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## G = C7×Q82order 448 = 26·7

### Direct product of C7, Q8 and Q8

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

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22 — C7×Q82
 Chief series C1 — C2 — C22 — C2×C14 — C2×C28 — C7×C4⋊C4 — C7×C4⋊Q8 — C7×Q82
 Lower central C1 — C22 — C7×Q82
 Upper central C1 — C2×C14 — C7×Q82

Generators and relations for C7×Q82
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, ce=ec, ede-1=d-1 >

Subgroups: 266 in 212 conjugacy classes, 182 normal (8 characteristic)
C1, C2, C2, C4, C4, C22, C7, C2×C4, Q8, Q8, C14, C14, C42, C4⋊C4, C2×Q8, C28, C28, C2×C14, C4×Q8, C4⋊Q8, C2×C28, C7×Q8, C7×Q8, Q82, C4×C28, C7×C4⋊C4, Q8×C14, Q8×C28, C7×C4⋊Q8, C7×Q82
Quotients: C1, C2, C22, C7, Q8, C23, C14, C2×Q8, C24, C2×C14, C22×Q8, 2+ 1+4, C7×Q8, C22×C14, Q82, Q8×C14, C23×C14, Q8×C2×C14, C7×2+ 1+4, C7×Q82

Smallest permutation representation of C7×Q82
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 98 35 78)(2 92 29 79)(3 93 30 80)(4 94 31 81)(5 95 32 82)(6 96 33 83)(7 97 34 84)(8 400 18 387)(9 401 19 388)(10 402 20 389)(11 403 21 390)(12 404 15 391)(13 405 16 392)(14 406 17 386)(22 408 447 397)(23 409 448 398)(24 410 442 399)(25 411 443 393)(26 412 444 394)(27 413 445 395)(28 407 446 396)(36 103 48 85)(37 104 49 86)(38 105 43 87)(39 99 44 88)(40 100 45 89)(41 101 46 90)(42 102 47 91)(50 119 70 130)(51 113 64 131)(52 114 65 132)(53 115 66 133)(54 116 67 127)(55 117 68 128)(56 118 69 129)(57 107 75 120)(58 108 76 121)(59 109 77 122)(60 110 71 123)(61 111 72 124)(62 112 73 125)(63 106 74 126)(134 203 154 214)(135 197 148 215)(136 198 149 216)(137 199 150 217)(138 200 151 211)(139 201 152 212)(140 202 153 213)(141 191 159 204)(142 192 160 205)(143 193 161 206)(144 194 155 207)(145 195 156 208)(146 196 157 209)(147 190 158 210)(162 231 182 242)(163 225 176 243)(164 226 177 244)(165 227 178 245)(166 228 179 239)(167 229 180 240)(168 230 181 241)(169 219 187 232)(170 220 188 233)(171 221 189 234)(172 222 183 235)(173 223 184 236)(174 224 185 237)(175 218 186 238)(246 326 266 315)(247 327 260 309)(248 328 261 310)(249 329 262 311)(250 323 263 312)(251 324 264 313)(252 325 265 314)(253 316 271 303)(254 317 272 304)(255 318 273 305)(256 319 267 306)(257 320 268 307)(258 321 269 308)(259 322 270 302)(274 354 294 343)(275 355 288 337)(276 356 289 338)(277 357 290 339)(278 351 291 340)(279 352 292 341)(280 353 293 342)(281 344 299 331)(282 345 300 332)(283 346 301 333)(284 347 295 334)(285 348 296 335)(286 349 297 336)(287 350 298 330)(358 438 378 427)(359 439 372 421)(360 440 373 422)(361 441 374 423)(362 435 375 424)(363 436 376 425)(364 437 377 426)(365 428 383 415)(366 429 384 416)(367 430 385 417)(368 431 379 418)(369 432 380 419)(370 433 381 420)(371 434 382 414)
(1 294 35 274)(2 288 29 275)(3 289 30 276)(4 290 31 277)(5 291 32 278)(6 292 33 279)(7 293 34 280)(8 215 18 197)(9 216 19 198)(10 217 20 199)(11 211 21 200)(12 212 15 201)(13 213 16 202)(14 214 17 203)(22 208 447 195)(23 209 448 196)(24 210 442 190)(25 204 443 191)(26 205 444 192)(27 206 445 193)(28 207 446 194)(36 299 48 281)(37 300 49 282)(38 301 43 283)(39 295 44 284)(40 296 45 285)(41 297 46 286)(42 298 47 287)(50 266 70 246)(51 260 64 247)(52 261 65 248)(53 262 66 249)(54 263 67 250)(55 264 68 251)(56 265 69 252)(57 271 75 253)(58 272 76 254)(59 273 77 255)(60 267 71 256)(61 268 72 257)(62 269 73 258)(63 270 74 259)(78 343 98 354)(79 337 92 355)(80 338 93 356)(81 339 94 357)(82 340 95 351)(83 341 96 352)(84 342 97 353)(85 331 103 344)(86 332 104 345)(87 333 105 346)(88 334 99 347)(89 335 100 348)(90 336 101 349)(91 330 102 350)(106 322 126 302)(107 316 120 303)(108 317 121 304)(109 318 122 305)(110 319 123 306)(111 320 124 307)(112 321 125 308)(113 327 131 309)(114 328 132 310)(115 329 133 311)(116 323 127 312)(117 324 128 313)(118 325 129 314)(119 326 130 315)(134 406 154 386)(135 400 148 387)(136 401 149 388)(137 402 150 389)(138 403 151 390)(139 404 152 391)(140 405 153 392)(141 411 159 393)(142 412 160 394)(143 413 161 395)(144 407 155 396)(145 408 156 397)(146 409 157 398)(147 410 158 399)(162 371 182 382)(163 365 176 383)(164 366 177 384)(165 367 178 385)(166 368 179 379)(167 369 180 380)(168 370 181 381)(169 359 187 372)(170 360 188 373)(171 361 189 374)(172 362 183 375)(173 363 184 376)(174 364 185 377)(175 358 186 378)(218 427 238 438)(219 421 232 439)(220 422 233 440)(221 423 234 441)(222 424 235 435)(223 425 236 436)(224 426 237 437)(225 415 243 428)(226 416 244 429)(227 417 245 430)(228 418 239 431)(229 419 240 432)(230 420 241 433)(231 414 242 434)
