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## G = C7×C42.30C22order 448 = 26·7

### Direct product of C7 and C42.30C22

direct product, metabelian, nilpotent (class 3), monomial, 2-elementary

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C4 — C7×C42.30C22
 Chief series C1 — C2 — C4 — C2×C4 — C2×C28 — Q8×C14 — C7×Q8⋊C4 — C7×C42.30C22
 Lower central C1 — C2 — C2×C4 — C7×C42.30C22
 Upper central C1 — C2×C14 — C4×C28 — C7×C42.30C22

Generators and relations for C7×C42.30C22
G = < a,b,c,d,e | a7=b4=c4=1, d2=c2, e2=c, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, dbd-1=b-1, ebe-1=bc2, dcd-1=c-1, ce=ec, ede-1=b2c-1d >

Subgroups: 146 in 90 conjugacy classes, 50 normal (18 characteristic)
C1, C2, C2, C4, C4, C22, C7, C8, C2×C4, C2×C4, C2×C4, Q8, C14, C14, C42, C4⋊C4, C4⋊C4, C2×C8, C2×Q8, C28, C28, C2×C14, C8⋊C4, Q8⋊C4, C42.C2, C4⋊Q8, C56, C2×C28, C2×C28, C2×C28, C7×Q8, C42.30C22, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×C56, Q8×C14, C7×C8⋊C4, C7×Q8⋊C4, C7×C42.C2, C7×C4⋊Q8, C7×C42.30C22
Quotients: C1, C2, C22, C7, D4, C23, C14, C2×D4, C4○D4, C2×C14, C4.4D4, C8.C22, C7×D4, C22×C14, C42.30C22, D4×C14, C7×C4○D4, C7×C4.4D4, C7×C8.C22, C7×C42.30C22

