Copied to
clipboard

## G = C23×Dic14order 448 = 26·7

### Direct product of C23 and Dic14

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
 Upper central C1 — C24 — C23×C4

Generators and relations for C23×Dic14
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 >

Subgroups: 2692 in 850 conjugacy classes, 543 normal (9 characteristic)
C1, C2, C2, C4, C4, C22, C7, C2×C4, C2×C4, Q8, C23, C14, C14, C22×C4, C22×C4, C2×Q8, C24, Dic7, C28, C2×C14, C23×C4, C23×C4, C22×Q8, Dic14, C2×Dic7, C2×C28, C22×C14, Q8×C23, C2×Dic14, C22×Dic7, C22×C28, C23×C14, C22×Dic14, C23×Dic7, C23×C28, C23×Dic14
Quotients: C1, C2, C22, Q8, C23, D7, C2×Q8, C24, D14, C22×Q8, C25, Dic14, C22×D7, Q8×C23, C2×Dic14, C23×D7, C22×Dic14, D7×C24, C23×Dic14

Smallest permutation representation of C23×Dic14
Regular action on 448 points
Generators in S448
(1 130)(2 131)(3 132)(4 133)(5 134)(6 135)(7 136)(8 137)(9 138)(10 139)(11 140)(12 113)(13 114)(14 115)(15 116)(16 117)(17 118)(18 119)(19 120)(20 121)(21 122)(22 123)(23 124)(24 125)(25 126)(26 127)(27 128)(28 129)(29 77)(30 78)(31 79)(32 80)(33 81)(34 82)(35 83)(36 84)(37 57)(38 58)(39 59)(40 60)(41 61)(42 62)(43 63)(44 64)(45 65)(46 66)(47 67)(48 68)(49 69)(50 70)(51 71)(52 72)(53 73)(54 74)(55 75)(56 76)(85 359)(86 360)(87 361)(88 362)(89 363)(90 364)(91 337)(92 338)(93 339)(94 340)(95 341)(96 342)(97 343)(98 344)(99 345)(100 346)(101 347)(102 348)(103 349)(104 350)(105 351)(106 352)(107 353)(108 354)(109 355)(110 356)(111 357)(112 358)(141 193)(142 194)(143 195)(144 196)(145 169)(146 170)(147 171)(148 172)(149 173)(150 174)(151 175)(152 176)(153 177)(154 178)(155 179)(156 180)(157 181)(158 182)(159 183)(160 184)(161 185)(162 186)(163 187)(164 188)(165 189)(166 190)(167 191)(168 192)(197 420)(198 393)(199 394)(200 395)(201 396)(202 397)(203 398)(204 399)(205 400)(206 401)(207 402)(208 403)(209 404)(210 405)(211 406)(212 407)(213 408)(214 409)(215 410)(216 411)(217 412)(218 413)(219 414)(220 415)(221 416)(222 417)(223 418)(224 419)(225 374)(226 375)(227 376)(228 377)(229 378)(230 379)(231 380)(232 381)(233 382)(234 383)(235 384)(236 385)(237 386)(238 387)(239 388)(240 389)(241 390)(242 391)(243 392)(244 365)(245 366)(246 367)(247 368)(248 369)(249 370)(250 371)(251 372)(252 373)(253 322)(254 323)(255 324)(256 325)(257 326)(258 327)(259 328)(260 329)(261 330)(262 331)(263 332)(264 333)(265 334)(266 335)(267 336)(268 309)(269 310)(270 311)(271 312)(272 313)(273 314)(274 315)(275 316)(276 317)(277 318)(278 319)(279 320)(280 321)(281 442)(282 443)(283 444)(284 445)(285 446)(286 447)(287 448)(288 421)(289 422)(290 423)(291 424)(292 425)(293 426)(294 427)(295 428)(296 429)(297 430)(298 431)(299 432)(300 433)(301 434)(302 435)(303 436)(304 437)(305 438)(306 439)(307 440)(308 441)