(1 50 47 74)(2 51 48 75)(3 52 49 76)(4 53 43 77)(5 54 44 71)(6 55 45 72)(7 56 46 73)(8 415 443 439)(9 416 444 440)(10 417 445 441)(11 418 446 435)(12 419 447 436)(13 420 448 437)(14 414 442 438)(15 432 22 425)(16 433 23 426)(17 434 24 427)(18 428 25 421)(19 429 26 422)(20 430 27 423)(21 431 28 424)(29 64 36 57)(30 65 37 58)(31 66 38 59)(32 67 39 60)(33 68 40 61)(34 69 41 62)(35 70 42 63)(78 130 102 106)(79 131 103 107)(80 132 104 108)(81 133 105 109)(82 127 99 110)(83 128 100 111)(84 129 101 112)(85 120 92 113)(86 121 93 114)(87 122 94 115)(88 123 95 116)(89 124 96 117)(90 125 97 118)(91 126 98 119)(134 162 158 186)(135 163 159 187)(136 164 160 188)(137 165 161 189)(138 166 155 183)(139 167 156 184)(140 168 157 185)(141 169 148 176)(142 170 149 177)(143 171 150 178)(144 172 151 179)(145 173 152 180)(146 174 153 181)(147 175 154 182)(190 218 214 242)(191 219 215 243)(192 220 216 244)(193 221 217 245)(194 222 211 239)(195 223 212 240)(196 224 213 241)(197 225 204 232)(198 226 205 233)(199 227 206 234)(200 228 207 235)(201 229 208 236)(202 230 209 237)(203 231 210 238)(246 298 270 274)(247 299 271 275)(248 300 272 276)(249 301 273 277)(250 295 267 278)(251 296 268 279)(252 297 269 280)(253 288 260 281)(254 289 261 282)(255 290 262 283)(256 291 263 284)(257 292 264 285)(258 293 265 286)(259 294 266 287)(302 354 326 330)(303 355 327 331)(304 356 328 332)(305 357 329 333)(306 351 323 334)(307 352 324 335)(308 353 325 336)(309 344 316 337)(310 345 317 338)(311 346 318 339)(312 347 319 340)(313 348 320 341)(314 349 321 342)(315 350 322 343)(358 386 382 410)(359 387 383 411)(360 388 384 412)(361 389 385 413)(362 390 379 407)(363 391 380 408)(364 392 381 409)(365 393 372 400)(366 394 373 401)(367 395 374 402)(368 396 375 403)(369 397 376 404)(370 398 377 405)(371 399 378 406)
(1 134 47 158)(2 135 48 159)(3 136 49 160)(4 137 43 161)(5 138 44 155)(6 139 45 156)(7 140 46 157)(8 331 443 355)(9 332 444 356)(10 333 445 357)(11 334 446 351)(12 335 447 352)(13 336 448 353)(14 330 442 354)(15 348 22 341)(16 349 23 342)(17 350 24 343)(18 344 25 337)(19 345 26 338)(20 346 27 339)(21 347 28 340)(29 148 36 141)(30 149 37 142)(31 150 38 143)(32 151 39 144)(33 152 40 145)(34 153 41 146)(35 154 42 147)(50 186 74 162)(51 187 75 163)(52 188 76 164)(53 189 77 165)(54 183 71 166)(55 184 72 167)(56 185 73 168)(57 176 64 169)(58 177 65 170)(59 178 66 171)(60 179 67 172)(61 180 68 173)(62 181 69 174)(63 182 70 175)(78 214 102 190)(79 215 103 191)(80 216 104 192)(81 217 105 193)(82 211 99 194)(83 212 100 195)(84 213 101 196)(85 204 92 197)(86 205 93 198)(87 206 94 199)(88 207 95 200)(89 208 96 201)(90 209 97 202)(91 210 98 203)(106 242 130 218)(107 243 131 219)(108 244 132 220)(109 245 133 221)(110 239 127 222)(111 240 128 223)(112 241 129 224)(113 232 120 225)(114 233 121 226)(115 234 122 227)(116 235 123 228)(117 236 124 229)(118 237 125 230)(119 238 126 231)(246 358 270 382)(247 359 271 383)(248 360 272 384)(249 361 273 385)(250 362 267 379)(251 363 268 380)(252 364 269 381)(253 365 260 372)(254 366 261 373)(255 367 262 374)(256 368 263 375)(257 369 264 376)(258 370 265 377)(259 371 266 378)(274 386 298 410)(275 387 299 411)(276 388 300 412)(277 389 301 413)(278 390 295 407)(279 391 296 408)(280 392 297 409)(281 393 288 400)(282 394 289 401)(283 395 290 402)(284 396 291 403)(285 397 292 404)(286 398 293 405)(287 399 294 406)(302 414 326 438)(303 415 327 439)(304 416 328 440)(305 417 329 441)(306 418 323 435)(307 419 324 436)(308 420 325 437)(309 421 316 428)(310 422 317 429)(311 423 318 430)(312 424 319 431)(313 425 320 432)(314 426 321 433)(315 427 322 434)

