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G = C7×Q82  order 448 = 26·7

Direct product of C7, Q8 and Q8

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

Aliases: C7×Q82, C14.1672+ (1+4), C4⋊Q8.14C14, C4.20(Q8×C14), (Q8×C28).23C2, (C4×Q8).10C14, C28.126(C2×Q8), C42.52(C2×C14), C14.66(C22×Q8), (C4×C28).293C22, (C2×C14).378C24, (C2×C28).966C23, C22.52(C23×C14), (Q8×C14).186C22, C2.19(C7×2+ (1+4)), C2.12(Q8×C2×C14), (C7×C4⋊Q8).29C2, C4⋊C4.78(C2×C14), (C2×Q8).29(C2×C14), (C7×C4⋊C4).403C22, (C2×C4).39(C22×C14), SmallGroup(448,1341)

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

Subgroups: 266 in 212 conjugacy classes, 182 normal (8 characteristic)
C1, C2, C2 [×2], C4 [×12], C4 [×9], C22, C7, C2×C4 [×15], Q8 [×8], Q8 [×6], C14, C14 [×2], C42 [×9], C4⋊C4 [×18], C2×Q8 [×8], C28 [×12], C28 [×9], C2×C14, C4×Q8 [×6], C4⋊Q8 [×9], C2×C28 [×15], C7×Q8 [×8], C7×Q8 [×6], Q82, C4×C28 [×9], C7×C4⋊C4 [×18], Q8×C14 [×8], Q8×C28 [×6], C7×C4⋊Q8 [×9], C7×Q82

Quotients:
C1, C2 [×15], C22 [×35], C7, Q8 [×8], C23 [×15], C14 [×15], C2×Q8 [×12], C24, C2×C14 [×35], C22×Q8 [×2], 2+ (1+4), C7×Q8 [×8], C22×C14 [×15], Q82, Q8×C14 [×12], C23×C14, Q8×C2×C14 [×2], C7×2+ (1+4), C7×Q82

Generators and relations
 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 >

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

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

(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)(8 418 446 435)(9 419 447 436)(10 420 448 437)(11 414 442 438)(12 415 443 439)(13 416 444 440)(14 417 445 441)(15 429 22 425)(16 430 23 426)(17 431 24 427)(18 432 25 421)(19 433 26 422)(20 434 27 423)(21 428 28 424)(29 68 40 57)(30 69 41 58)(31 70 42 59)(32 64 36 60)(33 65 37 61)(34 66 38 62)(35 67 39 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)(85 124 96 113)(86 125 97 114)(87 126 98 115)(88 120 92 116)(89 121 93 117)(90 122 94 118)(91 123 95 119)(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)(141 169 152 180)(142 170 153 181)(143 171 154 182)(144 172 148 176)(145 173 149 177)(146 174 150 178)(147 175 151 179)(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)(197 225 208 236)(198 226 209 237)(199 227 210 238)(200 228 204 232)(201 229 205 233)(202 230 206 234)(203 231 207 235)(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)(253 292 264 281)(254 293 265 282)(255 294 266 283)(256 288 260 284)(257 289 261 285)(258 290 262 286)(259 291 263 287)(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)(309 348 320 337)(310 349 321 338)(311 350 322 339)(312 344 316 340)(313 345 317 341)(314 346 318 342)(315 347 319 343)(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)(365 393 376 404)(366 394 377 405)(367 395 378 406)(368 396 372 400)(369 397 373 401)(370 398 374 402)(371 399 375 403)

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

Matrix representation ►G ⊆ GL4(𝔽29) generated by

25000
02500
0070
0007
,
0100
28000
00280
00028
,
142100
211500
0010
0001
,
28000
02800
0001
00280
,
28000
02800
00170
00012
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] >;
 

175 conjugacy classes

class 1 2A2B2C4A···4L4M···4U7A···7F14A···14R28A···28BT28BU···28DV
order12224···44···47···714···1428···2828···28
size11112···24···41···11···12···24···4

175 irreducible representations

dim1111112244
type+++-+
imageC1C2C2C7C14C14Q8C7×Q82+ (1+4)C7×2+ (1+4)
kernelC7×Q82Q8×C28C7×C4⋊Q8Q82C4×Q8C4⋊Q8C7×Q8Q8C14C2
# reps1696365484816

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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