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## G = C7×Q8⋊3Q8order 448 = 26·7

### Direct product of C7 and Q8⋊3Q8

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

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22 — C7×Q8⋊3Q8
 Chief series C1 — C2 — C22 — C2×C14 — C2×C28 — C7×C4⋊C4 — C7×C4⋊Q8 — C7×Q8⋊3Q8
 Lower central C1 — C22 — C7×Q8⋊3Q8
 Upper central C1 — C2×C14 — C7×Q8⋊3Q8

Generators and relations for C7×Q83Q8
G = < a,b,c,d,e | a7=b4=d4=1, c2=b2, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, be=eb, cd=dc, ece-1=b2c, ede-1=d-1 >

Subgroups: 234 in 200 conjugacy classes, 166 normal (20 characteristic)
C1, C2, C4, C4, C22, C7, C2×C4, C2×C4, Q8, Q8, C14, C42, C4⋊C4, C4⋊C4, C2×Q8, C2×Q8, C28, C28, C2×C14, C4×Q8, C4×Q8, C42.C2, C4⋊Q8, C2×C28, C2×C28, C7×Q8, C7×Q8, Q83Q8, C4×C28, C7×C4⋊C4, C7×C4⋊C4, Q8×C14, Q8×C14, Q8×C28, Q8×C28, C7×C42.C2, C7×C4⋊Q8, C7×Q83Q8
Quotients: C1, C2, C22, C7, Q8, C23, C14, C2×Q8, C4○D4, C24, C2×C14, C22×Q8, C2×C4○D4, 2- 1+4, C7×Q8, C22×C14, Q83Q8, Q8×C14, C7×C4○D4, C23×C14, Q8×C2×C14, C14×C4○D4, C7×2- 1+4, C7×Q83Q8

