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G = C157Q32order 480 = 25·3·5

1st semidirect product of C15 and Q32 acting via Q32/Q16=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C157Q32, C8.7D30, C60.6D4, Q16.D15, C30.42D8, C40.15D6, C24.15D10, Dic60.3C2, C120.12C22, C33(C5⋊Q32), C53(C3⋊Q32), (C5×Q16).1S3, (C3×Q16).1D5, C153C16.1C2, C6.20(D4⋊D5), C2.7(D4⋊D15), C4.4(C157D4), (C15×Q16).1C2, C10.20(D4⋊S3), C20.18(C3⋊D4), C12.20(C5⋊D4), SmallGroup(480,189)

Series: Derived Chief Lower central Upper central

C1C120 — C157Q32
C1C5C15C30C60C120Dic60 — C157Q32
C15C30C60C120 — C157Q32
C1C2C4C8Q16

Generators and relations for C157Q32
 G = < a,b,c | a15=b16=1, c2=b8, bab-1=a-1, ac=ca, cbc-1=b-1 >

4C4
60C4
2Q8
30Q8
4C12
20Dic3
4C20
12Dic5
15Q16
15C16
2C3×Q8
10Dic6
2C5×Q8
6Dic10
4C60
4Dic15
15Q32
5Dic12
5C3⋊C16
3C52C16
3Dic20
2Dic30
2Q8×C15
5C3⋊Q32
3C5⋊Q32

