Copied to
clipboard

?

G = C22×Dic7⋊C4  order 448 = 26·7

Direct product of C22 and Dic7⋊C4

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C22×Dic7⋊C4, C24.76D14, C23.18Dic14, (C23×C4).6D7, (C23×C28).9C2, C23.68(C4×D7), C14.37(C23×C4), Dic7⋊5(C22×C4), (C22×C14).27Q8, C14.18(C22×Q8), (C2×C28).702C23, (C2×C14).281C24, (C22×Dic7)⋊11C4, (C22×C4).411D14, (C22×C14).203D4, C14.129(C22×D4), (C23×Dic7).9C2, C2.2(C22×Dic14), C22.39(C23×D7), C23.102(C7⋊D4), C22.38(C2×Dic14), C23.333(C22×D7), (C23×C14).103C22, (C22×C28).506C22, (C22×C14).410C23, (C2×Dic7).276C23, (C22×Dic7).227C22, C14⋊2(C2×C4⋊C4), C7⋊2(C22×C4⋊C4), (C2×C14)⋊8(C4⋊C4), C22.78(C2×C4×D7), C2.37(D7×C22×C4), (C2×C14).53(C2×Q8), C2.1(C22×C7⋊D4), (C2×Dic7)⋊24(C2×C4), (C2×C14).570(C2×D4), C22.99(C2×C7⋊D4), (C2×C4).655(C22×D7), (C2×C14).157(C22×C4), (C22×C14).104(C2×C4), SmallGroup(448,1236)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C14 — C22×Dic7⋊C4
Chief series
C1 — C7 — C14 — C2×C14 — C2×Dic7 — C22×Dic7 — C23×Dic7 — C22×Dic7⋊C4
Lower central
C7 — C14 — C22×Dic7⋊C4

Subgroups: 1284 in 418 conjugacy classes, 247 normal (17 characteristic)
C1, C2 [×3], C2 [×12], C4 [×16], C22, C22 [×34], C7, C2×C4 [×4], C2×C4 [×56], C23 [×15], C14 [×3], C14 [×12], C4⋊C4 [×16], C22×C4 [×6], C22×C4 [×28], C24, Dic7 [×8], Dic7 [×4], C28 [×4], C2×C14, C2×C14 [×34], C2×C4⋊C4 [×12], C23×C4, C23×C4 [×2], C2×Dic7 [×32], C2×Dic7 [×12], C2×C28 [×4], C2×C28 [×12], C22×C14 [×15], C22×C4⋊C4, Dic7⋊C4 [×16], C22×Dic7 [×20], C22×Dic7 [×4], C22×C28 [×6], C22×C28 [×4], C23×C14, C2×Dic7⋊C4 [×12], C23×Dic7 [×2], C23×C28, C22×Dic7⋊C4

Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], D4 [×4], Q8 [×4], C23 [×15], D7, C4⋊C4 [×16], C22×C4 [×14], C2×D4 [×6], C2×Q8 [×6], C24, D14 [×7], C2×C4⋊C4 [×12], C23×C4, C22×D4, C22×Q8, Dic14 [×4], C4×D7 [×4], C7⋊D4 [×4], C22×D7 [×7], C22×C4⋊C4, Dic7⋊C4 [×16], C2×Dic14 [×6], C2×C4×D7 [×6], C2×C7⋊D4 [×6], C23×D7, C2×Dic7⋊C4 [×12], C22×Dic14, D7×C22×C4, C22×C7⋊D4, C22×Dic7⋊C4

Generators and relations
 G = < a,b,c,d,e | a2=b2=c14=e4=1, d2=c7, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd-1=c-1, ce=ec, ede-1=c7d >

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

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

(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)

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

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

Matrix representation ►G ⊆ GL5(𝔽29)

10000
028000
00100
00010
00001
,
280000
028000
002800
000280
000028
,
10000
01000
00100
00060
00005
,
10000
028000
00100
000028
00010
,
120000
01000
002800
000280
00001

G:=sub<GL(5,GF(29))| [1,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,28],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,6,0,0,0,0,0,5],[1,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,28,0],[12,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,1] >;
 

136 conjugacy classes

class 1 2A···2O4A···4H4I···4X7A7B7C14A···14AS28A···28AV
order12···24···44···477714···1428···28
size11···12···214···142222···22···2

136 irreducible representations

dim1111122222222
type+++++-+++-
imageC1C2C2C2C4D4Q8D7D14D14Dic14C4×D7C7⋊D4
kernelC22×Dic7⋊C4C2×Dic7⋊C4C23×Dic7C23×C28C22×Dic7C22×C14C22×C14C23×C4C22×C4C24C23C23C23
# reps1122116443183242424

In GAP, Magma, Sage, TeX 

C_2^2\times Dic_7\rtimes C_4
 
% in TeX
 
G:=Group("C2^2xDic7:C4");
 
// GroupNames label
 
G:=SmallGroup(448,1236);
 
// by ID
 
G=gap.SmallGroup(448,1236);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,1123,80,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^14=e^4=1,d^2=c^7,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,d*c*d^-1=c^-1,c*e=e*c,e*d*e^-1=c^7*d>;
 
// generators/relations
 

׿
×
⋊
ℤ
𝔽
○
≀