direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: C7×Q8⋊Q8, C28.53SD16, Q8⋊1(C7×Q8), (C7×Q8)⋊8Q8, C4⋊C8.9C14, C4⋊Q8.5C14, (C4×Q8).6C14, C4.13(Q8×C14), C4.Q8.4C14, (C2×C28).331D4, (Q8×C28).19C2, C28.119(C2×Q8), C4.12(C7×SD16), C42.21(C2×C14), Q8⋊C4.4C14, C2.10(C14×SD16), C14.90(C2×SD16), C22.96(D4×C14), C28.312(C4○D4), (C2×C28).931C23, (C4×C28).263C22, (C2×C56).302C22, C14.94(C22⋊Q8), (Q8×C14).263C22, C14.140(C8.C22), (C7×C4⋊C8).22C2, C4.24(C7×C4○D4), (C7×C4⋊Q8).20C2, C4⋊C4.12(C2×C14), (C2×C8).39(C2×C14), (C2×C4).132(C7×D4), (C7×C4.Q8).11C2, C2.13(C7×C22⋊Q8), (C2×C14).652(C2×D4), (C2×Q8).50(C2×C14), C2.15(C7×C8.C22), (C7×C4⋊C4).234C22, (C7×Q8⋊C4).13C2, (C2×C4).106(C22×C14), SmallGroup(448,883)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7×Q8⋊Q8
G = < a,b,c,d,e | a7=b4=d4=1, c2=b2, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=ebe-1=b-1, bd=db, cd=dc, ece-1=b-1c, ede-1=d-1 >
Subgroups: 154 in 96 conjugacy classes, 58 normal (34 characteristic)
C1, C2, C4, C4, C4, C22, C7, C8, C2×C4, C2×C4, Q8, Q8, C14, C42, C42, C4⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×Q8, C2×Q8, C28, C28, C28, C2×C14, Q8⋊C4, C4⋊C8, C4.Q8, C4×Q8, C4⋊Q8, C56, C2×C28, C2×C28, C7×Q8, C7×Q8, Q8⋊Q8, C4×C28, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×C56, Q8×C14, Q8×C14, C7×Q8⋊C4, C7×C4⋊C8, C7×C4.Q8, Q8×C28, C7×C4⋊Q8, C7×Q8⋊Q8
Quotients: C1, C2, C22, C7, D4, Q8, C23, C14, SD16, C2×D4, C2×Q8, C4○D4, C2×C14, C22⋊Q8, C2×SD16, C8.C22, C7×D4, C7×Q8, C22×C14, Q8⋊Q8, C7×SD16, D4×C14, Q8×C14, C7×C4○D4, C7×C22⋊Q8, C14×SD16, C7×C8.C22, C7×Q8⋊Q8
►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 83 69 85)(2 84 70 86)(3 78 64 87)(4 79 65 88)(5 80 66 89)(6 81 67 90)(7 82 68 91)(8 18 31 41)(9 19 32 42)(10 20 33 36)(11 21 34 37)(12 15 35 38)(13 16 29 39)(14 17 30 40)(22 43 444 435)(23 44 445 436)(24 45 446 437)(25 46 447 438)(26 47 448 439)(27 48 442 440)(28 49 443 441)(50 95 59 71)(51 96 60 72)(52 97 61 73)(53 98 62 74)(54 92 63 75)(55 93 57 76)(56 94 58 77)(99 108 129 117)(100 109 130 118)(101 110 131 119)(102 111 132 113)(103 112 133 114)(104 106 127 115)(105 107 128 116)(120 134 153 143)(121 135 154 144)(122 136 148 145)(123 137 149 146)(124 138 150 147)(125 139 151 141)(126 140 152 142)(155 173 185 164)(156 174 186 165)(157 175 187 166)(158 169 188 167)(159 170 189 168)(160 171 183 162)(161 172 184 163)(176 199 209 190)(177 200 210 191)(178 201 204 192)(179 202 205 193)(180 203 206 194)(181 197 207 195)(182 198 208 196)(211 220 241 229)(212 221 242 230)(213 222 243 231)(214 223 244 225)(215 224 245 226)(216 218 239 227)(217 219 240 228)(232 246 265 255)(233 247 266 256)(234 248 260 257)(235 249 261 258)(236 250 262 259)(237 251 263 253)(238 252 264 254)(267 276 297 285)(268 277 298 286)(269 278 299 287)(270 279 300 281)(271 280 301 282)(272 274 295 283)(273 275 296 284)(288 302 321 311)(289 303 322 312)(290 304 316 313)(291 305 317 314)(292 306 318 315)(293 307 319 309)(294 308 320 310)(323 341 353 332)(324 342 354 333)(325 343 355 334)(326 337 356 335)(327 338 357 336)(328 339 351 330)(329 340 352 331)(344 367 377 358)(345 368 378 359)(346 369 372 360)(347 370 373 361)(348 371 374 362)(349 365 375 363)(350 366 376 364)(379 388 409 397)(380 389 410 398)(381 390 411 399)(382 391 412 393)(383 392 413 394)(384 386 407 395)(385 387 408 396)(400 414 433 423)(401 415 434 424)(402 416 428 425)(403 417 429 426)(404 418 430 427)(405 419 431 421)(406 420 432 422)
(1 125 69 151)(2 126 70 152)(3 120 64 153)(4 121 65 154)(5 122 66 148)(6 123 67 149)(7 124 68 150)(8 433 31 400)(9 434 32 401)(10 428 33 402)(11 429 34 403)(12 430 35 404)(13 431 29 405)(14 432 30 406)(15 418 38 427)(16 419 39 421)(17 420 40 422)(18 414 41 423)(19 415 42 424)(20 416 36 425)(21 417 37 426)(22 409 444 379)(23 410 445 380)(24 411 446 381)(25 412 447 382)(26 413 448 383)(27 407 442 384)(28 408 443 385)(43 388 435 397)(44 389 436 398)(45 390 437 399)(46 391 438 393)(47 392 439 394)(48 386 440 395)(49 387 441 396)(50 115 59 106)(51 116 60 107)(52 117 61 108)(53 118 62 109)(54 119 63 110)(55 113 57 111)(56 114 58 112)(71 104 95 127)(72 105 96 128)(73 99 97 129)(74 100 