Smallest permutation representation of C7×C42.30C22
Regular action on 448 points
Generators in S448
(1 147 35 139 27 131 19)(2 148 36 140 28 132 20)(3 149 37 141 29 133 21)(4 150 38 142 30 134 22)(5 151 39 143 31 135 23)(6 152 40 144 32 136 24)(7 145 33 137 25 129 17)(8 146 34 138 26 130 18)(9 122 58 162 50 154 42)(10 123 59 163 51 155 43)(11 124 60 164 52 156 44)(12 125 61 165 53 157 45)(13 126 62 166 54 158 46)(14 127 63 167 55 159 47)(15 128 64 168 56 160 48)(16 121 57 161 49 153 41)(65 169 193 81 185 73 177)(66 170 194 82 186 74 178)(67 171 195 83 187 75 179)(68 172 196 84 188 76 180)(69 173 197 85 189 77 181)(70 174 198 86 190 78 182)(71 175 199 87 191 79 183)(72 176 200 88 192 80 184)(89 229 217 105 209 97 201)(90 230 218 106 210 98 202)(91 231 219 107 211 99 203)(92 232 220 108 212 100 204)(93 225 221 109 213 101 205)(94 226 222 110 214 102 206)(95 227 223 111 215 103 207)(96 228 224 112 216 104 208)(113 446 330 438 322 430 314)(114 447 331 439 323 431 315)(115 448 332 440 324 432 316)(116 441 333 433 325 425 317)(117 442 334 434 326 426 318)(118 443 335 435 327 427 319)(119 444 336 436 328 428 320)(120 445 329 437 321 429 313)(233 341 365 249 357 241 349)(234 342 366 250 358 242 350)(235 343 367 251 359 243 351)(236 344 368 252 360 244 352)(237 337 361 253 353 245 345)(238 338 362 254 354 246 346)(239 339 363 255 355 247 347)(240 340 364 256 356 248 348)(257 281 389 273 381 265 373)(258 282 390 274 382 266 374)(259 283 391 275 383 267 375)(260 284 392 276 384 268 376)(261 285 385 277 377 269 369)(262 286 386 278 378 270 370)(263 287 387 279 379 271 371)(264 288 388 280 380 272 372)(289 397 421 305 413 297 405)(290 398 422 306 414 298 406)(291 399 423 307 415 299 407)(292 400 424 308 416 300 408)(293 393 417 309 409 301 401)(294 394 418 310 410 302 402)(295 395 419 311 411 303 403)(296 396 420 312 412 304 404)
(1 92 173 42)(2 89 174 47)(3 94 175 44)(4 91 176 41)(5 96 169 46)(6 93 170 43)(7 90 171 48)(8 95 172 45)(9 147 232 197)(10 152 225 194)(11 149 226 199)(12 146 227 196)(13 151 228 193)(14 148 229 198)(15 145 230 195)(16 150 231 200)(17 202 67 160)(18 207 68 157)(19 204 69 154)(20 201 70 159)(21 206 71 156)(22 203 72 153)(23 208 65 158)(24 205 66 155)(25 210 75 168)(26 215 76 165)(27 212 77 162)(28 209 78 167)(29 214 79 164)(30 211 80 161)(31 216 73 166)(32 213 74 163)(33 218 83 128)(34 223 84 125)(35 220 85 122)(36 217 86 127)(37 222 87 124)(38 219 88 121)(39 224 81 126)(40 221 82 123)(49 134 99 184)(50 131 100 181)(51 136 101 178)(52 133 102 183)(53 130 103 180)(54 135 104 177)(55 132 97 182)(56 129 98 179)(57 142 107 192)(58 139 108 189)(59 144 109 186)(60 141 110 191)(61 138 111 188)(62 143 112 185)(63 140 105 190)(64 137 106 187)(113 417 287 366)(114 422 288 363)(115 419 281 368)(116 424 282 365)(117 421 283 362)(118 418 284 367)(119 423 285 364)(120 420 286 361)(233 425 292 374)(234 430 293 371)(235 427 294 376)(236 432 295 373)(237 429 296 370)(238 426 289 375)(239 431 290 372)(240 428 291 369)(241 433 300 382)(242 438 301 379)(243 435 302 384)(244 440 303 381)(245 437 304 378)(246 434 297 383)(247 439 298 380)(248 436 299 377)(249 441 308 390)(250 446 309 387)(251 443 310 392)(252 448 311 389)(253 445 312 386)(254 442 305 391)(255 447 306 388)(256 444 307 385)(257 344 316 395)(258 341 317 400)(259 338 318 397)(260 343 319 394)(261 340 320 399)(262 337 313 396)(263 342 314 393)(264 339 315 398)(265 352 324 403)(266 349 325 408)(267 346 326 405)(268 351 327 402)(269 348 328 407)(270 345 321 404)(271 350 322 401)(272 347 323 406)(273 360 332 411)(274 357 333 416)(275 354 334 413)(276 359 335 410)(277 356 336 415)(278 353 329 412)(279 358 330 409)(280 355 331 414)