Smallest permutation representation of C157Q32
Regular action on 480 points
Generators in S480
(1 427 68 267 222 117 84 150 318 370 302 346 179 172 21)(2 22 173 180 347 303 371 319 151 85 118 223 268 69 428)(3 429 70 269 224 119 86 152 320 372 304 348 181 174 23)(4 24 175 182 349 289 373 305 153 87 120 209 270 71 430)(5 431 72 271 210 121 88 154 306 374 290 350 183 176 25)(6 26 161 184 351 291 375 307 155 89 122 211 272 73 432)(7 417 74 257 212 123 90 156 308 376 292 352 185 162 27)(8 28 163 186 337 293 377 309 157 91 124 213 258 75 418)(9 419 76 259 214 125 92 158 310 378 294 338 187 164 29)(10 30 165 188 339 295 379 311 159 93 126 215 260 77 420)(11 421 78 261 216 127 94 160 312 380 296 340 189 166 31)(12 32 167 190 341 297 381 313 145 95 128 217 262 79 422)(13 423 80 263 218 113 96 146 314 382 298 342 191 168 17)(14 18 169 192 343 299 383 315 147 81 114 219 264 65 424)(15 425 66 265 220 115 82 148 316 384 300 344 177 170 19)(16 20 171 178 345 301 369 317 149 83 116 221 266 67 426)(33 104 458 253 331 281 193 57 433 397 356 137 478 237 415)(34 416 238 479 138 357 398 434 58 194 282 332 254 459 105)(35 106 460 255 333 283 195 59 435 399 358 139 480 239 401)(36 402 240 465 140 359 400 436 60 196 284 334 256 461 107)(37 108 462 241 335 285 197 61 437 385 360 141 466 225 403)(38 404 226 467 142 361 386 438 62 198 286 336 242 463 109)(39 110 464 243 321 287 199 63 439 387 362 143 468 227 405)(40 406 228 469 144 363 388 440 64 200 288 322 244 449 111)(41 112 450 245 323 273 201 49 441 389 364 129 470 229 407)(42 408 230 471 130 365 390 442 50 202 274 324 246 451 97)(43 98 452 247 325 275 203 51 443 391 366 131 472 231 409)(44 410 232 473 132 367 392 444 52 204 276 326 248 453 99)(45 100 454 249 327 277 205 53 445 393 368 133 474 233 411)(46 412 234 475 134 353 394 446 54 206 278 328 250 455 101)(47 102 456 251 329 279 207 55 447 395 354 135 476 235 413)(48 414 236 477 136 355 396 448 56 208 280 330 252 457 103)
(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)
(1 470 9 478)(2 469 10 477)(3 468 11 476)(4 467 12 475)(5 466 13 474)(6 465 14 473)(7 480 15 472)(8 479 16 471)(17 133 25 141)(18 132 26 140)(19 131 27 139)(20 130 28 138)(21 129 29 137)(22 144 30 136)(23 143 31 135)(24 142 32 134)(33 267 41 259)(34 266 42 258)(35 265 43 257)(36 264 44 272)(37 263 45 271)(38 262 46 270)(39 261 47 269)(40 260 48 268)(49 294 57 302)(50 293 58 301)(51 292 59 300)(52 291 60 299)(53 290 61 298)(54 289 62 297)(55 304 63 296)(56 303 64 295)(65 410 73 402)(66 409 74 401)(67 408 75 416)(68 407 76 415)(69 406 77 414)(70 405 78 413)(71 404 79 412)(72 403 80 411)(81 248 89 256)(82 247 90 255)(83 246 91 254)(84 245 92 253)(85 244 93 252)(86 243 94 251)(87 242 95 250)(88 241 96 249)(97 213 105 221)(98 212 106 220)(99 211 107 219)(100 210 108 218)(101 209 109 217)(102 224 110 216)(103 223 111 215)(104 222 112 214)(113 454 121 462)(114 453 122 461)(115 452 123 460)(116 451 124 459)(117 450 125 458)(118 449 126 457)(119 464 127 456)(120 463 128 455)(145 328 153 336)(146 327 154 335)(147 326 155 334)(148 325 156 333)(149 324 157 332)(150 323 158 331)(151 322 159 330)(152 321 160 329)(161 359 169 367)(162 358 170 366)(163 357 171 365)(164 356 172 364)(165 355 173 363)(166 354 174 362)(167 353 175 361)(168 368 176 360)(177 391 185 399)(178 390 186 398)(179 389 187 397)(180 388 188 396)(181 387 189 395)(182 386 190 394)(183 385 191 393)(184 400 192 392)(193 370 201 378)(194 369 202 377)(195 384 203 376)(196 383 204 375)(197 382 205 374)(198 381 206 373)(199 380 207 372)(200 379 208 371)(225 423 233 431)(226 422 234 430)(227 421 235 429)(228 420 236 428)(229 419 237 427)(230 418 238 426)(231 417 239 425)(232 432 240 424)(273 310 281 318)(274 309 282 317)(275 308 283 316)(276 307 284 315)(277 306 285 314)(278 305 286 313)(279 320 287 312)(280 319 288 311)(337 434 345 442)(338 433 346 441)(339 448 347 440)(340 447 348 439)(341 446 349 438)(342 445 350 437)(343 444 351 436)(344 443 352 435)