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

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

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

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 2 2 4 4 type + + + - + image C1 C2 C2 C7 C14 C14 Q8 C7×Q8 2+ 1+4 C7×2+ 1+4 kernel C7×Q82 Q8×C28 C7×C4⋊Q8 Q82 C4×Q8 C4⋊Q8 C7×Q8 Q8 C14 C2 # reps 1 6 9 6 36 54 8 48 1 6

Matrix representation of C7×Q82 in GL4(𝔽29) generated by

 25 0 0 0 0 25 0 0 0 0 7 0 0 0 0 7
,
 0 1 0 0 28 0 0 0 0 0 28 0 0 0 0 28
,
 14 21 0 0 21 15 0 0 0 0 1 0 0 0 0 1
,
 28 0 0 0 0 28 0 0 0 0 0 1 0 0 28 0
,
 28 0 0 0 0 28 0 0 0 0 17 0 0 0 0 12
G:=sub<GL(4,GF(29))| [25,0,0,0,0,25,0,0,0,0,7,0,0,0,0,7],[0,28,0,0,1,0,0,0,0,0,28,0,0,0,0,28],[14,21,0,0,21,15,0,0,0,0,1,0,0,0,0,1],[28,0,0,0,0,28,0,0,0,0,0,28,0,0,1,0],[28,0,0,0,0,28,0,0,0,0,17,0,0,0,0,12] >;

C7×Q82 in GAP, Magma, Sage, TeX

C_7\times Q_8^2
% in TeX

G:=Group("C7xQ8^2");
// GroupNames label

G:=SmallGroup(448,1341);
// by ID

G=gap.SmallGroup(448,1341);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,2352,1597,792,4790,1192,1690,416]);
// 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,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations

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