386)(291,391,297,385)(292,390,298,396)(293,389,299,395)(294,388,300,394)(373,425,379,431)(374,424,380,430)(375,423,381,429)(376,422,382,428)(377,421,383,427)(378,432,384,426)>;
G:=Group( (1,279)(2,280)(3,281)(4,282)(5,283)(6,284)(7,285)(8,286)(9,287)(10,288)(11,277)(12,278)(13,160)(14,161)(15,162)(16,163)(17,164)(18,165)(19,166)(20,167)(21,168)(22,157)(23,158)(24,159)(25,195)(26,196)(27,197)(28,198)(29,199)(30,200)(31,201)(32,202)(33,203)(34,204)(35,193)(36,194)(37,62)(38,63)(39,64)(40,65)(41,66)(42,67)(43,68)(44,69)(45,70)(46,71)(47,72)(48,61)(49,384)(50,373)(51,374)(52,375)(53,376)(54,377)(55,378)(56,379)(57,380)(58,381)(59,382)(60,383)(73,175)(74,176)(75,177)(76,178)(77,179)(78,180)(79,169)(80,170)(81,171)(82,172)(83,173)(84,174)(85,319)(86,320)(87,321)(88,322)(89,323)(90,324)(91,313)(92,314)(93,315)(94,316)(95,317)(96,318)(97,334)(98,335)(99,336)(100,325)(101,326)(102,327)(103,328)(104,329)(105,330)(106,331)(107,332)(108,333)(109,451)(110,452)(111,453)(112,454)(113,455)(114,456)(115,445)(116,446)(117,447)(118,448)(119,449)(120,450)(121,386)(122,387)(123,388)(124,389)(125,390)(126,391)(127,392)(128,393)(129,394)(130,395)(131,396)(132,385)(133,214)(134,215)(135,216)(136,205)(137,206)(138,207)(139,208)(140,209)(141,210)(142,211)(143,212)(144,213)(145,425)(146,426)(147,427)(148,428)(149,429)(150,430)(151,431)(152,432)(153,421)(154,422)(155,423)(156,424)(181,260)(182,261)(183,262)(184,263)(185,264)(186,253)(187,254)(188,255)(189,256)(190,257)(191,258)(192,259)(217,247)(218,248)(219,249)(220,250)(221,251)(222,252)(223,241)(224,242)(225,243)(226,244)(227,245)(228,246)(229,364)(230,365)(231,366)(232,367)(233,368)(234,369)(235,370)(236,371)(237,372)(238,361)(239,362)(240,363)(265,407)(266,408)(267,397)(268,398)(269,399)(270,400)(271,401)(272,402)(273,403)(274,404)(275,405)(276,406)(289,471)(290,472)(291,473)(292,474)(293,475)(294,476)(295,477)(296,478)(297,479)(298,480)(299,469)(300,470)(301,410)(302,411)(303,412)(304,413)(305,414)(306,415)(307,416)(308,417)(309,418)(310,419)(311,420)(312,409)(337,441)(338,442)(339,443)(340,444)(341,433)(342,434)(343,435)(344,436)(345,437)(346,438)(347,439)(348,440)(349,457)(350,458)(351,459)(352,460)(353,461)(354,462)(355,463)(356,464)(357,465)(358,466)(359,467)(360,468), (1,295,272,309,339,80,208,257,72,425)(2,296,273,310,340,81,209,258,61,426)(3,297,274,311,341,82,210,259,62,427)(4,298,275,312,342,83,211,260,63,428)(5,299,276,301,343,84,212,261,64,429)(6,300,265,302,344,73,213,262,65,430)(7,289,266,303,345,74,214,263,66,431)(8,290,267,304,346,75,215,264,67,432)(9,291,268,305,347,76,216,253,68,421)(10,292,269,306,348,77,205,254,69,422)(11,293,270,307,337,78,206,255,70,423)(12,294,271,308,338,79,207,256,71,424)(13,236,111,336,374,355,394,314,217,200)(14,237,112,325,375,356,395,315,218,201)(15,238,113,326,376,357,396,316,219,202)(16,239,114,327,377,358,385,317,220,203)(17,240,115,328,378,359,386,318,221,204)(18,229,116,329,379,360,387,319,222,193)(19,230,117,330,380,349,388,320,223,194)(20,231,118,331