98 130)(75 101 92 131)(76 102 93 132)(77 103 94 133)(78 143 87 134)(79 144 88 135)(80 145 89 136)(81 146 90 137)(82 147 91 138)(83 141 85 139)(84 142 86 140)(155 241 185 211)(156 242 186 212)(157 243 187 213)(158 244 188 214)(159 245 189 215)(160 239 183 216)(161 240 184 217)(162 227 171 218)(163 228 172 219)(164 229 173 220)(165 230 174 221)(166 231 175 222)(167 225 169 223)(168 226 170 224)(176 265 209 232)(177 266 210 233)(178 260 204 234)(179 261 205 235)(180 262 206 236)(181 263 207 237)(182 264 208 238)(190 255 199 246)(191 256 200 247)(192 257 201 248)(193 258 202 249)(194 259 203 250)(195 253 197 251)(196 254 198 252)(267 341 297 332)(268 342 298 333)(269 343 299 334)(270 337 300 335)(271 338 301 336)(272 339 295 330)(273 340 296 331)(274 328 283 351)(275 329 284 352)(276 323 285 353)(277 324 286 354)(278 325 287 355)(279 326 281 356)(280 327 282 357)(288 367 321 358)(289 368 322 359)(290 369 316 360)(291 370 317 361)(292 371 318 362)(293 365 319 363)(294 366 320 364)(302 344 311 377)(303 345 312 378)(304 346 313 372)(305 347 314 373)(306 348 315 374)(307 349 309 375)(308 350 310 376)
(1 171 59 207)(2 172 60 208)(3 173 61 209)(4 174 62 210)(5 175 63 204)(6 169 57 205)(7 170 58 206)(8 323 435 367)(9 324 436 368)(10 325 437 369)(11 326 438 370)(12 327 439 371)(13 328 440 365)(14 329 441 366)(15 338 26 374)(16 339 27 375)(17 340 28 376)(18 341 22 377)(19 342 23 378)(20 343 24 372)(21 337 25 373)(29 351 48 363)(30 352 49 364)(31 353 43 358)(32 354 44 359)(33 355 45 360)(34 356 46 361)(35 357 47 362)(36 334 446 346)(37 335 447 347)(38 336 448 348)(39 330 442 349)(40 331 443 350)(41 332 444 344)(42 333 445 345)(50 181 69 162)(51 182 70 163)(52 176 64 164)(53 177 65 165)(54 178 66 166)(55 179 67 167)(56 180 68 168)(71 195 83 183)(72 196 84 184)(73 190 78 185)(74 191 79 186)(75 192 80 187)(76 193 81 188)(77 194 82 189)(85 160 95 197)(86 161 96 198)(87 155 97 199)(88 156 98 200)(89 157 92 201)(90 158 93 202)(91 159 94 203)(99 255 143 211)(100 256 144 212)(101 257 145 213)(102 258 146 214)(103 259 147 215)(104 253 141 216)(105 254 142 217)(106 237 125 218)(107 238 126 219)(108 232 120 220)(109 233 121 221)(110 234 122 222)(111 235 123 223)(112 236 124 224)(113 261 149 225)(114 262 150 226)(115 263 151 227)(116 264 152 228)(117 265 153 229)(118 266 154 230)(119 260 148 231)(127 251 139 239)(128 252 140 240)(129 246 134 241)(130 247 135 242)(131 248 136 243)(132 249 137 244)(133 250 138 245)(267 379 311 423)(268 380 312 424)(269 381 313 425)(270 382 314 426)(271 383 315 427)(272 384 309 421)(273 385 310 422)(274 386 293 405)(275 387 294 406)(276 388 288 400)(277 389 289 401)(278 390 290 402)(279 391 291 403)(280 392 292 404)(281 393 317 429)(282 394 318 430)(283 395 319 431)(284 396 320 432)(285 397 321 433)(286 398 322 434)(287 399 316 428)(295 407 307 419)(296 408 308 420)(297 409 302 414)(298 410 303 415)(299 411 304 416)(300 412 305 417)(301 413 306 418)
(1 283 59 319)(2 284 60 320)(3 285 61 321)(4 286 62 322)(5 287 63 316)(6 281 57 317)(7 282 58 318)(8 255 435 211)(9 256 436 212)(10 257 437 213)(11 258 438 214)(12 259 439 215)(13 253 440 216)(14 254 441 217)(15 262 26 226)(16 263 27 227)(17 264 28 228)(18 265 22 229)(19 266 23 230)(20 260 24 231)(21 261 25 225)(29 251 48 239)(30 252 49 240)(31 246 43 241)(32 247 44 242)(33 248 45 243)(34 249 46 244)(35 250 47 245)(36 234 446 222)(37 235 447 223)(38 236 448 224)(39 237 442 218)(40 238 443 219)(41 232 444 220)(42 233 445 221)(50 293 69 274)(51 294 70 275)(52 288 64 276)(53 289 65 277)(54 290 66 278)(55 291 67 279)(56 292 68 280)(71 307 83 295)(72 308 84 296)(73 302 78 297)(74 303 79 298)(75 304 80 299)(76 305 81 300)(77 306 82 301)(85 272 95 309)(86 273 96 310)(87 267 97 311)(88 268 98 312)(89 269 92 313)(90 270 93 314)(91 271 94 315)(99 367 143 323)(100 368 144 324)(101 369 145 325)(102 370 146 326)(103 371 147 327)(104 365 141 328)(105 366 142 329)(106 349 125 330)(107 350 126 331)(108 344 120 332)(109 345 121 333)(110 346 122 334)(111 347 123 335)(112 348 124 336)(113 373 149 337)(114 374 150 338)(115 375 151 339)(116 376 152 340)(117 377 153 341)(118 378 154 342)(119 372 148 343)(127 363 139 351)(128 364 140 352)(129 358 134 353)(130 359 135 354)(131 360 136 355)(132 361 137 356)(133 362 138 357)(155 423 199 379)(156 424 200 380)(157 425 201 381)(158 426 202 382)(159 427 203 383)(160 421 197 384)(161 422 198 385)(162 405 181 386)(163 406 182 387)(164 400 176 388)(165 401 177 389)(166 402 178 390)(167 403 179 391)(168 404 180 392)(169 429 205 393)(170 430 206 394)(171 431 207 395)(172 432 208 396)(173 433 209 397)(174 434 210 398)(175 428 204 399)(183 419 195 407)(184 420 196 408)(185 414 190 409)(186 415 191 410)(187 416 192 411)(188 417 193 412)(189 418 194 413)
