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## G = C22.23(Q8×D7)  order 448 = 26·7

### 15th central extension by C22 of Q8×D7

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C14 — C22.23(Q8×D7)
 Chief series C1 — C7 — C14 — C2×C14 — C22×C14 — C22×Dic7 — C2×Dic7⋊C4 — C22.23(Q8×D7)
 Lower central C7 — C2×C14 — C22.23(Q8×D7)
 Upper central C1 — C23 — C2×C4⋊C4

Generators and relations for C22.23(Q8×D7)
G = < a,b,c,d,e,f | a2=b2=c4=e7=1, d2=ac2, f2=a, ab=ba, ac=ca, ad=da, ae=ea, af=fa, fcf-1=bc=cb, fdf-1=bd=db, be=eb, bf=fb, dcd-1=c-1, ce=ec, de=ed, fef-1=e-1 >

Subgroups: 580 in 154 conjugacy classes, 69 normal (51 characteristic)
C1, C2, C4, C22, C7, C2×C4, C2×C4, C23, C14, C42, C4⋊C4, C22×C4, C22×C4, Dic7, C28, C2×C14, C2.C42, C2×C42, C2×C4⋊C4, C2×C4⋊C4, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, C23.63C23, C4×Dic7, Dic7⋊C4, C7×C4⋊C4, C22×Dic7, C22×C28, C14.C42, C2×C4×Dic7, C2×Dic7⋊C4, C14×C4⋊C4, C22.23(Q8×D7)
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C22×C4, C2×D4, C2×Q8, C4○D4, D14, C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C22.D4, C42.C2, C422C2, C4×D7, C7⋊D4, C22×D7, C23.63C23, C2×C4×D7, C4○D28, D42D7, Q8×D7, Q82D7, C2×C7⋊D4, Dic73Q8, Dic7.Q8, C4⋊C47D7, C4⋊C4⋊D7, C4×C7⋊D4, C23.18D14, D143Q8, C22.23(Q8×D7)