Smallest permutation representation of C7×Q83Q8
Regular action on 448 points
Generators in S448
(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)
(1 75 39 63)(2 76 40 57)(3 77 41 58)(4 71 42 59)(5 72 36 60)(6 73 37 61)(7 74 38 62)(8 420 23 429)(9 414 24 430)(10 415 25 431)(11 416 26 432)(12 417 27 433)(13 418 28 434)(14 419 22 428)(15 435 445 423)(16 436 446 424)(17 437 447 425)(18 438 448 426)(19 439 442 427)(20 440 443 421)(21 441 444 422)(29 51 48 67)(30 52 49 68)(31 53 43 69)(32 54 44 70)(33 55 45 64)(34 56 46 65)(35 50 47 66)(78 119 94 131)(79 113 95 132)(80 114 96 133)(81 115 97 127)(82 116 98 128)(83 117 92 129)(84 118 93 130)(85 107 104 123)(86 108 105 124)(87 109 99 125)(88 110 100 126)(89 111 101 120)(90 112 102 121)(91 106 103 122)(134 187 150 175)(135 188 151 169)(136 189 152 170)(137 183 153 171)(138 184 154 172)(139 185 148 173)(140 186 149 174)(141 179 160 163)(142 180 161 164)(143 181 155 165)(144 182 156 166)(145 176 157 167)(146 177 158 168)(147 178 159 162)(190 243 206 231)(191 244 207 225)(192 245 208 226)(193 239 209 227)(194 240 210 228)(195 241 204 229)(196 242 205 230)(197 235 216 219)(198 236 217 220)(199 237 211 221)(200 238 212 222)(201 232 213 223)(202 233 214 224)(203 234 215 218)(246 287 262 299)(247 281 263 300)(248 282 264 301)(249 283 265 295)(250 284 266 296)(251 285 260 297)(252 286 261 298)(253 275 272 291)(254 276 273 292)(255 277 267 293)(256 278 268 294)(257 279 269 288)(258 280 270 289)(259 274 271 290)(302 343 318 355)(303 337 319 356)(304 338 320 357)(305 339 321 351)(306 340 322 352)(307 341 316 353)(308 342 317 354)(309 331 328 347)(310 332 329 348)(311 333 323 349)(312 334 324 350)(313 335 325 344)(314 336 326 345)(315 330 327 346)(358 411 374 399)(359 412 375 393)(360 413 376 394)(361 407 377 395)(362 408 378 396)(363 409 372 397)(364 410 373 398)(365 403 384 387)(366 404 385 388)(367 405 379 389)(368 406 380 390)(369 400 381 391)(370 401 382 392)(371 402 383 386)
(1 159 39 147)(2 160 40 141)(3 161 41 142)(4 155 42 143)(5 156 36 144)(6 157 37 145)(7 158 38 146)(8 336 23 345)(9 330 24 346)(10 331 25 347)(11 332 26 348)(12 333 27 349)(13 334 28 350)(14 335 22 344)(15 351 445 339)(16 352 446 340)(17 353 447 341)(18 354 448 342)(19 355 442 343)(20 356 443 337)(21 357 444 338)(29 135 48 151)(30 136 49 152)(31 137 43 153)(32 138 44 154)(33 139 45 148)(34 140 46 149)(35 134 47 150)(50 175 66 187)(51 169 67 188)(52 170 68 189)(53 171 69 183)(54 172 70 184)(55 173 64 185)(56 174 65 186)(57 163 76 179)(58 164 77 180)(59 165 71 181)(60 166 72 182)(61 167 73 176)(62 168 74 177)(63 162 75 178)(78 203 94 215)(79 197 95 216)(80 198 96 217)(81 199 97 211)(82 200 98 212)(83 201 92 213)(84 202 93 214)(85 191 104 207)(86 192 105 208)(87 193 99 209)(88 194 100 210)(89 195 101 204)(90 196 102 205)(91 190 103 206)(106 231 122 243)(107 225 123 244)(108 226 124 245)(109 227 125 239)(110 228 126 240)(111 229 120 241)(112 230 121 242)(113 219 132 235)(114 220 133 236)(115 221 127 237)(116 222 128 238)(117 223 129 232)(118 224 130 233)(119 218 131 234)(246 383 262 371)(247 384 263 365)(248 385 264 366)(249 379 265 367)(250 380 266 368)(251 381 260 369)(252 382 261 370)(253 375 272 359)(254 376 273 360)(255 377 267 361)(256 378 268 362)(257 372 269 363)(258 373 270 364)(259 374 271 358)(274 411 290 399)(275 412 291 393)(276 413 292 394)(277 407 293 395)(278 408 294 396)(279 409 288 397)(280 410 289 398)(281 403 300 387)(282 404 301 388)(283 405 295 389)(284 406 296 390)(285 400 297 391)(286 401 298 392)(287 402 299 386)(302 439 318 427)(303 440 319 421)(304 441 320 422)(305 435 321 423)(306 436 322 424)(307 437 316 425)(308 438 317 426)(309 431 328 415)(310 432 329 416)(311 433 323 417)(312 434 324 418)(313 428 325 419)(314 429 326 420)(315 430 327 414)
(1 91 35 94)(2 85 29 95)(3 86 30 96)(4 87 31 97)(5 88 32 98)(6 89 33 92)(7 90 34 93)(8 401 18 398)(9 402 19 399)(10 403 20 393)(11 404 21 394)(12 405 15 395)(13 406 16 396)(14 400 17 397)(22 391 447 409)(23 392 448 410)(24 386 442 411)(25 387 443 412)(26 388 444 413)(27 389 445 407)(28 390 446 408)(36 100 44 82)(37 101 45 83)(38 102 46 84)(39 103 47 78)(40 104 48 79)(41 105 49 80)(42 99 43 81)(50 131 75 106)(51 132 76 107)(52 133 77 108)(53 127 71 109)(54 128 72 110)(55 129 73 111)(56 130 74 112)(57 123 67 113)(58 124 68 114)(59 125 69 115)(60 126 70 116)(61 120 64 117)(62 121 65 118)(63 122 66 119)(134 215 159 190)(135 216 160 191)(136 217 161 192)(137 211 155 193)(138 212 156 194)(139 213 157 195)(140 214 158 196)(141 207 151 197)(142 208 152 198)(143 209 153 199)(144 210 154 200)(145 204 148 201)(146 205 149 202)(147 206 150 203)(162 243 187 218)(163 244 188 219)(164 245 189 220)(165 239 183 221)(166 240 184 222)(167 241 185 223)(168 242 186 224)(169 235 179 225)(170 236 180 226)(171 237 181 227)(172 238 182 228)(173 232 176 229)(174 233 177 230)(175 234 178 231)(246 302 271 327)(247 303 272 328)(248 304 273 329)(249 305 267 323)(250 306 268 324)(251 307 269 325)(252 308 270 326)(253 309 263 319)(254 310 264 320)(255 311 265 321)(256 312 266 322)(257 313 260 316)(258 314 261 317)(259 315 262 318)(274 330 299 355)(275 331 300 356)(276 332 301 357)(277 333 295 351)(278 334 296 352)(279 335 297 353)(280 336 298 354)(281 337 291 347)(282 338 292 348)(283 339 293 349)(284 340 294 350)(285 341 288 344)(286 342 289 345)(287 343 290 346)(358 414 383 439)(359 415 384 440)(360 416 385 441)(361 417 379 435)(362 418 380 436)(363 419 381 437)(364 420 382 438)(365 421 375 431)(366 422 376 432)(367 423 377 433)(368 424 378 434)(369 425 372 428)(370 426 373 429)(371 427 374 430)
(1 259 35 262)(2 253 29 263)(3 254 30 264)(4 255 31 265)(5 256 32 266)(6 257 33 260)(7 258 34 261)(8 230 18 233)(9 231 19 234)(10 225 20 235)(11 226 21 236)(12 227 15 237)(13 228 16 238)(14 229 17 232)(22 241 447 223)(23 242 448 224)(24 243 442 218)(25 244 443 219)(26 245 444 220)(27 239 445 221)(28 240 446 222)(36 268 44 250)(37 269 45 251)(38 270 46 252)(39 271 47 246)(40 272 48 247)(41 273 49 248)(42 267 43 249)(50 299 75 274)(51 300 76 275)(52 301 77 276)(53 295 71 277)(54 296 72 278)(55 297 73 279)(56 298 74 280)(57 291 67 281)(58 292 68 282)(59 293 69 283)(60 294 70 284)(61 288 64 285)(62 289 65 286)(63 290 66 287)(78 327 103 302)(79 328 104 303)(80 329 105 304)(81 323 99 305)(82 324 100 306)(83 325 101 307)(84 326 102 308)(85 319 95 309)(86 320 96 310)(87 321 97 311)(88 322 98 312)(89 316 92 313)(90 317 93 314)(91 318 94 315)(106 355 131 330)(107 356 132 331)(108 357 133 332)(109 351 127 333)(110 352 128 334)(111 353 129 335)(112 354 130 336)(113 347 123 337)(114 348 124 338)(115 349 125 339)(116 350 126 340)(117 344 120 341)(118 345 121 342)(119 346 122 343)(134 383 159 358)(135 384 160 359)(136 385 161 360)(137 379 155 361)(138 380 156 362)(139 381 157 363)(140 382 158 364)(141 375 151 365)(142 376 152 366)(143 377 153 367)(144 378 154 368)(145 372 148 369)(146 373 149 370)(147 374 150 371)(162 411 187 386)(163 412 188 387)(164 413 189 388)(165 407 183 389)(166 408 184 390)(167 409 185 391)(168 410 186 392)(169 403 179 393)(170 404 180 394)(171 405 181 395)(172 406 182 396)(173 400 176 397)(174 401 177 398)(175 402 178 399)(190 439 215 414)(191 440 216 415)(192 441 217 416)(193 435 211 417)(194 436 212 418)(195 437 213 419)(196 438 214 420)(197 431 207 421)(198 432 208 422)(199 433 209 423)(200 434 210 424)(201 428 204 425)(202 429 205 426)(203 430 206 427)