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), (1,83,69,85)(2,84,70,86)(3,78,64,87)(4,79,65,88)(5,80,66,89)(6,81,67,90)(7,82,68,91)(8,18,31,41)(9,19,32,42)(10,20,33,36)(11,21,34,37)(12,15,35,38)(13,16,29,39)(14,17,30,40)(22,43,444,435)(23,44,445,436)(24,45,446,437)(25,46,447,438)(26,47,448,439)(27,48,442,440)(28,49,443,441)(50,95,59,71)(51,96,60,72)(52,97,61,73)(53,98,62,74)(54,92,63,75)(55,93,57,76)(56,94,58,77)(99,108,129,117)(100,109,130,118)(101,110,131,119)(102,111,132,113)(103,112,133,114)(104,106,127,115)(105,107,128,116)(120,134,153,143)(121,135,154,144)(122,136,148,145)(123,137,149,146)(124,138,150,147)(125,139,151,141)(126,140,152,142)(155,173,185,164)(156,174,186,165)(157,175,187,166)(158,169,188,167)(159,170,189,168)(160,171,183,162)(161,172,184,163)(176,199,209,190)(177,200,210,191)(178,201,204,192)(179,202,205,193)(180,203,206,194)(181,197,207,195)(182,198,208,196)(211,220,241,229)(212,221,242,230)(213,222,243,231)(214,223,244,225)(215,224,245,226)(216,218,239,227)(217,219,240,228)(232,246,265,255)(233,247,266,256)(234,248,260,257)(235,249,261,258)(236,250,262,259)(237,251,263,253)(238,252,264,254)(267,276,297,285)(268,277,298,286)(269,278,299,287)(270,279,300,281)(271,280,301,282)(272,274,295,283)(273,275,296,284)(288,302,321,311)(289,303,322,312)(290,304,316,313)(291,305,317,314)(292,306,318,315)(293,307,319,309)(294,308,320,310)(323,341,353,332)(324,342,354,333)(325,343,355,334)(326,337,356,335)(327,338,357,336)(328,339,351,330)(329,340,352,331)(344,367,377,358)(345,368,378,359)(346,369,372,360)(347,370,373,361)(348,371,374,362)(349,365,375,363)(350,366,376,364)(379,388,409,397)(380,389,410,398)(381,390,411,399)(382,391,412,393)(383,392,413,394)(384,386,407,395)(385,387,408,396)(400,414,433,423)(401,415,434,424)(402,416,428,425)(403,417,429,426)(404,418,430,427)(405,419,431,421)(406,420,432,422), (1,125,69,151)(2,126,70,152)(3,120,64,153)(4,121,65,154)(5,122,66,148)(6,123,67,149)(7,124,68,150)(8,433,31,400)(9,434,32,401)(10,428,33,402)(11,429,34,403)(12,430,35,404)(13,431,29,405)(14,432,30,406)(15,418,38,427)(16,419,39,421)(17,420,40,422)(18,414,41,423)(19,415,42,424)(20,416,36,425)(21,417,37,426)(22,409,444,379)(23,410,445,380)(24,411,446,381)(25,412,447,382)(26,413,448,383)(27,407,442,384)(28,408,443,385)(43,388,435,397)(44,389,436,398)(45,390,437,399)(46,391,438,393)(47,392,439,394)(48,386,440,395)(49,387,441,396)(50,115,59,106)(51,116,60,107)(52,117,61,108)(53,118,62,109)(54,119,63,110)(55,113,57,111)(56,114,58,112)(71,104,95,127)(72,105,96,128)(73,99,97,129)(74,100,98,130)(75,101,92,131)(76,102,93,132)(77,103,94,133)(78,143,87,134)(79,144,88,135)(80,145,89,136)(81,146,90,137)(82,147,91,138)(83,141,85,139)(84,142,86,140)(155,241,185,211)(156,242,186,212)(157,243,187,213)(158,244,188,214)(159,245,189,215)(160,239,183,216)(161,240,184,217)(162,227,171,218)(163,228,172,219)(164,229,173,220)(165,230,174,221)(166,231,175,222)(167,225,169,223)(168,226,170,224)(176,265,209,232)(177,266,210,233)(178,260,204,234)(179,261,205,235)(180,262,206,236)(181,263,207,237)(182,264,208,238)(190,255,199,246)(191,256,200,247)(192,257,201,248)(193,258,202,249)(194,259,203,250)(195,253,197,251)(196,254,198,252)(267,341,297,332)(268,342,298,333)(269,343,299,334)(270,337,300,335)(271,338,301,336)(272,339,295,330)(273,340,296,331)(274,328,283,351)(275,329,284,352)(276,323,285,353)(277,324,286,354)(278,325,287,355)(279,326,281,356)(280,327,282,357)(288,367,321,358)(289,368,322,359)(290,369,316,360)(291,370,317,361)(292,371,318,362)(293,365,319