G:=sub<Sym(480)| (1,427,68,267,222,117,84,150,318,370,302,346,179,172,21)(2,22,173,180,347,303,371,319,151,85,118,223,268,69,428)(3,429,70,269,224,119,86,152,320,372,304,348,181,174,23)(4,24,175,182,349,289,373,305,153,87,120,209,270,71,430)(5,431,72,271,210,121,88,154,306,374,290,350,183,176,25)(6,26,161,184,351,291,375,307,155,89,122,211,272,73,432)(7,417,74,257,212,123,90,156,308,376,292,352,185,162,27)(8,28,163,186,337,293,377,309,157,91,124,213,258,75,418)(9,419,76,259,214,125,92,158,310,378,294,338,187,164,29)(10,30,165,188,339,295,379,311,159,93,126,215,260,77,420)(11,421,78,261,216,127,94,160,312,380,296,340,189,166,31)(12,32,167,190,341,297,381,313,145,95,128,217,262,79,422)(13,423,80,263,218,113,96,146,314,382,298,342,191,168,17)(14,18,169,192,343,299,383,315,147,81,114,219,264,65,424)(15,425,66,265,220,115,82,148,316,384,300,344,177,170,19)(16,20,171,178,345,301,369,317,149,83,116,221,266,67,426)(33,104,458,253,331,281,193,57,433,397,356,137,478,237,415)(34,416,238,479,138,357,398,434,58,194,282,332,254,459,105)(35,106,460,255,333,283,195,59,435,399,358,139,480,239,401)(36,402,240,465,140,359,400,436,60,196,284,334,256,461,107)(37,108,462,241,335,285,197,61,437,385,360,141,466,225,403)(38,404,226,467,142,361,386,438,62,198,286,336,242,463,109)(39,110,464,243,321,287,199,63,439,387,362,143,468,227,405)(40,406,228,469,144,363,388,440,64,200,288,322,244,449,111)(41,112,450,245,323,273,201,49,441,389,364,129,470,229,407)(42,408,230,471,130,365,390,442,50,202,274,324,246,451,97)(43,98,452,247,325,275,203,51,443,391,366,131,472,231,409)(44,410,232,473,132,367,392,444,52,204,276,326,248,453,99)(45,100,454,249,327,277,205,53,445,393,368,133,474,233,411)(46,412,234,475,134,353,394,446,54,206,278,328,250,455,101)(47,102,456,251,329,279,207,55,447,395,354,135,476,235,413)(48,414,236,477,136,355,396,448,56,208,280,330,252,457,103), (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), (1,470,9,478)(2,469,10,477)(3,468,11,476)(4,467,12,475)(5,466,13,474)(6,465,14,473)(7,480,15,472)(8,479,16,471)(17,133,25,141)(18,132,26,140)(19,131,27,139)(20,130,28,138)(21,129,29,137)(22,144,30,136)(23,143,31,135)(24,142,32,134)(33,267,41,259)(34,266,42,258)(35,265,43,257)(36,264,44,272)(37,263,45,271)(38,262,46,270)(39,261,47,269)(40,260,48,268)(49,294,57,302)(50,293,58,301)(51,292,59,300)(52,291,60,299)(53,290,61,298)(54,289,62,297)(55,304,63,296)(56,303,64,295)(65,410,73,402)(66,409,74,401)(67,408,75,416)(68,407,76,415)(69,406,77,414)(70,405,78,413)(71,404,79,412)(72,403,80,411)(81,248,89,256)(82,247,90,255)(83,246,91,254)(84,245,92,253)(85,244,93,252)(86,243,94,251)(87,242,95,250)(88,241,96,249)(97,213,105,221)(98,212,106,220)(99,211,107,219)(100,210,108,218)(101,209,109,217)(102,224,110,216)(103,223,111,215)(104,222,112,214)(113,454,121,462)(114,453,122,461)(115,452,123,460)(116,451,124,459)(117,450,125,458)(118,449,126,457)(119,464,127,456)(120,463,128,455)(145,328,153,336)(146,327,154,335)(147,326,155,334)(148,325,156,333)(149,324,157,332)(150,323,158,331)(151,322,159,330)(152,321,160,329)(161,359,169,367)(162,358,170,366)(163,357,171,365)(164,356,172,364)(165,355,173,363)(166,354,174,362)(167,353,175,361)(168,368,176,360)(177,391,185,399)(178,390,186,398)(179,389,187,397)(180,388,188,396)(181,387,189,395)(182,386,190,394)(183,385,191,393)(184,400,192,392)(193,370,201,378)(194,369,202,377)(195,384,203,376)(196,383,204,375)(197,382,205,374)(198,381,206,373)(199,380,207,372)(200,379,208,371)(225,423,233,431)(226,422,234,430)(227,421,235,429)(228,420,236,428)(229,419,237,427)(230,418,238,426)(231,417,239,425)(232,432,240,424)(273,310,281,318)(274,309,282,317)(275,308,283,316)(276,307,284,315)(277,306,285,314)(278,305,286,313)(279,320,287,312)(280,319,288,311)(337,434,345,442)(338,433,346,441)(339,448,347,440)(340,447,348,439)(341,446,349,438)(342,445,350,437)(343,444,351,436)(344,443,352,435)>;