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

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

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

175 conjugacy classes

 class 1 2A 2B 2C 4A ··· 4L 4M ··· 4U 7A ··· 7F 14A ··· 14R 28A ··· 28BT 28BU ··· 28DV order 1 2 2 2 4 ··· 4 4 ··· 4 7 ··· 7 14 ··· 14 28 ··· 28 28 ··· 28 size 1 1 1 1 2 ··· 2 4 ··· 4 1 ··· 1 1 ··· 1 2 ··· 2 4 ··· 4

175 irreducible representations

 dim 1 1 1 1 1 1 1 1 2 2 2 2 4 4 type + + + + - - image C1 C2 C2 C2 C7 C14 C14 C14 Q8 C4○D4 C7×Q8 C7×C4○D4 2- 1+4 C7×2- 1+4 kernel C7×Q8⋊3Q8 Q8×C28 C7×C42.C2 C7×C4⋊Q8 Q8⋊3Q8 C4×Q8 C42.C2 C4⋊Q8 C7×Q8 C28 Q8 C4 C14 C2 # reps 1 6 6 3 6 36 36 18 4 4 24 24 1 6

Matrix representation of C7×Q83Q8 in GL4(𝔽29) generated by

 25 0 0 0 0 25 0 0 0 0 25 0 0 0 0 25
,
 1 0 0 0 0 1 0 0 0 0 28 2 0 0 28 1
,
 28 0 0 0 0 28 0 0 0 0 6 1 0 0 21 23
,
 1 27 0 0 1 28 0 0 0 0 1 0 0 0 0 1
,
 12 0 0 0 12 17 0 0 0 0 17 24 0 0 17 12
G:=sub<GL(4,GF(29))| [25,0,0,0,0,25,0,0,0,0,25,0,0,0,0,25],[1,0,0,0,0,1,0,0,0,0,28,28,0,0,2,1],[28,0,0,0,0,28,0,0,0,0,6,21,0,0,1,23],[1,1,0,0,27,28,0,0,0,0,1,0,0,0,0,1],[12,12,0,0,0,17,0,0,0,0,17,17,0,0,24,12] >;

C7×Q83Q8 in GAP, Magma, Sage, TeX

C_7\times Q_8\rtimes_3Q_8
% in TeX

G:=Group("C7xQ8:3Q8");
// GroupNames label

G:=SmallGroup(448,1340);
// by ID

G=gap.SmallGroup(448,1340);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1568,1597,792,4790,1192,1690,416]);
// Polycyclic

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

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