,363)(294,366,320,364)(302,344,311,377)(303,345,312,378)(304,346,313,372)(305,347,314,373)(306,348,315,374)(307,349,309,375)(308,350,310,376), (1,171,59,207)(2,172,60,208)(3,173,61,209)(4,174,62,210)(5,175,63,204)(6,169,57,205)(7,170,58,206)(8,323,435,367)(9,324,436,368)(10,325,437,369)(11,326,438,370)(12,327,439,371)(13,328,440,365)(14,329,441,366)(15,338,26,374)(16,339,27,375)(17,340,28,376)(18,341,22,377)(19,342,23,378)(20,343,24,372)(21,337,25,373)(29,351,48,363)(30,352,49,364)(31,353,43,358)(32,354,44,359)(33,355,45,360)(34,356,46,361)(35,357,47,362)(36,334,446,346)(37,335,447,347)(38,336,448,348)(39,330,442,349)(40,331,443,350)(41,332,444,344)(42,333,445,345)(50,181,69,162)(51,182,70,163)(52,176,64,164)(53,177,65,165)(54,178,66,166)(55,179,67,167)(56,180,68,168)(71,195,83,183)(72,196,84,184)(73,190,78,185)(74,191,79,186)(75,192,80,187)(76,193,81,188)(77,194,82,189)(85,160,95,197)(86,161,96,198)(87,155,97,199)(88,156,98,200)(89,157,92,201)(90,158,93,202)(91,159,94,203)(99,255,143,211)(100,256,144,212)(101,257,145,213)(102,258,146,214)(103,259,147,215)(104,253,141,216)(105,254,142,217)(106,237,125,218)(107,238,126,219)(108,232,120,220)(109,233,121,221)(110,234,122,222)(111,235,123,223)(112,236,124,224)(113,261,149,225)(114,262,150,226)(115,263,151,227)(116,264,152,228)(117,265,153,229)(118,266,154,230)(119,260,148,231)(127,251,139,239)(128,252,140,240)(129,246,134,241)(130,247,135,242)(131,248,136,243)(132,249,137,244)(133,250,138,245)(267,379,311,423)(268,380,312,424)(269,381,313,425)(270,382,314,426)(271,383,315,427)(272,384,309,421)(273,385,310,422)(274,386,293,405)(275,387,294,406)(276,388,288,400)(277,389,289,401)(278,390,290,402)(279,391,291,403)(280,392,292,404)(281,393,317,429)(282,394,318,430)(283,395,319,431)(284,396,320,432)(285,397,321,433)(286,398,322,434)(287,399,316,428)(295,407,307,419)(296,408,308,420)(297,409,302,414)(298,410,303,415)(299,411,304,416)(300,412,305,417)(301,413,306,418), (1,283,59,319)(2,284,60,320)(3,285,61,321)(4,286,62,322)(5,287,63,316)(6,281,57,317)(7,282,58,318)(8,255,435,211)(9,256,436,212)(10,257,437,213)(11,258,438,214)(12,259,439,215)(13,253,440,216)(14,254,441,217)(15,262,26,226)(16,263,27,227)(17,264,28,228)(18,265,22,229)(19,266,23,230)(20,260,24,231)(21,261,25,225)(29,251,48,239)(30,252,49,240)(31,246,43,241)(32,247,44,242)(33,248,45,243)(34,249,46,244)(35,250,47,245)(36,234,446,222)(37,235,447,223)(38,236,448,224)(39,237,442,218)(40,238,443,219)(41,232,444,220)(42,233,445,221)(50,293,69,274)(51,294,70,275)(52,288,64,276)(53,289,65,277)(54,290,66,278)(55,291,67,279)(56,292,68,280)(71,307,83,295)(72,308,84,296)(73,302,78,297)(74,303,79,298)(75,304,80,299)(76,305,81,300)(77,306,82,301)(85,272,95,309)(86,273,96,310)(87,267,97,311)(88,268,98,312)(89,269,92,313)(90,270,93,314)(91,271,94,315)(99,367,143,323)(100,368,144,324)(101,369,145,325)(102,370,146,326)(103,371,147,327)(104,365,141,328)(105,366,142,329)(106,349,125,330)(107,350,126,331)(108,344,120,332)(109,345,121,333)(110,346,122,334)(111,347,123,335)(112,348,124,336)(113,373,149,337)(114,374,150,338)(115,375,151,339)(116,376,152,340)(117,377,153,341)(118,378,154,342)(119,372,148,343)(127,363,139,351)(128,364,140,352)(129,358,134,353)(130,359,135,354)(131,360,136,355)(132,361,137,356)(133,362,138,357)(155,423,199,379)(156,424,200,380)(157,425,201,381)(158,426,202,382)(159,427,203,383)(160,421,197,384)(161,422,198,385)(162,405,181,386)(163,406,182,387)(164,400,176,388)(165,401,177,389)(166,402,178,390)(167,403,179,391)(168,404,180,392)(169,429,205,393)(170,430,206,394)(171,431,207,395)(172,432,208,396)(173,433,209,397)(174,434,210,398)(175,428,204,399)(183,419,195,407)(184,420,196,408)(185,414,190,409)(186,415,191,410)(187,416,192,411)(188,417,193,412)(189,418,194,413)>;