(1 435)(2 436)(3 437)(4 438)(5 439)(6 440)(7 441)(8 442)(9 443)(10 444)(11 445)(12 446)(13 447)(14 448)(15 421)(16 422)(17 423)(18 424)(19 425)(20 426)(21 427)(22 428)(23 429)(24 430)(25 431)(26 432)(27 433)(28 434)(29 419)(30 420)(31 393)(32 394)(33 395)(34 396)(35 397)(36 398)(37 399)(38 400)(39 401)(40 402)(41 403)(42 404)(43 405)(44 406)(45 407)(46 408)(47 409)(48 410)(49 411)(50 412)(51 413)(52 414)(53 415)(54 416)(55 417)(56 418)(57 204)(58 205)(59 206)(60 207)(61 208)(62 209)(63 210)(64 211)(65 212)(66 213)(67 214)(68 215)(69 216)(70 217)(71 218)(72 219)(73 220)(74 221)(75 222)(76 223)(77 224)(78 197)(79 198)(80 199)(81 200)(82 201)(83 202)(84 203)(85 148)(86 149)(87 150)(88 151)(89 152)(90 153)(91 154)(92 155)(93 156)(94 157)(95 158)(96 159)(97 160)(98 161)(99 162)(100 163)(101 164)(102 165)(103 166)(104 167)(105 168)(106 141)(107 142)(108 143)(109 144)(110 145)(111 146)(112 147)(113 285)(114 286)(115 287)(116 288)(117 289)(118 290)(119 291)(120 292)(121 293)(122 294)(123 295)(124 296)(125 297)(126 298)(127 299)(128 300)(129 301)(130 302)(131 303)(132 304)(133 305)(134 306)(135 307)(136 308)(137 281)(138 282)(139 283)(140 284)(169 356)(170 357)(171 358)(172 359)(173 360)(174 361)(175 362)(176 363)(177 364)(178 337)(179 338)(180 339)(181 340)(182 341)(183 342)(184 343)(185 344)(186 345)(187 346)(188 347)(189 348)(190 349)(191 350)(192 351)(193 352)(194 353)(195 354)(196 355)(225 328)(226 329)(227 330)(228 331)(229 332)(230 333)(231 334)(232 335)(233 336)(234 309)(235 310)(236 311)(237 312)(238 313)(239 314)(240 315)(241 316)(242 317)(243 318)(244 319)(245 320)(246 321)(247 322)(248 323)(249 324)(250 325)(251 326)(252 327)(253 368)(254 369)(255 370)(256 371)(257 372)(258 373)(259 374)(260 375)(261 376)(262 377)(263 378)(264 379)(265 380)(266 381)(267 382)(268 383)(269 384)(270 385)(271 386)(272 387)(273 388)(274 389)(275 390)(276 391)(277 392)(278 365)(279 366)(280 367)
(1 393)(2 394)(3 395)(4 396)(5 397)(6 398)(7 399)(8 400)(9 401)(10 402)(11 403)(12 404)(13 405)(14 406)(15 407)(16 408)(17 409)(18 410)(19 411)(20 412)(21 413)(22 414)(23 415)(24 416)(25 417)(26 418)(27 419)(28 420)(29 433)(30 434)(31 435)(32 436)(33 437)(34 438)(35 439)(36 440)(37 441)(38 442)(39 443)(40 444)(41 445)(42 446)(43 447)(44 448)(45 421)(46 422)(47 423)(48 424)(49 425)(50 426)(51 427)(52 428)(53 429)(54 430)(55 431)(56 432)(57 308)(58 281)(59 282)(60 283)(61 284)(62 285)(63 286)(64 287)(65 288)(66 289)(67 290)(68 291)(69 292)(70 293)(71 294)(72 295)(73 296)(74 297)(75 298)(76 299)(77 300)(78 301)(79 302)(80 303)(81 304)(82 305)(83 306)(84 307)(85 365)(86 366)(87 367)(88 368)(89 369)(90 370)(91 371)(92 372)(93 373)(94 374)(95 375)(96 376)(97 377)(98 378)(99 379)(100 380)(101 381)(102 382)(103 383)(104 384)(105 385)(106 386)(107 387)(108 388)(109 389)(110 390)(111 391)(112 392)(113 209)(114 210)(115 211)(116 212)(117 213)(118 214)(119 215)(120 216)(121 217)(122 218)(123 219)(124 220)(125 221)(126 222)(127 223)(128 224)(129 197)(130 198)(131 199)(132 200)(133 201)(134 202)(135 203)(136 204)(137 205)(138 206)(139 207)(140 208)(141 271)(142 272)(143 273)(144 274)(145 275)(146 276)(147 277)(148 278)(149 279)(150 280)(151 253)(152 254)(153 255)(154 256)(155 257)(156 258)(157 259)(158 260)(159 261)(160 262)(161 263)(162 264)(163 265)(164 266)(165 267)(166 268)(167 269)(168 270)(169 316)(170 317)(171 318)(172 319)(173 320)(174 321)(175 322)(176 323)(177 324)(178 325)(179 326)(180 327)(181 328)(182 329)(183 330)(184 331)(185 332)(186 333)(187 334)(188 335)(189 336)(190 309)(191 310)(192 311)(193 312)(194 313)(195 314)(196 315)(225 340)(226 341)(227 342)(228 343)(229 344)(230 345)(231 346)(232 347)(233 348)(234 349)(235 350)(236 351)(237 352)(238 353)(239 354)(240 355)(241 356)(242 357)(243 358)(244 359)(245 360)(246 361)(247 362)(248 363)(249 364)(250 337)(251 338)(252 339)