(1 3 5 7)(2 4 6 8)(9 11 13 15)(10 12 14 16)(17 19 21 23)(18 20 22 24)(25 27 29 31)(26 28 30 32)(33 35 37 39)(34 36 38 40)(41 43 45 47)(42 44 46 48)(49 51 53 55)(50 52 54 56)(57 59 61 63)(58 60 62 64)(65 67 69 71)(66 68 70 72)(73 75 77 79)(74 76 78 80)(81 83 85 87)(82 84 86 88)(89 91 93 95)(90 92 94 96)(97 99 101 103)(98 100 102 104)(105 107 109 111)(106 108 110 112)(113 115 117 119)(114 116 118 120)(121 123 125 127)(122 124 126 128)(129 131 133 135)(130 132 134 136)(137 139 141 143)(138 140 142 144)(145 147 149 151)(146 148 150 152)(153 155 157 159)(154 156 158 160)(161 163 165 167)(162 164 166 168)(169 171 173 175)(170 172 174 176)(177 179 181 183)(178 180 182 184)(185 187 189 191)(186 188 190 192)(193 195 197 199)(194 196 198 200)(201 203 205 207)(202 204 206 208)(209 211 213 215)(210 212 214 216)(217 219 221 223)(218 220 222 224)(225 227 229 231)(226 228 230 232)(233 235 237 239)(234 236 238 240)(241 243 245 247)(242 244 246 248)(249 251 253 255)(250 252 254 256)(257 259 261 263)(258 260 262 264)(265 267 269 271)(266 268 270 272)(273 275 277 279)(274 276 278 280)(281 283 285 287)(282 284 286 288)(289 291 293 295)(290 292 294 296)(297 299 301 303)(298 300 302 304)(305 307 309 311)(306 308 310 312)(313 315 317 319)(314 316 318 320)(321 323 325 327)(322 324 326 328)(329 331 333 335)(330 332 334 336)(337 339 341 343)(338 340 342 344)(345 347 349 351)(346 348 350 352)(353 355 357 359)(354 356 358 360)(361 363 365 367)(362 364 366 368)(369 371 373 375)(370 372 374 376)(377 379 381 383)(378 380 382 384)(385 387 389 391)(386 388 390 392)(393 395 397 399)(394 396 398 400)(401 403 405 407)(402 404 406 408)(409 411 413 415)(410 412 414 416)(417 419 421 423)(418 420 422 424)(425 427 429 431)(426 428 430 432)(433 435 437 439)(434 436 438 440)(441 443 445 447)(442 444 446 448)
(1 395 5 399)(2 339 6 343)(3 393 7 397)(4 337 8 341)(9 281 13 285)(10 118 14 114)(11 287 15 283)(12 116 16 120)(17 289 21 293)(18 233 22 237)(19 295 23 291)(20 239 24 235)(25 297 29 301)(26 241 30 245)(27 303 31 299)(28 247 32 243)(33 305 37 309)(34 249 38 253)(35 311 39 307)(36 255 40 251)(41 313 45 317)(42 257 46 261)(43 319 47 315)(44 263 48 259)(49 321 53 325)(50 265 54 269)(51 327 55 323)(52 271 56 267)(57 329 61 333)(58 273 62 277)(59 335 63 331)(60 279 64 275)(65 240 69 236)(66 294 70 290)(67 238 71 234)(68 292 72 296)(73 248 77 244)(74 302 78 298)(75 246 79 242)(76 300 80 304)(81 256 85 252)(82 310 86 306)(83 254 87 250)(84 308 88 312)(89 264 93 260)(90 318 94 314)(91 262 95 258)(92 316 96 320)(97 272 101 268)(98 326 102 322)(99 270 103 266)(100 324 104 328)(105 280 109 276)(106 334 110 330)(107 278 111 274)(108 332 112 336)(113 230 117 226)(115 228 119 232)(121 445 125 441)(122 389 126 385)(123 443 127 447)(124 387 128 391)(129 405 133 401)(130 349 134 345)(131 403 135 407)(132 347 136 351)(137 413 141 409)(138 357 142 353)(139 411 143 415)(140 355 144 359)(145 421 149 417)(146 365 150 361)(147 419 151 423)(148 363 152 367)(153 429 157 425)(154 373 158 369)(155 427 159 431)(156 371 160 375)(161 437 165 433)(162 381 166 377)(163 435 167 439)(164 379 168 383)(169 340 173 344)(170 394 174 398)(171 338 175 342)(172 400 176 396)(177 348 181 352)(178 402 182 406)(179 346 183 350)(180 408 184 404)(185 356 189 360)(186 410 190 414)(187 354 191 358)(188 416 192 412)(193 364 197 368)(194 418 198 422)(195 362 199 366)(196 424 200 420)(201 372 205 376)(202 426 206 430)(203 370 207 374)(204 432 208 428)(209 380 213 384)(210 434 214 438)(211 378 215 382)(212 440 216 436)(217 388 221 392)(218 442 222 446)(219 386 223 390)(220 448 224 444)(225 284 229 288)(227 282 231 286)
(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)