G:=Group( (1,427,68,267,222,117,84,150,318,370,302,346,179,172,21)(2,22,173,180,347,303,371,319,151,85,118,223,268,69,428)(3,429,70,269,224,119,86,152,320,372,304,348,181,174,23)(4,24,175,182,349,289,373,305,153,87,120,209,270,71,430)(5,431,72,271,210,121,88,154,306,374,290,350,183,176,25)(6,26,161,184,351,291,375,307,155,89,122,211,272,73,432)(7,417,74,257,212,123,90,156,308,376,292,352,185,162,27)(8,28,163,186,337,293,377,309,157,91,124,213,258,75,418)(9,419,76,259,214,125,92,158,310,378,294,338,187,164,29)(10,30,165,188,339,295,379,311,159,93,126,215,260,77,420)(11,421,78,261,216,127,94,160,312,380,296,340,189,166,31)(12,32,167,190,341,297,381,313,145,95,128,217,262,79,422)(13,423,80,263,218,113,96,146,314,382,298,342,191,168,17)(14,18,169,192,343,299,383,315,147,81,114,219,264,65,424)(15,425,66,265,220,115,82,148,316,384,300,344,177,170,19)(16,20,171,178,345,301,369,317,149,83,116,221,266,67,426)(33,104,458,253,331,281,193,57,433,397,356,137,478,237,415)(34,416,238,479,138,357,398,434,58,194,282,332,254,459,105)(35,106,460,255,333,283,195,59,435,399,358,139,480,239,401)(36,402,240,465,140,359,400,436,60,196,284,334,256,461,107)(37,108,462,241,335,285,197,61,437,385,360,141,466,225,403)(38,404,226,467,142,361,386,438,62,198,286,336,242,463,109)(39,110,464,243,321,287,199,63,439,387,362,143,468,227,405)(40,406,228,469,144,363,388,440,64,200,288,322,244,449,111)(41,112,450,245,323,273,201,49,441,389,364,129,470,229,407)(42,408,230,471,130,365,390,442,50,202,274,324,246,451,97)(43,98,452,247,325,275,203,51,443,391,366,131,472,231,409)(44,410,232,473,132,367,392,444,52,204,276,326,248,453,99)(45,100,454,249,327,277,205,53,445,393,368,133,474,233,411)(46,412,234,475,134,353,394,446,54,206,278,328,250,455,101)(47,102,456,251,329,279,207,55,447,395,354,135,476,235,413)(48,414,236,477,136,355,396,448,56,208,280,330,252,457,103), (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), (1,470,9,478)(2,469,10,477)(3,468,11,476)(4,467,12,475)(5,466,13,474)(6,465,14,473)(7,480,15,472)(8,479,16,471)(17,133,25,141)(18,132,26,140)(19,131,27,139)(20,130,28,138)(21,129,29,137)(22,144,30,136)(23,143,31,135)(24,142,32,134)(33,267,41,259)(34,266,42,258)(35,265,43,257)(36,264,44,272)(37,263,45,271)(38,262,46,270)(39,261,47,269)(40,260,48,268)(49,294,57,302)(50,293,58,301)(51,292,59,300)(52,291,60,299)(53,290,61,298)(54,289,62,297)(55,304,63,296)(56,303,64,295)(65,410,73,402)(66,409,74,401)(67,408,75,416)(68,407,76,415)(69,406,77,414)(70,405,78,413)(71,404,79,412)(72,403,80,411)(81,248,89,256)(82,247,90,255)(83,246,91,254)(84,245,92,253)(85,244,93,252)(86,243,94,251)(87,242,95,250)(88,241,96,249)(97,213,105,221)(98,212,106,220)(99,211,107,219)(100,210,108,218)(101,209,109,217)(102,224,110,216)(103,223,111,215)(104,222,112,214)(113,454,121,462)(114,453,122,461)(115,452,123,460)(116,451,124,459)(117,450,125,458)(118,449,126,457)(119,464,127,456)(120,463,128,455)(145,328,153,336)(146,327,154,335)(147,326,155,334)(148,325,156,333)(149,324,157,332)(150,323,158,331)(151,322,159,330)(152,321,160,329)(161,359,169,367)(162,358,170,366)(163,357,171,365)(164,356,172,364)(165,355,173,363)(166,354,174,362)(167,353,175,361)(168,368,176,360)(177,391,185,399)(178,390,186,398)(179,389,187,397)(180,388,188,396)(181,387,189,395)(182,386,190,394)(183,385,191,393)(184,400,192,392)(193,370,201,378)(194,369,202,377)(195,384,203,376)(196,383,204,375)(197,382,205,374)(198,381,206,373)(199,380,207,372)(200,379,208,371)(225,423,233,431)(226,422,234,430)(227,421,235,429)(228,420,236,428)(229,419,237,427)(230,418,238,426)(231,417,239,425)(232,432,240,424)(273,310,281,318)(274,309,282,317)(275,308,283,316)(276,307,284,315)(277,306,285,314)(278,305,286,313)(279,320,287,312)(280,319,288,311)(337,434,345,442)(338,433,346,441)(339,448,347,440)(340,447,348,439)(341,446,349,438)(342,445,350,437)(343,444,351,436)(344,443,352,435) );