,381,350,389,321,224,195)(21,232,119,332,382,351,390,322,225,196)(22,233,120,333,383,352,391,323,226,197)(23,234,109,334,384,353,392,324,227,198)(24,235,110,335,373,354,393,313,228,199)(25,167,366,448,106,58,458,124,87,242)(26,168,367,449,107,59,459,125,88,243)(27,157,368,450,108,60,460,126,89,244)(28,158,369,451,97,49,461,127,90,245)(29,159,370,452,98,50,462,128,91,246)(30,160,371,453,99,51,463,129,92,247)(31,161,372,454,100,52,464,130,93,248)(32,162,361,455,101,53,465,131,94,249)(33,163,362,456,102,54,466,132,95,250)(34,164,363,445,103,55,467,121,96,251)(35,165,364,446,104,56,468,122,85,252)(36,166,365,447,105,57,457,123,86,241)(37,147,281,479,404,420,433,172,141,192)(38,148,282,480,405,409,434,173,142,181)(39,149,283,469,406,410,435,174,143,182)(40,150,284,470,407,411,436,175,144,183)(41,151,285,471,408,412,437,176,133,184)(42,152,286,472,397,413,438,177,134,185)(43,153,287,473,398,414,439,178,135,186)(44,154,288,474,399,415,440,179,136,187)(45,155,277,475,400,416,441,180,137,188)(46,156,278,476,401,417,442,169,138,189)(47,145,279,477,402,418,443,170,139,190)(48,146,280,478,403,419,444,171,140,191), (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)(433,434,435,436,437,438,439,440,441,442,443,444)(445,446,447,448,449,450,451,452,453,454,455,456)(457,458,459,460,461,462,463,464,465,466,467,468)(469,470,471,472,473,474,475,476,477,478,479,480), (1,360,7,354)(2,359,8,353)(3,358,9,352)(4,357,10,351)(5,356,11,350)(6,355,12,349)(13,79,19,73)(14,78,20,84)(15,77,21,83)(16,76,22,82)(17,75,23,81)(18,74,24,80)(25,435,31,441)(26,434,32,440)(27,433,33,439)(28,444,34,438)(29,443,35,437)(30,442,36,436)(37,102,43,108)(38,101,44,107)(39,100,45,106)(40,99,46,105)(41,98,47,104)(42,97,48,103)(49,146,55,152)(50,145,56,151)(51,156,57,150)(52,155,58,149)(53,154,59,148)(54,153,60,147)(61,328,67,334)(62,327,68,333)(63,326,69,332)(64,325,70,331)(65,336,71,330)(66,335,72,329)(85,408,91,402)(86,407,92,401)(87,406,93,400)(88,405,94,399)(89,404,95,398)(90,403,96,397)(109,258,115,264)(110,257,116,263)(111,256,117,262)(112,255,118,261)(113,254,119,260)(114,253,120,259)(121,472,127,478)(122,471,128,477)(123,470,129,476)(124,469,130,475)(125,480,131,474)(126,479,132,473)(133,370,139,364)(134,369,140,363)(135,368,141,362)(136,367,142,361)(137,366,143,372)(138,365,144,371)(157,172,163,178)(158,171,164,177)(159,170,165,176)(160,169,166,175)(161,180,167,174)(162,179,168,173)(181,455,187,449)(182,454,188,448)(183,453,189,447)(184,452,190,446)(185,451,191,445)(186,450,192,456)(193,345,199,339)(194,344,200,338)(195,343,201,337)(196,342,202,348)(197,341,203,347)(198,340,204,346)(205,232,211,238)(206,231,212,237)(207,230,213,236)(208,229,214,235)(209,240,215,234)(210,239,216,233)(217,308,223,302)(218,307,224,301)(219,306,225,312)(220,305,226,311)(221,304,227,310)(222,303,228,309)(241,411,247,417)(242,410,248,416)(243,409,249,415)(244,420,250,414)(245,419,251,413)(246,418,252,412)(265,314,271,320)(266,313,272,319)(267,324,273,318)(268,323,274,317)(269,322,275,316)(270,321,276,315)(277,458,283,464)(278,457,284,463)(279,468,285,462)(280,467,286,461)(281,466,287,460)(282,465,288,459)(289,393,295,387)(290,392,296,386)(291,391,297,385)(292,390,298,396)(293,389,299,395)(294,388,300,394)(373,425,379,431)(374,424,380,430)(375,423,381,429)(376,422,382,428)(377,421,383,427)(378,432,384,426) );
