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G = C23×Dic14  order 448 = 26·7

Direct product of C23 and Dic14

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

Aliases: C23×Dic14, C14.1C25, C28.64C24, C24.80D14, Dic7.1C24, C7⋊1(Q8×C23), C14⋊1(C22×Q8), (C22×C14)⋊8Q8, C2.3(D7×C24), C4.61(C23×D7), (C23×C4).13D7, (C23×C28).14C2, (C2×C28).790C23, (C2×C14).323C24, (C22×C4).450D14, C22.51(C23×D7), (C23×Dic7).11C2, C23.344(C22×D7), (C22×C14).430C23, (C22×C28).531C22, (C23×C14).113C22, (C2×Dic7).295C23, (C22×Dic7).238C22, (C2×C14)⋊7(C2×Q8), (C2×C4).741(C22×D7), SmallGroup(448,1365)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C14 — C23×Dic14
Chief series
C1 — C7 — C14 — Dic7 — C2×Dic7 — C22×Dic7 — C23×Dic7 — C23×Dic14
Lower central
C7 — C14 — C23×Dic14

Subgroups: 2692 in 850 conjugacy classes, 543 normal (9 characteristic)
C1, C2, C2 [×14], C4 [×8], C4 [×16], C22 [×35], C7, C2×C4 [×28], C2×C4 [×56], Q8 [×64], C23 [×15], C14, C14 [×14], C22×C4 [×14], C22×C4 [×28], C2×Q8 [×112], C24, Dic7 [×16], C28 [×8], C2×C14 [×35], C23×C4, C23×C4 [×2], C22×Q8 [×28], Dic14 [×64], C2×Dic7 [×56], C2×C28 [×28], C22×C14 [×15], Q8×C23, C2×Dic14 [×112], C22×Dic7 [×28], C22×C28 [×14], C23×C14, C22×Dic14 [×28], C23×Dic7 [×2], C23×C28, C23×Dic14

Quotients:
C1, C2 [×31], C22 [×155], Q8 [×8], C23 [×155], D7, C2×Q8 [×28], C24 [×31], D14 [×15], C22×Q8 [×14], C25, Dic14 [×8], C22×D7 [×35], Q8×C23, C2×Dic14 [×28], C23×D7 [×15], C22×Dic14 [×14], D7×C24, C23×Dic14

Generators and relations
 G = < a,b,c,d,e | a2=b2=c2=d28=1, e2=d14, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

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

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

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

(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)

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

Matrix representation ►G ⊆ GL5(𝔽29)

10000
028000
002800
00010
00001
,
10000
028000
00100
000280
000028
,
280000
028000
002800
000280
000028
,
10000
01000
00100
0002416
0001322
,
280000
01000
002800
0001010
0001619

G:=sub<GL(5,GF(29))| [1,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,28],[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],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,24,13,0,0,0,16,22],[28,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,10,16,0,0,0,10,19] >;
 

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

dim111122222
type++++-+++-
imageC1C2C2C2Q8D7D14D14Dic14
kernelC23×Dic14C22×Dic14C23×Dic7C23×C28C22×C14C23×C4C22×C4C24C23
# reps128218342348

In GAP, Magma, Sage, TeX 

C_2^3\times Dic_{14}
 
% in TeX
 
G:=Group("C2^3xDic14");
 
// GroupNames label
 
G:=SmallGroup(448,1365);
 
// by ID
 
G=gap.SmallGroup(448,1365);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,1684,102,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^28=1,e^2=d^14,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,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
 
// generators/relations
 

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