G=PermutationGroup([(1,427,68,267,222,117,84,150,318,370,302,346,179,172,21),(2,22,173,180,347,303,371,319,151,85,118,223,268,69,428),(3,429,70,269,224,119,86,152,320,372,304,348,181,174,23),(4,24,175,182,349,289,373,305,153,87,120,209,270,71,430),(5,431,72,271,210,121,88,154,306,374,290,350,183,176,25),(6,26,161,184,351,291,375,307,155,89,122,211,272,73,432),(7,417,74,257,212,123,90,156,308,376,292,352,185,162,27),(8,28,163,186,337,293,377,309,157,91,124,213,258,75,418),(9,419,76,259,214,125,92,158,310,378,294,338,187,164,29),(10,30,165,188,339,295,379,311,159,93,126,215,260,77,420),(11,421,78,261,216,127,94,160,312,380,296,340,189,166,31),(12,32,167,190,341,297,381,313,145,95,128,217,262,79,422),(13,423,80,263,218,113,96,146,314,382,298,342,191,168,17),(14,18,169,192,343,299,383,315,147,81,114,219,264,65,424),(15,425,66,265,220,115,82,148,316,384,300,344,177,170,19),(16,20,171,178,345,301,369,317,149,83,116,221,266,67,426),(33,104,458,253,331,281,193,57,433,397,356,137,478,237,415),(34,416,238,479,138,357,398,434,58,194,282,332,254,459,105),(35,106,460,255,333,283,195,59,435,399,358,139,480,239,401),(36,402,240,465,140,359,400,436,60,196,284,334,256,461,107),(37,108,462,241,335,285,197,61,437,385,360,141,466,225,403),(38,404,226,467,142,361,386,438,62,198,286,336,242,463,109),(39,110,464,243,321,287,199,63,439,387,362,143,468,227,405),(40,406,228,469,144,363,388,440,64,200,288,322,244,449,111),(41,112,450,245,323,273,201,49,441,389,364,129,470,229,407),(42,408,230,471,130,365,390,442,50,202,274,324,246,451,97),(43,98,452,247,325,275,203,51,443,391,366,131,472,231,409),(44,410,232,473,132,367,392,444,52,204,276,326,248,453,99),(45,100,454,249,327,277,205,53,445,393,368,133,474,233,411),(46,412,234,475,134,353,394,446,54,206,278,328,250,455,101),(47,102,456,251,329,279,207,55,447,395,354,135,476,235,413),(48,414,236,477,136,355,396,448,56,208,280,330,252,457,103)], [(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)], [(1,470,9,478),(2,469,10,477),(3,468,11,476),(4,467,12,475),(5,466,13,474),(6,465,14,473),(7,480,15,472),(8,479,16,471),(17,133,25,141),(18,132,26,140),(19,131,27,139),(20,130,28,138),(21,129,29,137),(22,144,30,136),(23,143,31,135),(24,142,32,134),(33,267,41,259),(34,266,42,258),(35,265,43,257),(36,264,44,272),(37,263,45,271),(38,262,46,270),(39,261,47,269),(40,260,48,268),(49,294,57,302),(50,293,58,301),(51,292,59,300),(52,291,60,299),(53,290,61,298),(54,289,62,297),(55,304,63,296),(56,303,64,295),(65,410,73,402),(66,409,74,401),(67,408,75,416),(68,407,76,415),(69,406,77,414),(70,405,78,413),(71,404,79,412),(72,403,80,411),(81,248,89,256),(82,247,90,255),(83,246,91,254),(84,245,92,253),(85,244,93,252),(86,243,94,251),(87,242,95,250),(88,241,96,249),(97,213,105,221),(98,212,106,220),(99,211,107,219),(100,210,108,218),(101,209,109,217),(102,224,110,216),(103,223,111,215),(104,222,112,214),(113,454,121,462),(114,453,122,461),(115,452,123,460),(116,451,124,459),(117,450,125,458),(118,449,126,457),(119,464,127,456),(120,463,128,455),(145,328,153,336),(146,327,154,335),(147,326,155,334),(148,325,156,333),(149,324,157,332),(150,323,158,331),(151,322,159,330),(152,321,160,329),(161,359,169,367),(162,358,170,366),(163,357,171,365),(164,356,172,364),(165,355,173,363),(166,354,174,362),(167,353,175,361),(168,368,176,360),(177,391,185,399),(178,390,186,398),(179,389,187,397),(180,388,188,396),(181,387,189,395),(182,386,190,394),(183,385,191,393),(184,400,192,392),(193,370,201,378),(194,369,202,377),(195,384,203,376),(196,383,204,375),(197,382,205,374),(198,381,206,373),(199,380,207,372),(200,379,208,371),(225,423,233,431),(226,422,234,430),(227,421,235,429),(228,420,236,428),(229,419,237,427),(230,418,238,426),(231,417,239,425),(232,432,240,424),(273,310,281,318),(274,309,282,317),(275,308,283,316),(276,307,284,315),(277,306,285,314),(278,305,286,313),(279,320,287,312),(280,319,288,311),(337,434,345,442),(338,433,346,441),(339,448,347,440),(340,447,348,439),(341,446,349,438),(342,445,350,437),(343,444,351,436),(344,443,352,435)])