Smallest permutation representation of C22.23(Q8×D7)
Regular action on 448 points
Generators in S448
(1 36)(2 37)(3 38)(4 39)(5 40)(6 41)(7 42)(8 29)(9 30)(10 31)(11 32)(12 33)(13 34)(14 35)(15 50)(16 51)(17 52)(18 53)(19 54)(20 55)(21 56)(22 43)(23 44)(24 45)(25 46)(26 47)(27 48)(28 49)(57 92)(58 93)(59 94)(60 95)(61 96)(62 97)(63 98)(64 85)(65 86)(66 87)(67 88)(68 89)(69 90)(70 91)(71 106)(72 107)(73 108)(74 109)(75 110)(76 111)(77 112)(78 99)(79 100)(80 101)(81 102)(82 103)(83 104)(84 105)(113 148)(114 149)(115 150)(116 151)(117 152)(118 153)(119 154)(120 141)(121 142)(122 143)(123 144)(124 145)(125 146)(126 147)(127 162)(128 163)(129 164)(130 165)(131 166)(132 167)(133 168)(134 155)(135 156)(136 157)(137 158)(138 159)(139 160)(140 161)(169 204)(170 205)(171 206)(172 207)(173 208)(174 209)(175 210)(176 197)(177 198)(178 199)(179 200)(180 201)(181 202)(182 203)(183 218)(184 219)(185 220)(186 221)(187 222)(188 223)(189 224)(190 211)(191 212)(192 213)(193 214)(194 215)(195 216)(196 217)(225 260)(226 261)(227 262)(228 263)(229 264)(230 265)(231 266)(232 253)(233 254)(234 255)(235 256)(236 257)(237 258)(238 259)(239 274)(240 275)(241 276)(242 277)(243 278)(244 279)(245 280)(246 267)(247 268)(248 269)(249 270)(250 271)(251 272)(252 273)(281 316)(282 317)(283 318)(284 319)(285 320)(286 321)(287 322)(288 309)(289 310)(290 311)(291 312)(292 313)(293 314)(294 315)(295 330)(296 331)(297 332)(298 333)(299 334)(300 335)(301 336)(302 323)(303 324)(304 325)(305 326)(306 327)(307 328)(308 329)(337 372)(338 373)(339 374)(340 375)(341 376)(342 377)(343 378)(344 365)(345 366)(346 367)(347 368)(348 369)(349 370)(350 371)(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)(393 428)(394 429)(395 430)(396 431)(397 432)(398 433)(399 434)(400 421)(401 422)(402 423)(403 424)(404 425)(405 426)(406 427)(407 442)(408 443)(409 444)(410 445)(411 446)(412 447)(413 448)(414 435)(415 436)(416 437)(417 438)(418 439)(419 440)(420 441)
(1 22)(2 23)(3 24)(4 25)(5 26)(6 27)(7 28)(8 15)(9 16)(10 17)(11 18)(12 19)(13 20)(14 21)(29 50)(30 51)(31 52)(32 53)(33 54)(34 55)(35 56)(36 43)(37 44)(38 45)(39 46)(40 47)(41 48)(42 49)(57 78)(58 79)(59 80)(60 81)(61 82)(62 83)(63 84)(64 71)(65 72)(66 73)(67 74)(68 75)(69 76)(70 77)(85 106)(86 107)(87 108)(88 109)(89 110)(90 111)(91 112)(92 99)(93 100)(94 101)(95 102)(96 103)(97 104)(98 105)(113 134)(114 135)(115 136)(116 137)(117 138)(118 139)(119 140)(120 127)(121 128)(122 129)(123 130)(124 131)(125 132)(126 133)(141 162)(142 163)(143 164)(144 165)(145 166)(146 167)(147 168)(148 155)(149 156)(150 157)(151 158)(152 159)(153 160)(154 161)(169 190)(170 191)(171 192)(172 193)(173 194)(174 195)(175 196)(176 183)(177 184)(178 185)(179 186)(180 187)(181 188)(182 189)(197 218)(198 219)(199 220)(200 221)(201 222)(202 223)(203 224)(204 211)(205 212)(206 213)(207 214)(208 215)(209 216)(210 217)(225 246)(226 247)(227 248)(228 249)(229 250)(230 251)(231 252)(232 239)(233 240)(234 241)(235 242)(236 243)(237 244)(238 245)(253 274)(254 275)(255 276)(256 277)(257 278)(258 279)(259 280)(260 267)(261 268)(262 269)(263 270)(264 271)(265 272)(266 273)(281 302)(282 303)(283 304)(284 305)(285 306)(286 307)(287 308)(288 295)(289 296)(290 297)(291 298)(292 299)(293 300)(294 301)(309 330)(310 331)(311 332)(312 333)(313 334)(314 335)(315 336)(316 323)(317 324)(318 325)(319 326)(320 327)(321 328)(322 329)(337 358)(338 359)(339 360)(340 361)(341 362)(342 363)(343 364)(344 351)(345 352)(346 353)(347 354)(348 355)(349 356)(350 357)(365 386)(366 387)(367 388)(368 389)(369 390)(370 391)(371 392)(372 379)(373 380)(374 381)(375 382)(376 383)(377 384)(378 385)(393 414)(394 415)(395 416)(396 417)(397 418)(398 419)(399 420)(400 407)(401 408)(402 409)(403 410)(404 411)(405 412)(406 413)(421 442)(422 443)(423 444)(424 445)(425 446)(426 447)(427 448)(428 435)(429 436)(430 437)(431 438)(432 439)(433 440)(434 441)
(1 120 8 113)(2 121 9 114)(3 122 10 115)(4 123 11 116)(5 124 12 117)(6 125 13 118)(7 126 14 119)(15 134 22 127)(16 135 23 128)(17 136 24 129)(18 137 25 130)(19 138 26 131)(20 139 27 132)(21 140 28 133)(29 148 36 141)(30 149 37 142)(31 150 38 143)(32 151 39 144)(33 152 40 145)(34 153 41 146)(35 154 42 147)(43 162 50 155)(44 163 51 156)(45 164 52 157)(46 165 53 158)(47 166 54 159)(48 167 55 160)(49 168 56 161)(57 176 64 169)(58 177 65 170)(59 178 66 171)(60 179 67 172)(61 180 68 173)(62 181 69 174)(63 182 70 175)(71 190 78 183)(72 191 79 184)(73 192 80 185)(74 193 81 186)(75 194 82 187)(76 195 83 188)(77 196 84 189)(85 204 92 197)(86 205 93 198)(87 206 94 199)(88 207 95 200)(89 208 96 201)(90 209 97 202)(91 210 98 203)(99 218 106 211)(100 219 107 212)(101 220 108 213)(102 221 109 214)(103 