(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)
(1 175 15 189)(2 174 16 188)(3 173 17 187)(4 172 18 186)(5 171 19 185)(6 170 20 184)(7 169 21 183)(8 196 22 182)(9 195 23 181)(10 194 24 180)(11 193 25 179)(12 192 26 178)(13 191 27 177)(14 190 28 176)(29 249 43 235)(30 248 44 234)(31 247 45 233)(32 246 46 232)(33 245 47 231)(34 244 48 230)(35 243 49 229)(36 242 50 228)(37 241 51 227)(38 240 52 226)(39 239 53 225)(40 238 54 252)(41 237 55 251)(42 236 56 250)(57 390 71 376)(58 389 72 375)(59 388 73 374)(60 387 74 373)(61 386 75 372)(62 385 76 371)(63 384 77 370)(64 383 78 369)(65 382 79 368)(66 381 80 367)(67 380 81 366)(68 379 82 365)(69 378 83 392)(70 377 84 391)(85 291 99 305)(86 290 100 304)(87 289 101 303)(88 288 102 302)(89 287 103 301)(90 286 104 300)(91 285 105 299)(92 284 106 298)(93 283 107 297)(94 282 108 296)(95 281 109 295)(96 308 110 294)(97 307 111 293)(98 306 112 292)(113 168 127 154)(114 167 128 153)(115 166 129 152)(116 165 130 151)(117 164 131 150)(118 163 132 149)(119 162 133 148)(120 161 134 147)(121 160 135 146)(122 159 136 145)(123 158 137 144)(124 157 138 143)(125 156 139 142)(126 155 140 141)(197 254 211 268)(198 253 212 267)(199 280 213 266)(200 279 214 265)(201 278 215 264)(202 277 216 263)(203 276 217 262)(204 275 218 261)(205 274 219 260)(206 273 220 259)(207 272 221 258)(208 271 222 257)(209 270 223 256)(210 269 224 255)(309 420 323 406)(310 419 324 405)(311 418 325 404)(312 417 326 403)(313 416 327 402)(314 415 328 401)(315 414 329 400)(316 413 330 399)(317 412 331 398)(318 411 332 397)(319 410 333 396)(320 409 334 395)(321 408 335 394)(322 407 336 393)(337 446 351 432)(338 445 352 431)(339 444 353 430)(340 443 354 429)(341 442 355 428)(342 441 356 427)(343 440 357 426)(344 439 358 425)(345 438 359 424)(346 437 360 423)(347 436 361 422)(348 435 362 421)(349 434 363 448)(350 433 364 447)

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

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

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

136 conjugacy classes

 class 1 2A ··· 2O 4A ··· 4H 4I ··· 4X 7A 7B 7C 14A ··· 14AS 28A ··· 28AV order 1 2 ··· 2 4 ··· 4 4 ··· 4 7 7 7 14 ··· 14 28 ··· 28 size 1 1 ··· 1 2 ··· 2 14 ··· 14 2 2 2 2 ··· 2 2 ··· 2

136 irreducible representations

 dim 1 1 1 1 2 2 2 2 2 type + + + + - + + + - image C1 C2 C2 C2 Q8 D7 D14 D14 Dic14 kernel C23×Dic14 C22×Dic14 C23×Dic7 C23×C28 C22×C14 C23×C4 C22×C4 C24 C23 # reps 1 28 2 1 8 3 42 3 48

Matrix representation of C23×Dic14 in GL5(𝔽29)

 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 16 0 0 0 13 22
,
 28 0 0 0 0 0 1 0 0 0 0 0 28 0 0 0 0 0 10 10 0 0 0 16 19

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] >;

C23×Dic14 in GAP, Magma, Sage, TeX

C_2^3\times {\rm 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

׿
×
𝔽