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## G = C7×Q8.Q8order 448 = 26·7

### Direct product of C7 and Q8.Q8

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

Series: Derived Chief Lower central Upper central

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

Generators and relations for C7×Q8.Q8
G = < a,b,c,d,e | a7=b4=d4=1, c2=b2, e2=b2d2, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=ebe-1=b-1, bd=db, cd=dc, ece-1=b-1c, ede-1=b2d-1 >

Subgroups: 138 in 90 conjugacy classes, 54 normal (50 characteristic)
C1, C2, C4, C4, C22, C7, C8, C2×C4, C2×C4, Q8, Q8, C14, C42, C42, C4⋊C4, C4⋊C4, C2×C8, C2×Q8, C28, C28, C2×C14, Q8⋊C4, C4⋊C8, C4.Q8, C2.D8, C4×Q8, C42.C2, C56, C2×C28, C2×C28, C7×Q8, C7×Q8, Q8.Q8, C4×C28, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×C56, Q8×C14, C7×Q8⋊C4, C7×C4⋊C8, C7×C4.Q8, C7×C2.D8, Q8×C28, C7×C42.C2, C7×Q8.Q8
Quotients: C1, C2, C22, C7, D4, Q8, C23, C14, C2×D4, C2×Q8, C4○D4, C2×C14, C22⋊Q8, C4○D8, C8.C22, C7×D4, C7×Q8, C22×C14, Q8.Q8, D4×C14, Q8×C14, C7×C4○D4, C7×C22⋊Q8, C7×C4○D8, C7×C8.C22, C7×Q8.Q8

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

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

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

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

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 1 1 2 2 2 2 2 2 2 2 4 4 type + + + + + + + + - - image C1 C2 C2 C2 C2 C2 C2 C7 C14 C14 C14 C14 C14 C14 D4 Q8 C4○D4 C4○D8 C7×D4 C7×Q8 C7×C4○D4 C7×C4○D8 C8.C22 C7×C8.C22 kernel C7×Q8.Q8 C7×Q8⋊C4 C7×C4⋊C8 C7×C4.Q8 C7×C2.D8 Q8×C28 C7×C42.C2 Q8.Q8 Q8⋊C4 C4⋊C8 C4.Q8 C2.D8 C4×Q8 C42.C2 C2×C28 C7×Q8 C28 C14 C2×C4 Q8 C4 C2 C14 C2 # reps 1 2 1 1 1 1 1 6 12 6 6 6 6 6 2 2 2 4 12 12 12 24 1 6

Matrix representation of C7×Q8.Q8 in GL4(𝔽113) generated by

 106 0 0 0 0 106 0 0 0 0 106 0 0 0 0 106
,
 1 0 0 0 0 1 0 0 0 0 1 111 0 0 1 112
,
 112 0 0 0 0 112 0 0 0 0 35 82 0 0 76 78
,
 0 1 0 0 112 0 0 0 0 0 98 0 0 0 0 98
,
 97 46 0 0 46 16 0 0 0 0 64 104 0 0 3 49
G:=sub<GL(4,GF(113))| [106,0,0,0,0,106,0,0,0,0,106,0,0,0,0,106],[1,0,0,0,0,1,0,0,0,0,1,1,0,0,111,112],[112,0,0,0,0,112,0,0,0,0,35,76,0,0,82,78],[0,112,0,0,1,0,0,0,0,0,98,0,0,0,0,98],[97,46,0,0,46,16,0,0,0,0,64,3,0,0,104,49] >;

C7×Q8.Q8 in GAP, Magma, Sage, TeX

C_7\times Q_8.Q_8
% in TeX

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

G:=SmallGroup(448,887);
// by ID

G=gap.SmallGroup(448,887);
# by ID

G:=PCGroup([7,-2,-2,-2,-7,-2,-2,-2,392,813,1968,2438,1192,14117,3547,124]);
// Polycyclic

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

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