G=PermutationGroup([(1,279),(2,280),(3,281),(4,282),(5,283),(6,284),(7,285),(8,286),(9,287),(10,288),(11,277),(12,278),(13,160),(14,161),(15,162),(16,163),(17,164),(18,165),(19,166),(20,167),(21,168),(22,157),(23,158),(24,159),(25,195),(26,196),(27,197),(28,198),(29,199),(30,200),(31,201),(32,202),(33,203),(34,204),(35,193),(36,194),(37,62),(38,63),(39,64),(40,65),(41,66),(42,67),(43,68),(44,69),(45,70),(46,71),(47,72),(48,61),(49,384),(50,373),(51,374),(52,375),(53,376),(54,377),(55,378),(56,379),(57,380),(58,381),(59,382),(60,383),(73,175),(74,176),(75,177),(76,178),(77,179),(78,180),(79,169),(80,170),(81,171),(82,172),(83,173),(84,174),(85,319),(86,320),(87,321),(88,322),(89,323),(90,324),(91,313),(92,314),(93,315),(94,316),(95,317),(96,318),(97,334),(98,335),(99,336),(100,325),(101,326),(102,327),(103,328),(104,329),(105,330),(106,331),(107,332),(108,333),(109,451),(110,452),(111,453),(112,454),(113,455),(114,456),(115,445),(116,446),(117,447),(118,448),(119,449),(120,450),(121,386),(122,387),(123,388),(124,389),(125,390),(126,391),(127,392),(128,393),(129,394),(130,395),(131,396),(132,385),(133,214),(134,215),(135,216),(136,205),(137,206),(138,207),(139,208),(140,209),(141,210),(142,211),(143,212),(144,213),(145,425),(146,426),(147,427),(148,428),(149,429),(150,430),(151,431),(152,432),(153,421),(154,422),(155,423),(156,424),(181,260),(182,261),(183,262),(184,263),(185,264),(186,253),(187,254),(188,255),(189,256),(190,257),(191,258),(192,259),(217,247),(218,248),(219,249),(220,250),(221,251),(222,252),(223,241),(224,242),(225,243),(226,244),(227,245),(228,246),(229,364),(230,365),(231,366),(232,367),(233,368),(234,369),(235,370),(236,371),(237,372),(238,361),(239,362),(240,363),(265,407),(266,408),(267,397),(268,398),(269,399),(270,400),(271,401),(272,402),(273,403),(274,404),(275,405),(276,406),(289,471),(290,472),(291,473),(292,474),(293,475),(294,476),(295,477),(296,478),(297,479),(298,480),(299,469),(300,470),(301,410),(302,411),(303,412),(304,413),(305,414),(306,415),(307,416),(308,417),(309,418),(310,419),(311,420),(312,409),(337,441),(338,442),(339,443),(340,444),(341,433),(342,434),(343,435),(344,436),(345,437),(346,438),(347,439),(348,440),(349,457),(350,458),(351,459),(352,460),(353,461),(354,462),(355,463),(356,464),(357,465),(358,466),(359,467),(360,468)], [(1,295,272,309,339,80,208,257,72,425),(2,296,273,310,340,81,209,258,61,426),(3,297,274,311,341,82,210,259,62,427),(4,298,275,312,342,83,211,260,63,428),(5,299,276,301,343,84,212,261,64,429),(6,300,265,302,344,73,213,262,65,430),(7,289,266,303,345,74,214,263,66,431),(8,290,267,304,346,75,215,264,67,432),(9,291,268,305,347,76,216,253,68,421),(