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

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

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

112 conjugacy classes

 class 1 2A 2B 2C 4A 4B 4C 4D 4E 4F 4G 4H 7A ··· 7F 8A 8B 8C 8D 14A ··· 14R 28A ··· 28L 28M ··· 28X 28Y ··· 28AV 56A ··· 56X order 1 2 2 2 4 4 4 4 4 4 4 4 7 ··· 7 8 8 8 8 14 ··· 14 28 ··· 28 28 ··· 28 28 ··· 28 56 ··· 56 size 1 1 1 1 2 2 4 4 8 8 8 8 1 ··· 1 4 4 4 4 1 ··· 1 2 ··· 2 4 ··· 4 8 ··· 8 4 ··· 4

112 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 2 2 2 2 4 4 type + + + + + + - image C1 C2 C2 C2 C2 C7 C14 C14 C14 C14 D4 C4○D4 C7×D4 C7×C4○D4 C8.C22 C7×C8.C22 kernel C7×C42.30C22 C7×C8⋊C4 C7×Q8⋊C4 C7×C42.C2 C7×C4⋊Q8 C42.30C22 C8⋊C4 Q8⋊C4 C42.C2 C4⋊Q8 C2×C28 C28 C2×C4 C4 C14 C2 # reps 1 1 4 1 1 6 6 24 6 6 2 4 12 24 2 12

Matrix representation of C7×C42.30C22 in GL6(𝔽113)

 1 0 0 0 0 0 0 1 0 0 0 0 0 0 49 0 0 0 0 0 0 49 0 0 0 0 0 0 49 0 0 0 0 0 0 49
,
 96 30 0 0 0 0 28 17 0 0 0 0 0 0 27 46 15 1 0 0 67 27 112 15 0 0 1 98 86 67 0 0 15 1 46 86
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 112 0 0 0 0 1 0 0 0 0 0 0 0 0 112 0 0 0 0 1 0
,
 33 111 0 0 0 0 92 80 0 0 0 0 0 0 63 22 59 42 0 0 22 50 42 54 0 0 54 71 91 63 0 0 71 59 63 22
,
 84 111 0 0 0 0 81 29 0 0 0 0 0 0 98 112 67 27 0 0 1 98 86 67 0 0 27 46 15 1 0 0 67 27 112 15

G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,49,0,0,0,0,0,0,49,0,0,0,0,0,0,49,0,0,0,0,0,0,49],[96,28,0,0,0,0,30,17,0,0,0,0,0,0,27,67,1,15,0,0,46,27,98,1,0,0,15,112,86,46,0,0,1,15,67,86],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,112,0,0,0,0,0,0,0,0,1,0,0,0,0,112,0],[33,92,0,0,0,0,111,80,0,0,0,0,0,0,63,22,54,71,0,0,22,50,71,59,0,0,59,42,91,63,0,0,42,54,63,22],[84,81,0,0,0,0,111,29,0,0,0,0,0,0,98,1,27,67,0,0,112,98,46,27,0,0,67,86,15,112,0,0,27,67,1,15] >;

C7×C42.30C22 in GAP, Magma, Sage, TeX

C_7\times C_4^2._{30}C_2^2
% in TeX

G:=Group("C7xC4^2.30C2^2");
// GroupNames label

G:=SmallGroup(448,899);
// by ID

G=gap.SmallGroup(448,899);
# by ID

G:=PCGroup([7,-2,-2,-2,-7,-2,-2,-2,1568,813,2360,2438,2403,310,9804,172,14117,124]);
// Polycyclic

G:=Group<a,b,c,d,e|a^7=b^4=c^4=1,d^2=c^2,e^2=c,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,d*b*d^-1=b^-1,e*b*e^-1=b*c^2,d*c*d^-1=c^-1,c*e=e*c,e*d*e^-1=b^2*c^-1*d>;
// generators/relations

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