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), (1,83,69,85)(2,84,70,86)(3,78,64,87)(4,79,65,88)(5,80,66,89)(6,81,67,90)(7,82,68,91)(8,18,31,41)(9,19,32,42)(10,20,33,36)(11,21,34,37)(12,15,35,38)(13,16,29,39)(14,17,30,40)(22,43,444,435)(23,44,445,436)(24,45,446,437)(25,46,447,438)(26,47,448,439)(27,48,442,440)(28,49,443,441)(50,95,59,71)(51,96,60,72)(52,97,61,73)(53,98,62,74)(54,92,63,75)(55,93,57,76)(56,94,58,77)(99,108,129,117)(100,109,130,118)(101,110,131,119)(102,111,132,113)(103,112,133,114)(104,106,127,115)(105,107,128,116)(120,134,153,143)(121,135,154,144)(122,136,148,145)(123,137,149,146)(124,138,150,147)(125,139,151,141)(126,140,152,142)(155,173,185,164)(156,174,186,165)(157,175,187,166)(158,169,188,167)(159,170,189,168)(160,171,183,162)(161,172,184,163)(176,199,209,190)(177,200,210,191)(178,201,204,192)(179,202,205,193)(180,203,206,194)(181,197,207,195)(182,198,208,196)(211,220,241,229)(212,221,242,230)(213,222,243,231)(214,223,244,225)(215,224,245,226)(216,218,239,227)(217,219,240,228)(232,246,265,255)(233,247,266,256)(234,248,260,257)(235,249,261,258)(236,250,262,259)(237,251,263,253)(238,252,264,254)(267,276,297,285)(268,277,298,286)(269,278,299,287)(270,279,300,281)(271,280,301,282)(272,274,295,283)(273,275,296,284)(288,302,321,311)(289,303,322,312)(290,304,316,313)(291,305,317,314)(292,306,318,315)(293,307,319,309)(294,308,320,310)(323,341,353,332)(324,342,354,333)(325,343,355,334)(326,337,356,335)(327,338,357,336)(328,339,351,330)(329,340,352,331)(344,367,377,358)(345,368,378,359)(346,369,372,360)(347,370,373,361)(348,371,374,362)(349,365,375,363)(350,366,376,364)(379,388,409,397)(380,389,410,398)(381,390,411,399)(382,391,412,393)(383,392,413,394)(384,386,407,395)(385,387,408,396)(400,414,433,423)(401,415,434,424)(402,416,428,425)(403,417,429,426)(404,418,430,427)(405,419,431,421)(406,420,432,422), (1,125,69,151)(2,126,70,152)(3,120,64,153)(4,121,65,154)(5,122,66,148)(6,123,67,149)(7,124,68,150)(8,433,31,400)(9,434,32,401)(10,428,33,402)(11,429,34,403)(12,430,35,404)(13,431,29,405)(14,432,30,406)(15,418,38,427)(16,419,39,421)(17,420,40,422)(18,414,41,423)(19,415,42,424)(20,416,36,425)(21,417,37,426)(22,409,444,379)(23,410,445,380)(24,411,446,381)(25,412,447,382)(26,413,448,383)(27,407,442,384)(28,408,443,385)(43,388,435,397)(44,389,436,398)(45,390,437,399)(46,391,438,393)(47,392,439,394)(48,386,440,395)(49,387,441,396)(50,115,59,106)(51,116,60,107)(52,117,61,108)(53,118,62,109)(54,119,63,110)(55,113,57,111)(56,114,58,112)(71,104,95,127)(72,105,96,128)(73,99,97,129)(74,100,98,130)(75,101,92,131)(76,102,93,132)(77,103,94,133)(78,143,87,134)(79,144,88,135)(80,145,89,136)(81,146,90,137)(82,147,91,138)(83,141,85,139)(84,142,86,140)(155,241,185,211)(156,242,186,212)(157,243,187,213)(158,244,188,214)(159,245,189,215)(160,239,183,216)(161,240,184,217)(162,227,171,218)(163,228,172,219)(164,229,173,220)(165,230,174,221)(166,231,175,222)(167,225,169,223)(168,226,170,224)(176,265,209,232)(177,266,210,233)(178,260,204,234)(179,261,205,235)(180,262,206,236)(181,263,207,237)(182,264,208,238)(190,255,199,246)(191,256,200,247)(192,257,201,248)(193,258,202,249)(194,259,203,250)(195,253,197,251)(196,254,198,252)(267,341,297,332)(268,342,298,333)(269,343,299,334)(270,337,300,335)(271,338,301,336)(272,339,295,330)(273,340,296,331)(274,328,283,351)(275,329,284,352)(276,323,285,353)(277,324,286,354)(278,325,287,355)(279,326,281,356)(280,327,282,357)(288,367,321,358)(289,368,322,359)(290,369,316,360)(291,370,317,361)(292,371,318,362)(293,365,319,363)(294,366,320,364)(302,344,311,377)(303,345,312,378)(304,346,313,372)(305,347,314,373)(306,348,315,374)(307,349,309,375)(308,350,310,376), (1,171,59,207)(2,172,60,208)(3,173,61,209)(4,174,62,210)(5,175,63,204)(6,169,57,205)(7,170,58,206)(8,323,435,367)(9,324,436,368)(10,325,437,369)(11,326,438,370)(12,327,439,371)(13,328,440,365)(14,329,441,366)(15,338,26,374)(16,339,27,375)(17,340,28,376)(18,341,22,377)(19,342,23,378)(20,343,24,372)(21,337,25,373)(29,351,48,363)(30,352,49,364)(31,353,43,358)(32,354,44,359)(33,355,45,360)(34,356,46,361)(35,357,47,362)(36,334,446,346)(37,335,447,347)(38,336,448,348)(39,330,442,349)(40,331,443,350)(41,332,444,344)(42,333,445,345)(50,181,69,162)(51,182,70,163)(52,176,64,164)(53,177,65,165)(54,178,66,166)(55,179,67,167)(56,180,68,168)(71,195,83,183)(72,196,84,184)(73,190,78,185)(74,191,79,186)(75,192,80,187)(76,193,81,188)(77,194,82,189)(85,160,95,197)(86,161,96,198)(87,155,97,199)(88,156,98,200)(89,157,92,201)(90