10,292,269,306,348,77,205,254,69,422),(11,293,270,307,337,78,206,255,70,423),(12,294,271,308,338,79,207,256,71,424),(13,236,111,336,374,355,394,314,217,200),(14,237,112,325,375,356,395,315,218,201),(15,238,113,326,376,357,396,316,219,202),(16,239,114,327,377,358,385,317,220,203),(17,240,115,328,378,359,386,318,221,204),(18,229,116,329,379,360,387,319,222,193),(19,230,117,330,380,349,388,320,223,194),(20,231,118,331,381,350,389,321,224,195),(21,232,119,332,382,351,390,322,225,196),(22,233,120,333,383,352,391,323,226,197),(23,234,109,334,384,353,392,324,227,198),(24,235,110,335,373,354,393,313,228,199),(25,167,366,448,106,58,458,124,87,242),(26,168,367,449,107,59,459,125,88,243),(27,157,368,450,108,60,460,126,89,244),(28,158,369,451,97,49,461,127,90,245),(29,159,370,452,98,50,462,128,91,246),(30,160,371,453,99,51,463,129,92,247),(31,161,372,454,100,52,464,130,93,248),(32,162,361,455,101,53,465,131,94,249),(33,163,362,456,102,54,466,132,95,250),(34,164,363,445,103,55,467,121,96,251),(35,165,364,446,104,56,468,122,85,252),(36,166,365,447,105,57,457,123,86,241),(37,147,281,479,404,420,433,172,141,192),(38,148,282,480,405,409,434,173,142,181),(39,149,283,469,406,410,435,174,143,182),(40,150,284,470,407,411,436,175,144,183),(41,151,285,471,408,412,437,176,133,184),(42,152,286,472,397,413,438,177,134,185),(43,153,287,473,398,414,439,178,135,186),(44,154,288,474,399,415,440,179,136,187),(45,155,277,475,400,416,441,180,137,188),(46,156,278,476,401,417,442,169,138,189),(47,145,279,477,402,418,443,170,139,190),(48,146,280,478,403,419,444,171,140,191)], [(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),(433,434,435,436,437,438,439,440,441,442,443,444),(445,446,447,448,449,450,451,452,453,454,455,456),(457,458,459,460,461,462,463,464,465,466,467,468),(469,470,471,472,473,474,475,476,477,478,479,480)], [(1,360,7,354),(2,359,8,353),(3,358,9,352),(4,357,10,351),(5,356,11,350),(6,355,12,349),(13,79,19,73),(14,78,20,84),(15,77,21,83),(16,76,22,82),(17,75,23,81),(18,74,24,80),(25,435,31,441),(26,434,32,440),(27,433,33,439),(28,444,34,438),(29,443,35,437),(30,442,36,436),(37,102,43,108),(38,101,44,107),(39,100,45,106),(40,99,46,105),(41,98,47,104),(42,97,48,103),(49,146,55,152),(50,145,56,151),(51,156,57,150),(52,155,58,149),(53,154,59,148),(54,153,60,147),(61,328,67,334),(62,327,68,333),(63,326,69,332),(64,325,70,331),(65,336,71,330),(66,335,72,329),(85,408,91,402),(86,407,92,401),(87,406,93,400),(88,405,94,399),(89,404,95,398),(90,403,96,397),(109,258,115,264),(110,257,116,263),(111,256,117,262),(112,255,118,261),(113,254,119,260),(114,253,120,259),(121,472,127,478),(122,471,128,477),(123,470,129,476),(124,469,130,475),(125,480,131,474),(126,479,132,473),(133,370,139,364),(134,369,140,363),(135,368,141,362),(136,367,142,361),(137,366,143,372),(138,365,144,371),(157,172,163,178),(158,171,164,177),(159,170,165,176),(160,169,166,175),(161,180,167,174),(162,179,168,173),(181,455,187,449),(182,454,188,448),(183,453,189,447),(184,452,190,446),(185