222 110 215)(104 223 111 216)(105 224 112 217)(225 358 232 351)(226 359 233 352)(227 360 234 353)(228 361 235 354)(229 362 236 355)(230 363 237 356)(231 364 238 357)(239 344 246 337)(240 345 247 338)(241 346 248 339)(242 347 249 340)(243 348 250 341)(244 349 251 342)(245 350 252 343)(253 386 260 379)(254 387 261 380)(255 388 262 381)(256 389 263 382)(257 390 264 383)(258 391 265 384)(259 392 266 385)(267 372 274 365)(268 373 275 366)(269 374 276 367)(270 375 277 368)(271 376 278 369)(272 377 279 370)(273 378 280 371)(281 414 288 407)(282 415 289 408)(283 416 290 409)(284 417 291 410)(285 418 292 411)(286 419 293 412)(287 420 294 413)(295 400 302 393)(296 401 303 394)(297 402 304 395)(298 403 305 396)(299 404 306 397)(300 405 307 398)(301 406 308 399)(309 442 316 435)(310 443 317 436)(311 444 318 437)(312 445 319 438)(313 446 320 439)(314 447 321 440)(315 448 322 441)(323 428 330 421)(324 429 331 422)(325 430 332 423)(326 431 333 424)(327 432 334 425)(328 433 335 426)(329 434 336 427)
(1 197 29 169)(2 198 30 170)(3 199 31 171)(4 200 32 172)(5 201 33 173)(6 202 34 174)(7 203 35 175)(8 204 36 176)(9 205 37 177)(10 206 38 178)(11 207 39 179)(12 208 40 180)(13 209 41 181)(14 210 42 182)(15 211 43 183)(16 212 44 184)(17 213 45 185)(18 214 46 186)(19 215 47 187)(20 216 48 188)(21 217 49 189)(22 218 50 190)(23 219 51 191)(24 220 52 192)(25 221 53 193)(26 222 54 194)(27 223 55 195)(28 224 56 196)(57 113 85 141)(58 114 86 142)(59 115 87 143)(60 116 88 144)(61 117 89 145)(62 118 90 146)(63 119 91 147)(64 120 92 148)(65 121 93 149)(66 122 94 150)(67 123 95 151)(68 124 96 152)(69 125 97 153)(70 126 98 154)(71 127 99 155)(72 128 100 156)(73 129 101 157)(74 130 102 158)(75 131 103 159)(76 132 104 160)(77 133 105 161)(78 134 106 162)(79 135 107 163)(80 136 108 164)(81 137 109 165)(82 138 110 166)(83 139 111 167)(84 140 112 168)(225 435 253 407)(226 436 254 408)(227 437 255 409)(228 438 256 410)(229 439 257 411)(230 440 258 412)(231 441 259 413)(232 442 260 414)(233 443 261 415)(234 444 262 416)(235 445 263 417)(236 446 264 418)(237 447 265 419)(238 448 266 420)(239 421 267 393)(240 422 268 394)(241 423 269 395)(242 424 270 396)(243 425 271 397)(244 426 272 398)(245 427 273 399)(246 428 274 400)(247 429 275 401)(248 430 276 402)(249 431 277 403)(250 432 278 404)(251 433 279 405)(252 434 280 406)(281 351 309 379)(282 352 310 380)(283 353 311 381)(284 354 312 382)(285 355 313 383)(286 356 314 384)(287 357 315 385)(288 358 316 386)(289 359 317 387)(290 360 318 388)(291 361 319 389)(292 362 320 390)(293 363 321 391)(294 364 322 392)(295 337 323 365)(296 338 324 366)(297 339 325 367)(298 340 326 368)(299 341 327 369)(300 342 328 370)(301 343 329 371)(302 344 330 372)(303 345 331 373)(304 346 332 374)(305 347 333 375)(306 348 334 376)(307 349 335 377)(308 350 336 378)
(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)
(1 320 36 285)(2 319 37 284)(3 318 38 283)(4 317 39 282)(5 316 40 281)(6 322 41 287)(7 321 42 286)(8 313 29 292)(9 312 30 291)(10 311 31 290)(11 310 32 289)(12 309 33 288)(13 315 34 294)(14 314 35 293)(15 334 50 299)(16 333 51 298)(17 332 52 297)(18 331 53 296)(19 330 54 295)(20 336 55 301)(21 335 56 300)(22 327 43 306)(23 326 44 305)(24 325 45 304)(25 324 46 303)(26 323 47 302)(27 329 48 308)(28 328 49 307)(57 236 92 257)(58 235 93 256)(59 234 94 255)(60 233 95 254)(61 232 96 253)(62 238 97 259)(63 237 98 258)(64 229 85 264)(65 228 86 263)(66 227 87 262)(67 226 88 261)(68 225 89 260)(69 231 90 266)(70 230 91 265)(71 250 106 271)(72 249 107 270)(73 248 108 269)(74 247 109 268)(75 246 110 267)(76 252 111 273)(77 251 112 272)(78 243 99 278)(79 242 100 277)(80 241 101 276)(81 240 102 275)(82 239 103 274)(83 245 104 280)(84 244 105 279)(113 425 148 404)(114 424 149 403)(115 423 150 402)(116 422 151 401)(117 421 152 400)(118 427 153 406)(119 426 154 405)(120 432 141 397)(121 431 142 396)(122 430 143 395)(123 429 144 394)(124 428 145 393)(125 434 146 399)(126 433 147 398)(127 439 162 418)(128 438 163 417)(129 437 164 416)(130 436 165 415)(131 435 166 414)(132 441 167 420)(133 440 168 419)(134 446 155 411)(135 445 156 410)(136 444 157 409)(137 443 158 408)(138 442 159 407)(139 448 160 413)(140 447 161 412)(169 341 204 376)(170 340 205 375)(171 339 206 374)(172 338 207 373)(173 337 208 372)(174 343 209 378)(175 342 210 377)(176 348 197 369)(177 347 198 368)(178 346 199 367)(179 345 200 366)(180 344 201 365)(181 350 202 371)(182 349 203 370)(183 355 218 390)(184 354 219 389)(185 353 220 388)(186 352 221 387)(187 351 222 386)(188 357 223 392)(189 356 224 391)(190 362 211 383)(191 361 212 382)(192 360 213 381)(193 359 214 380)(194 358 215 379)(195 364 216 385)(196 363 217 384)