,158,93,202)(91,159,94,203)(99,255,143,211)(100,256,144,212)(101,257,145,213)(102,258,146,214)(103,259,147,215)(104,253,141,216)(105,254,142,217)(106,237,125,218)(107,238,126,219)(108,232,120,220)(109,233,121,221)(110,234,122,222)(111,235,123,223)(112,236,124,224)(113,261,149,225)(114,262,150,226)(115,263,151,227)(116,264,152,228)(117,265,153,229)(118,266,154,230)(119,260,148,231)(127,251,139,239)(128,252,140,240)(129,246,134,241)(130,247,135,242)(131,248,136,243)(132,249,137,244)(133,250,138,245)(267,379,311,423)(268,380,312,424)(269,381,313,425)(270,382,314,426)(271,383,315,427)(272,384,309,421)(273,385,310,422)(274,386,293,405)(275,387,294,406)(276,388,288,400)(277,389,289,401)(278,390,290,402)(279,391,291,403)(280,392,292,404)(281,393,317,429)(282,394,318,430)(283,395,319,431)(284,396,320,432)(285,397,321,433)(286,398,322,434)(287,399,316,428)(295,407,307,419)(296,408,308,420)(297,409,302,414)(298,410,303,415)(299,411,304,416)(300,412,305,417)(301,413,306,418), (1,283,59,319)(2,284,60,320)(3,285,61,321)(4,286,62,322)(5,287,63,316)(6,281,57,317)(7,282,58,318)(8,255,435,211)(9,256,436,212)(10,257,437,213)(11,258,438,214)(12,259,439,215)(13,253,440,216)(14,254,441,217)(15,262,26,226)(16,263,27,227)(17,264,28,228)(18,265,22,229)(19,266,23,230)(20,260,24,231)(21,261,25,225)(29,251,48,239)(30,252,49,240)(31,246,43,241)(32,247,44,242)(33,248,45,243)(34,249,46,244)(35,250,47,245)(36,234,446,222)(37,235,447,223)(38,236,448,224)(39,237,442,218)(40,238,443,219)(41,232,444,220)(42,233,445,221)(50,293,69,274)(51,294,70,275)(52,288,64,276)(53,289,65,277)(54,290,66,278)(55,291,67,279)(56,292,68,280)(71,307,83,295)(72,308,84,296)(73,302,78,297)(74,303,79,298)(75,304,80,299)(76,305,81,300)(77,306,82,301)(85,272,95,309)(86,273,96,310)(87,267,97,311)(88,268,98,312)(89,269,92,313)(90,270,93,314)(91,271,94,315)(99,367,143,323)(100,368,144,324)(101,369,145,325)(102,370,146,326)(103,371,147,327)(104,365,141,328)(105,366,142,329)(106,349,125,330)(107,350,126,331)(108,344,120,332)(109,345,121,333)(110,346,122,334)(111,347,123,335)(112,348,124,336)(113,373,149,337)(114,374,150,338)(115,375,151,339)(116,376,152,340)(117,377,153,341)(118,378,154,342)(119,372,148,343)(127,363,139,351)(128,364,140,352)(129,358,134,353)(130,359,135,354)(131,360,136,355)(132,361,137,356)(133,362,138,357)(155,423,199,379)(156,424,200,380)(157,425,201,381)(158,426,202,382)(159,427,203,383)(160,421,197,384)(161,422,198,385)(162,405,181,386)(163,406,182,387)(164,400,176,388)(165,401,177,389)(166,402,178,390)(167,403,179,391)(168,404,180,392)(169,429,205,393)(170,430,206,394)(171,431,207,395)(172,432,208,396)(173,433,209,397)(174,434,210,398)(175,428,204,399)(183,419,195,407)(184,420,196,408)(185,414,190,409)(186,415,191,410)(187,416,192,411)(188,417,193,412)(189,418,194,413) );
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)], [(1,83,69,85),(2,84,70,86),(3,78,64,87),(4,79,65,88),(5,80,66,89),(6,81,67,90),(7,82,68,91),(8,18,31,41),(9,19,32,42),(10,20,33,36),(11,21,34,37),(12,15,35,38),(13,16,29,39),(14,17,30,40),(22,43,444,435),(23,44,445,436),(24,45,446,437),(25,46,447,438),(26,47,448,439),(27,48,442,440),(28,49,443,441),(50,95,59,71),(51,96,60,72),(52,97,61,73),(53,98,62,74),(54,92,63,75),(55,93,57,76),(56,94,58,77),(99,108,129,117),(100,109,130,118),(101,110,131,119),(102,111,132,113),(103,112,133,114),(104,106,127,115),(105,107,128,116),(120,134,153,143),(121,135,154,144),(122,136,148,145),(123,137,149,146),(124,138,150,147),(125,139,151,141),(126,140,152,142),(155,173,185,164),(156,174,186,165),(157,175,187,166),(158,169,188,167),(159,170,189,168),(160,171,183,162),(161,172,184,163),(176,199,209,190),(177,200,210,191),(178,201,204,192),(179,202,205,193),(180,203,206,194),(181,197,207,195),(182,198,208,196),(211,220,241,229),(212,221,242,230),(213,222,243,231),(214,223,244,225),(215,224,245,226),(216,218,239,227),(217,219,240,228),(232,246,265,255),(233,247,266,256),(234,248,260,257),(235,249,261,258),(236,250,262,259),(237,251,263,253),(238,252,264,254),(267,276,297,285),(268,277,298,286),(269,278,299,287),(270,279,300,281),(271,280,301,282),(272,274,295,283),(273,275