,451,191,445),(186,450,192,456),(193,345,199,339),(194,344,200,338),(195,343,201,337),(196,342,202,348),(197,341,203,347),(198,340,204,346),(205,232,211,238),(206,231,212,237),(207,230,213,236),(208,229,214,235),(209,240,215,234),(210,239,216,233),(217,308,223,302),(218,307,224,301),(219,306,225,312),(220,305,226,311),(221,304,227,310),(222,303,228,309),(241,411,247,417),(242,410,248,416),(243,409,249,415),(244,420,250,414),(245,419,251,413),(246,418,252,412),(265,314,271,320),(266,313,272,319),(267,324,273,318),(268,323,274,317),(269,322,275,316),(270,321,276,315),(277,458,283,464),(278,457,284,463),(279,468,285,462),(280,467,286,461),(281,466,287,460),(282,465,288,459),(289,393,295,387),(290,392,296,386),(291,391,297,385),(292,390,298,396),(293,389,299,395),(294,388,300,394),(373,425,379,431),(374,424,380,430),(375,423,381,429),(376,422,382,428),(377,421,383,427),(378,432,384,426)])
Matrix representation ►G ⊆ GL5(𝔽61)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 60 | 0 | 0 | 0 | 0 |
| 0 | 20 | 0 | 0 | 0 |
| 0 | 0 | 20 | 0 | 0 |
| 0 | 0 | 0 | 58 | 0 |
| 0 | 0 | 0 | 0 | 58 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 |
| 0 | 0 | 0 | 46 | 23 |
| 0 | 0 | 0 | 38 | 23 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 53 | 41 |
| 0 | 0 | 0 | 49 | 8 |
G:=sub<GL(5,GF(61))| [1,0,0,0,0,0,60,0,0,0,0,0,60,0,0,0,0,0,1,0,0,0,0,0,1],[60,0,0,0,0,0,20,0,0,0,0,0,20,0,0,0,0,0,58,0,0,0,0,0,58],[1,0,0,0,0,0,0,1,0,0,0,60,1,0,0,0,0,0,46,38,0,0,0,23,23],[1,0,0,0,0,0,1,0,0,0,0,1,60,0,0,0,0,0,53,49,0,0,0,41,8] >;
180 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3 | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 5A | 5B | 5C | 5D | 6A | ··· | 6G | 10A | ··· | 10AB | 12A | ··· | 12H | 15A | 15B | 15C | 15D | 20A | ··· | 20P | 20Q | ··· | 20AV | 30A | ··· | 30AB | 60A | ··· | 60AF |
| order | 1 | 2 | ··· | 2 | 3 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | 6 | ··· | 6 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 6 | ··· | 6 | 2 | ··· | 2 | 2 | ··· | 2 |
180 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | + | - | |||||||||
| image | C1 | C2 | C2 | C2 | C5 | C10 | C10 | C10 | S3 | Q8 | D6 | D6 | Dic6 | C5×S3 | C5×Q8 | S3×C10 | S3×C10 | C5×Dic6 |
| kernel | C2×C10×Dic6 | C10×Dic6 | Dic3×C2×C10 | C22×C60 | C22×Dic6 | C2×Dic6 | C22×Dic3 | C22×C12 | C22×C20 | C2×C30 | C2×C20 | C22×C10 | C2×C10 | C22×C4 | C2×C6 | C2×C4 | C23 | C22 |
| # reps | 1 | 12 | 2 | 1 | 4 | 48 | 8 | 4 | 1 | 4 | 6 | 1 | 8 | 4 | 16 | 24 | 4 | 32 |
In GAP, Magma, Sage, TeX
C_2\times C_{10}\times Dic_6 % in TeX
G:=Group("C2xC10xDic6"); // GroupNames label
G:=SmallGroup(480,1150);
// by ID
G=gap.SmallGroup(480,1150);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-5,-2,-3,560,2467,304,15686]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^10=c^12=1,d^2=c^6,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations
×
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ℤ
𝔽
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