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G = C22×C4×Dic7  order 448 = 26·7

Direct product of C22×C4 and Dic7

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

Aliases: C22×C4×Dic7, C24.75D14, (C2×C14)⋊4C42, C28⋊9(C22×C4), C14⋊2(C2×C42), C7⋊2(C22×C42), (C22×C28)⋊18C4, (C23×C4).15D7, C23.67(C4×D7), (C23×C28).21C2, C14.36(C23×C4), C2.2(C23×Dic7), (C2×C14).280C24, (C2×C28).884C23, (C22×C4).473D14, C23.44(C2×Dic7), C22.38(C23×D7), (C23×Dic7).12C2, C23.332(C22×D7), (C23×C14).102C22, (C22×C28).569C22, (C22×C14).409C23, (C2×Dic7).314C23, C22.29(C22×Dic7), (C22×Dic7).244C22, (C2×C28)⋊38(C2×C4), C2.3(D7×C22×C4), C22.77(C2×C4×D7), (C2×C4).828(C22×D7), (C2×C14).206(C22×C4), (C22×C14).141(C2×C4), SmallGroup(448,1235)

Series: Derived ►Chief ►Lower central ►Upper central

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

Generators and relations for C22×C4×Dic7
 G = < a,b,c,d,e | a2=b2=c4=d14=1, e2=d7, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

Subgroups: 1284 in 498 conjugacy classes, 367 normal (11 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C23, C14, C14, C42, C22×C4, C22×C4, C24, Dic7, C28, C2×C14, C2×C14, C2×C42, C23×C4, C23×C4, C2×Dic7, C2×C28, C22×C14, C22×C42, C4×Dic7, C22×Dic7, C22×C28, C23×C14, C2×C4×Dic7, C23×Dic7, C23×C28, C22×C4×Dic7
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C42, C22×C4, C24, Dic7, D14, C2×C42, C23×C4, C4×D7, C2×Dic7, C22×D7, C22×C42, C4×Dic7, C2×C4×D7, C22×Dic7, C23×D7, C2×C4×Dic7, D7×C22×C4, C23×Dic7, C22×C4×Dic7

Smallest permutation representation of C22×C4×Dic7
►Regular action on 448 points
Generators in S448
(1 310)(2 311)(3 312)(4 313)(5 314)(6 315)(7 316)(8 317)(9 318)(10 319)(11 320)(12 321)(13 322)(14 309)(15 120)(16 121)(17 122)(18 123)(19 124)(20 125)(21 126)(22 113)(23 114)(24 115)(25 116)(26 117)(27 118)(28 119)(29 245)(30 246)(31 247)(32 248)(33 249)(34 250)(35 251)(36 252)(37 239)(38 240)(39 241)(40 242)(41 243)(42 244)(43 213)(44 214)(45 215)(46 216)(47 217)(48 218)(49 219)(50 220)(51 221)(52 222)(53 223)(54 224)(55 211)(56 212)(57 101)(58 102)(59 103)(60 104)(61 105)(62 106)(63 107)(64 108)(65 109)(66 110)(67 111)(68 112)(69 99)(70 100)(71 422)(72 423)(73 424)(74 425)(75 426)(76 427)(77 428)(78 429)(79 430)(80 431)(81 432)(82 433)(83 434)(84 421)(85 159)(86 160)(87 161)(88 162)(89 163)(90 164)(91 165)(92 166)(93 167)(94 168)(95 155)(96 156)(97 157)(98 158)(127 336)(128 323)(129 324)(130 325)(131 326)(132 327)(133 328)(134 329)(135 330)(136 331)(137 332)(138 333)(139 334)(140 335)(141 206)(142 207)(143 208)(144 209)(145 210)(146 197)(147 198)(148 199)(149 200)(150 201)(151 202)(152 203)(153 204)(154 205)(169 235)(170 236)(171 237)(172 238)(173 225)(174 226)(175 227)(176 228)(177 229)(178 230)(179 231)(180 232)(181 233)(182 234)(183 359)(184 360)(185 361)(186 362)(187 363)(188 364)(189 351)(190 352)(191 353)(192 354)(193 355)(194 356)(195 357)(196 358)(253 381)(254 382)(255 383)(256 384)(257 385)(258 386)(259 387)(260 388)(261 389)(262 390)(263 391)(264 392)(265 379)(266 380)(267 367)(268 368)(269 369)(270 370)(271 371)(272 372)(273 373)(274 374)(275 375)(276 376)(277 377)(278 378)(279 365)(280 366)(281 345)(282 346)(283 347)(284 348)(285 349)(286 350)(287 337)(288 338)(289 339)(290 340)(291 341)(292 342)(293 343)(294 344)(295 440)(296 441)(297 442)(298 443)(299 444)(300 445)(301 446)(302 447)(303 448)(304 435)(305 436)(306 437)(307 438)(308 439)(393 413)(394 414)(395 415)(396 416)(397 417)(398 418)(399 419)(400 420)(401 407)(402 408)(403 409)(404 410)(405 411)(406 412)

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

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

(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)

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

160 conjugacy classes

class 1 2A···2O4A···4P4Q···4AV7A7B7C14A···14AS28A···28AV
order12···24···44···477714···1428···28
size11···11···17···72222···22···2

160 irreducible representations

dim11111122222
type+++++-++
imageC1C2C2C2C4C4D7Dic7D14D14C4×D7
kernelC22×C4×Dic7C2×C4×Dic7C23×Dic7C23×C28C22×Dic7C22×C28C23×C4C22×C4C22×C4C24C23
# reps11221321632418348

Matrix representation of C22×C4×Dic7 ►in GL5(𝔽29)

10000
01000
002800
00010
00001
,
280000
028000
002800
000280
000028
,
280000
028000
002800
000120
000012
,
280000
01000
00100
000128
000525
,
170000
01000
00100
0001217
000017

G:=sub<GL(5,GF(29))| [1,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,1],[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],[28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,12,0,0,0,0,0,12],[28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,5,0,0,0,28,25],[17,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,12,0,0,0,0,17,17] >;
 

C22×C4×Dic7 in GAP, Magma, Sage, TeX 

C_2^2\times C_4\times {\rm Dic}_7
 
% in TeX
 
G:=Group("C2^2xC4xDic7");
 
// GroupNames label
 
G:=SmallGroup(448,1235);
 
// by ID
 
G=gap.SmallGroup(448,1235);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,136,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^4=d^14=1,e^2=d^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,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
 
// generators/relations
 

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