60 conjugacy classes

class 1  2  3 4A4B4C5A5B 6 8A8B10A10B12A12B12C15A15B15C15D16A16B16C16D20A20B20C20D20E20F24A24B30A30B30C30D40A40B40C40D60A60B60C60D60E···60L120A···120H
order1234445568810101212121515151516161616202020202020242430303030404040406060606060···60120···120
size112281202222222488222230303030448888442222444444448···84···4

60 irreducible representations

dim1111222222222222444444
type+++++++++++-+++--+-
imageC1C2C2C2S3D4D5D6D8D10C3⋊D4D15Q32C5⋊D4D30C157D4D4⋊S3D4⋊D5C3⋊Q32C5⋊Q32D4⋊D15C157Q32
kernelC157Q32C153C16Dic60C15×Q16C5×Q16C60C3×Q16C40C30C24C20Q16C15C12C8C4C10C6C5C3C2C1
# reps1111112122244448122448

Matrix representation of C157Q32 in GL4(𝔽241) generated by

1488000
16113100
0010
0001
,
8720500
6315400
00183123
00188129
,
16519200
497600
00127240
00224114
G:=sub<GL(4,GF(241))| [148,161,0,0,80,131,0,0,0,0,1,0,0,0,0,1],[87,63,0,0,205,154,0,0,0,0,183,188,0,0,123,129],[165,49,0,0,192,76,0,0,0,0,127,224,0,0,240,114] >;

C157Q32 in GAP, Magma, Sage, TeX

C_{15}\rtimes_7Q_{32}
% in TeX

G:=Group("C15:7Q32");
// GroupNames label

G:=SmallGroup(480,189);
// by ID

G=gap.SmallGroup(480,189);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,85,120,254,135,142,675,346,80,2693,18822]);
// Polycyclic

G:=Group<a,b,c|a^15=b^16=1,c^2=b^8,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C157Q32 in TeX

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