,296,284),(288,302,321,311),(289,303,322,312),(290,304,316,313),(291,305,317,314),(292,306,318,315),(293,307,319,309),(294,308,320,310),(323,341,353,332),(324,342,354,333),(325,343,355,334),(326,337,356,335),(327,338,357,336),(328,339,351,330),(329,340,352,331),(344,367,377,358),(345,368,378,359),(346,369,372,360),(347,370,373,361),(348,371,374,362),(349,365,375,363),(350,366,376,364),(379,388,409,397),(380,389,410,398),(381,390,411,399),(382,391,412,393),(383,392,413,394),(384,386,407,395),(385,387,408,396),(400,414,433,423),(401,415,434,424),(402,416,428,425),(403,417,429,426),(404,418,430,427),(405,419,431,421),(406,420,432,422)], [(1,125,69,151),(2,126,70,152),(3,120,64,153),(4,121,65,154),(5,122,66,148),(6,123,67,149),(7,124,68,150),(8,433,31,400),(9,434,32,401),(10,428,33,402),(11,429,34,403),(12,430,35,404),(13,431,29,405),(14,432,30,406),(15,418,38,427),(16,419,39,421),(17,420,40,422),(18,414,41,423),(19,415,42,424),(20,416,36,425),(21,417,37,426),(22,409,444,379),(23,410,445,380),(24,411,446,381),(25,412,447,382),(26,413,448,383),(27,407,442,384),(28,408,443,385),(43,388,435,397),(44,389,436,398),(45,390,437,399),(46,391,438,393),(47,392,439,394),(48,386,440,395),(49,387,441,396),(50,115,59,106),(51,116,60,107),(52,117,61,108),(53,118,62,109),(54,119,63,110),(55,113,57,111),(56,114,58,112),(71,104,95,127),(72,105,96,128),(73,99,97,129),(74,100,98,130),(75,101,92,131),(76,102,93,132),(77,103,94,133),(78,143,87,134),(79,144,88,135),(80,145,89,136),(81,146,90,137),(82,147,91,138),(83,141,85,139),(84,142,86,140),(155,241,185,211),(156,242,186,212),(157,243,187,213),(158,244,188,214),(159,245,189,215),(160,239,183,216),(161,240,184,217),(162,227,171,218),(163,228,172,219),(164,229,173,220),(165,230,174,221),(166,231,175,222),(167,225,169,223),(168,226,170,224),(176,265,209,232),(177,266,210,233),(178,260,204,234),(179,261,205,235),(180,262,206,236),(181,263,207,237),(182,264,208,238),(190,255,199,246),(191,256,200,247),(192,257,201,248),(193,258,202,249),(194,259,203,250),(195,253,197,251),(196,254,198,252),(267,341,297,332),(268,342,298,333),(269,343,299,334),(270,337,300,335),(271,338,301,336),(272,339,295,330),(273,340,296,331),(274,328,283,351),(275,329,284,352),(276,323,285,353),(277,324,286,354),(278,325,287,355),(279,326,281,356),(280,327,282,357),(288,367,321,358),(289,368,322,359),(290,369,316,360),(291,370,317,361),(292,371,318,362),(293,365,319,363),(294,366,320,364),(302,344,311,377),(303,345,312,378),(304,346,313,372),(305,347,314,373),(306,348,315,374),(307,349,309,375),(308,350,310,376)], [(1,171,59,207),(2,172,60,208),(3,173,61,209),(4,174,62,210),(5,175,63,204),(6,169,57,205),(7,170,58,206),(8,323,435,367),(9,324,436,368),(10,325,437,369),(11,326,438,370),(12,327,439,371),(13,328,440,365),(14,329,441,366),(15,338,26,374),(16,339,27,375),(17,340,28,376),(18,341,22,377),(19,342,23,378),(20,343,24,372),(21,337,25,373),(29,351,48,363),(30,352,49,364),(31,353,43,358),(32,354,44,359),(33,355,45,360),(34,356,46,361),(35,357,47,362),(36,334,446,346),(37,335,447,347),(38,336,448,348),(39,330,442,349),(40,331,443,350),(41,332,444,344),(42,333,445,345),(50,181,69,162),(51,182,70,163),(52,176,64,164),(53,177,65,165),(54,178,66,166),(55,179,67,167),(56,180,68,168),(71,195,83,183),(72,196,84,184),(73,190,78,185),(74,191,79,186),(75,192,80,187),(76,193,81,188),(77,194,82,189),(85,160,95,197),(86,161,96,198),(87,155,97,199),(88,156,98,200),(89,157,92,201),(90,158,93,202),(91,159,94,203),(99,255,143,211),(100,256,144,212),(101,257,145,213),(102,258,146,214),(103,259,147,215),(104,253,141,216),(105,254,142,217),(106,237,125,218),(107,238,126,219),(108,232,120,220),(109,233,121,221),(110,234,122,222),(111,235,123,223),(112,236,124,224),(113,261,149,225),(114,262,150,226),(115,263,151,227),(116,264,152,228),(117,265,153,229),(118,266,154,230),(119,260,148,231),(127,251,139,239),(128,252,140,240),(129,246,134,241),(130,247,135,242),(131,248,136,243),(132,249,137,244),(133,250,138,245),(267,379,311,423),(268,380,312,424),(269,381,313,425),(270,382,314,426),(271,383,315,427),(272,384,309,421),(273,385,310,422),(274,386,293,405),(275