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G = Q8×C22×C14  order 448 = 26·7

Direct product of C22×C14 and Q8

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

Aliases: Q8×C22×C14, C14.22C25, C28.88C24, C2.2(C24×C14), (C23×C4).14C14, C24.40(C2×C14), C4.11(C23×C14), (C23×C28).27C2, (C2×C14).385C24, (C2×C28).977C23, C22.14(C23×C14), C23.74(C22×C14), (C23×C14).120C22, (C22×C28).605C22, (C22×C14).471C23, (C2×C4).145(C22×C14), (C22×C4).132(C2×C14), SmallGroup(448,1387)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2 — Q8×C22×C14
Chief series
C1 — C2 — C14 — C28 — C7×Q8 — Q8×C14 — Q8×C2×C14 — Q8×C22×C14
Lower central
C1 — C2 — Q8×C22×C14
Upper central
C1 — C23×C14 — Q8×C22×C14

Generators and relations for Q8×C22×C14
 G = < a,b,c,d,e | a2=b2=c14=d4=1, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

Subgroups: 850, all normal (8 characteristic)
C1, C2, C2, C4, C22, C7, C2×C4, Q8, C23, C14, C14, C22×C4, C2×Q8, C24, C28, C2×C14, C23×C4, C22×Q8, C2×C28, C7×Q8, C22×C14, Q8×C23, C22×C28, Q8×C14, C23×C14, C23×C28, Q8×C2×C14, Q8×C22×C14
Quotients: C1, C2, C22, C7, Q8, C23, C14, C2×Q8, C24, C2×C14, C22×Q8, C25, C7×Q8, C22×C14, Q8×C23, Q8×C14, C23×C14, Q8×C2×C14, C24×C14, Q8×C22×C14

Smallest permutation representation of Q8×C22×C14
►Regular action on 448 points
Generators in S448
(1 138)(2 139)(3 140)(4 127)(5 128)(6 129)(7 130)(8 131)(9 132)(10 133)(11 134)(12 135)(13 136)(14 137)(15 231)(16 232)(17 233)(18 234)(19 235)(20 236)(21 237)(22 238)(23 225)(24 226)(25 227)(26 228)(27 229)(28 230)(29 171)(30 172)(31 173)(32 174)(33 175)(34 176)(35 177)(36 178)(37 179)(38 180)(39 181)(40 182)(41 169)(42 170)(43 252)(44 239)(45 240)(46 241)(47 242)(48 243)(49 244)(50 245)(51 246)(52 247)(53 248)(54 249)(55 250)(56 251)(57 348)(58 349)(59 350)(60 337)(61 338)(62 339)(63 340)(64 341)(65 342)(66 343)(67 344)(68 345)(69 346)(70 347)(71 409)(72 410)(73 411)(74 412)(75 413)(76 414)(77 415)(78 416)(79 417)(80 418)(81 419)(82 420)(83 407)(84 408)(85 283)(86 284)(87 285)(88 286)(89 287)(90 288)(91 289)(92 290)(93 291)(94 292)(95 293)(96 294)(97 281)(98 282)(99 186)(100 187)(101 188)(102 189)(103 190)(104 191)(105 192)(106 193)(107 194)(108 195)(109 196)(110 183)(111 184)(112 185)(113 321)(114 322)(115 309)(116 310)(117 311)(118 312)(119 313)(120 314)(121 315)(122 316)(123 317)(124 318)(125 319)(126 320)(141 328)(142 329)(143 330)(144 331)(145 332)(146 333)(147 334)(148 335)(149 336)(150 323)(151 324)(152 325)(153 326)(154 327)(155 301)(156 302)(157 303)(158 304)(159 305)(160 306)(161 307)(162 308)(163 295)(164 296)(165 297)(166 298)(167 299)(168 300)(197 279)(198 280)(199 267)(200 268)(201 269)(202 270)(203 271)(204 272)(205 273)(206 274)(207 275)(208 276)(209 277)(210 278)(211 448)(212 435)(213 436)(214 437)(215 438)(216 439)(217 440)(218 441)(219 442)(220 443)(221 444)(222 445)(223 446)(224 447)(253 377)(254 378)(255 365)(256 366)(257 367)(258 368)(259 369)(260 370)(261 371)(262 372)(263 373)(264 374)(265 375)(266 376)(351 386)(352 387)(353 388)(354 389)(355 390)(356 391)(357 392)(358 379)(359 380)(360 381)(361 382)(362 383)(363 384)(364 385)(393 429)(394 430)(395 431)(396 432)(397 433)(398 434)(399 421)(400 422)(401 423)(402 424)(403 425)(404 426)(405 427)(406 428)

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

(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)

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

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

280 conjugacy classes

class 1 2A···2O4A···4X7A···7F14A···14CL28A···28EN
order12···24···47···714···1428···28
size11···12···21···11···12···2

280 irreducible representations

dim11111122
type+++-
imageC1C2C2C7C14C14Q8C7×Q8
kernelQ8×C22×C14C23×C28Q8×C2×C14Q8×C23C23×C4C22×Q8C22×C14C23
# reps1328618168848

Matrix representation of Q8×C22×C14 ►in GL5(𝔽29)

280000
01000
00100
00010
00001
,
10000
028000
00100
00010
00001
,
280000
01000
002800
000240
000024
,
280000
028000
002800
000028
00010
,
280000
028000
00100
000213
0001327

G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[28,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,24,0,0,0,0,0,24],[28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,28,0],[28,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,2,13,0,0,0,13,27] >;
 

Q8×C22×C14 in GAP, Magma, Sage, TeX 

Q_8\times C_2^2\times C_{14}
 
% in TeX
 
G:=Group("Q8xC2^2xC14");
 
// GroupNames label
 
G:=SmallGroup(448,1387);
 
// by ID
 
G=gap.SmallGroup(448,1387);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-7,-2,1568,3165,1576]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^14=d^4=1,e^2=d^2,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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