,387,294,406),(276,388,288,400),(277,389,289,401),(278,390,290,402),(279,391,291,403),(280,392,292,404),(281,393,317,429),(282,394,318,430),(283,395,319,431),(284,396,320,432),(285,397,321,433),(286,398,322,434),(287,399,316,428),(295,407,307,419),(296,408,308,420),(297,409,302,414),(298,410,303,415),(299,411,304,416),(300,412,305,417),(301,413,306,418)], [(1,283,59,319),(2,284,60,320),(3,285,61,321),(4,286,62,322),(5,287,63,316),(6,281,57,317),(7,282,58,318),(8,255,435,211),(9,256,436,212),(10,257,437,213),(11,258,438,214),(12,259,439,215),(13,253,440,216),(14,254,441,217),(15,262,26,226),(16,263,27,227),(17,264,28,228),(18,265,22,229),(19,266,23,230),(20,260,24,231),(21,261,25,225),(29,251,48,239),(30,252,49,240),(31,246,43,241),(32,247,44,242),(33,248,45,243),(34,249,46,244),(35,250,47,245),(36,234,446,222),(37,235,447,223),(38,236,448,224),(39,237,442,218),(40,238,443,219),(41,232,444,220),(42,233,445,221),(50,293,69,274),(51,294,70,275),(52,288,64,276),(53,289,65,277),(54,290,66,278),(55,291,67,279),(56,292,68,280),(71,307,83,295),(72,308,84,296),(73,302,78,297),(74,303,79,298),(75,304,80,299),(76,305,81,300),(77,306,82,301),(85,272,95,309),(86,273,96,310),(87,267,97,311),(88,268,98,312),(89,269,92,313),(90,270,93,314),(91,271,94,315),(99,367,143,323),(100,368,144,324),(101,369,145,325),(102,370,146,326),(103,371,147,327),(104,365,141,328),(105,366,142,329),(106,349,125,330),(107,350,126,331),(108,344,120,332),(109,345,121,333),(110,346,122,334),(111,347,123,335),(112,348,124,336),(113,373,149,337),(114,374,150,338),(115,375,151,339),(116,376,152,340),(117,377,153,341),(118,378,154,342),(119,372,148,343),(127,363,139,351),(128,364,140,352),(129,358,134,353),(130,359,135,354),(131,360,136,355),(132,361,137,356),(133,362,138,357),(155,423,199,379),(156,424,200,380),(157,425,201,381),(158,426,202,382),(159,427,203,383),(160,421,197,384),(161,422,198,385),(162,405,181,386),(163,406,182,387),(164,400,176,388),(165,401,177,389),(166,402,178,390),(167,403,179,391),(168,404,180,392),(169,429,205,393),(170,430,206,394),(171,431,207,395),(172,432,208,396),(173,433,209,397),(174,434,210,398),(175,428,204,399),(183,419,195,407),(184,420,196,408),(185,414,190,409),(186,415,191,410),(187,416,192,411),(188,417,193,412),(189,418,194,413)]])
133 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | 4K | 7A | ··· | 7F | 8A | 8B | 8C | 8D | 14A | ··· | 14R | 28A | ··· | 28X | 28Y | ··· | 28BB | 28BC | ··· | 28BN | 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 | 2 | 2 | 4 | ··· | 4 | 8 | 8 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
133 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | - | |||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C14 | D4 | Q8 | SD16 | C4○D4 | C7×D4 | C7×Q8 | C7×SD16 | C7×C4○D4 | C8.C22 | C7×C8.C22 |
| kernel | C7×Q8⋊Q8 | C7×Q8⋊C4 | C7×C4⋊C8 | C7×C4.Q8 | Q8×C28 | C7×C4⋊Q8 | Q8⋊Q8 | Q8⋊C4 | C4⋊C8 | C4.Q8 | C4×Q8 | C4⋊Q8 | C2×C28 | C7×Q8 | C28 | C28 | C2×C4 | Q8 | C4 | C4 | C14 | C2 |
| # reps | 1 | 2 | 1 | 2 | 1 | 1 | 6 | 12 | 6 | 12 | 6 | 6 | 2 | 2 | 4 | 2 | 12 | 12 | 24 | 12 | 1 | 6 |
Matrix representation of C7×Q8⋊Q8 ►in GL4(𝔽113) generated by
| 106 | 0 | 0 | 0 |
| 0 | 106 | 0 | 0 |
| 0 | 0 | 49 | 0 |
| 0 | 0 | 0 | 49 |
| 0 | 1 | 0 | 0 |
| 112 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 53 | 69 | 0 | 0 |
| 69 | 60 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 2 |
| 0 | 0 | 112 | 112 |
| 109 | 18 | 0 | 0 |
| 18 | 4 | 0 | 0 |
| 0 | 0 | 62 | 32 |
| 0 | 0 | 67 | 51 |
G:=sub<GL(4,GF(113))| [106,0,0,0,0,106,0,0,0,0,49,0,0,0,0,49],[0,112,0,0,1,0,0,0,0,0,1,0,0,0,0,1],[53,69,0,0,69,60,0,0,0,0,112,0,0,0,0,112],[1,0,0,0,0,1,0,0,0,0,1,112,0,0,2,112],[109,18,0,0,18,4,0,0,0,0,62,67,0,0,32,51] >;
C7×Q8⋊Q8 in GAP, Magma, Sage, TeX
C_7\times Q_8\rtimes Q_8
% in TeX
G:=Group("C7xQ8:Q8"); // GroupNames label
G:=SmallGroup(448,883);
// by ID
G=gap.SmallGroup(448,883);
# by ID
G:=PCGroup([7,-2,-2,-2,-7,-2,-2,-2,392,813,400,2438,1192,14117,3547,124]);
// 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=e*b*e^-1=b^-1,b*d=d*b,c*d=d*c,e*c*e^-1=b^-1*c,e*d*e^-1=d^-1>;
// generators/relations