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

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

88 conjugacy classes

 class 1 2A ··· 2G 4A 4B 4C 4D 4E 4F 4G 4H 4I ··· 4P 4Q 4R 4S 4T 7A 7B 7C 14A ··· 14U 28A ··· 28AJ order 1 2 ··· 2 4 4 4 4 4 4 4 4 4 ··· 4 4 4 4 4 7 7 7 14 ··· 14 28 ··· 28 size 1 1 ··· 1 2 2 2 2 4 4 4 4 14 ··· 14 28 28 28 28 2 2 2 2 ··· 2 4 ··· 4

88 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4 4 type + + + + + - + + + - - + image C1 C2 C2 C2 C2 C4 Q8 D4 D7 C4○D4 D14 C4×D7 C7⋊D4 C4○D28 D4⋊2D7 Q8×D7 Q8⋊2D7 kernel C22.23(Q8×D7) C14.C42 C2×C4×Dic7 C2×Dic7⋊C4 C14×C4⋊C4 Dic7⋊C4 C2×Dic7 C2×C28 C2×C4⋊C4 C2×C14 C22×C4 C2×C4 C2×C4 C22 C22 C22 C22 # reps 1 4 1 1 1 8 2 2 3 8 9 12 12 12 6 3 3

Matrix representation of C22.23(Q8×D7) in GL5(𝔽29)

 28 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 28 0 0 0 0 0 28
,
 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 24 13 0 0 0 16 5 0 0 0 0 0 0 1 0 0 0 28 0
,
 12 0 0 0 0 0 24 13 0 0 0 16 5 0 0 0 0 0 0 28 0 0 0 28 0
,
 1 0 0 0 0 0 3 28 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1
,
 17 0 0 0 0 0 5 2 0 0 0 17 24 0 0 0 0 0 12 0 0 0 0 0 12

G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,28],[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],[1,0,0,0,0,0,24,16,0,0,0,13,5,0,0,0,0,0,0,28,0,0,0,1,0],[12,0,0,0,0,0,24,16,0,0,0,13,5,0,0,0,0,0,0,28,0,0,0,28,0],[1,0,0,0,0,0,3,1,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,1],[17,0,0,0,0,0,5,17,0,0,0,2,24,0,0,0,0,0,12,0,0,0,0,0,12] >;

C22.23(Q8×D7) in GAP, Magma, Sage, TeX

C_2^2._{23}(Q_8\times D_7)
% in TeX

G:=Group("C2^2.23(Q8xD7)");
// GroupNames label

G:=SmallGroup(448,512);
// by ID

G=gap.SmallGroup(448,512);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,232,387,58,18822]);
// Polycyclic

G:=Group<a,b,c,d,e,f|a^2=b^2=c^4=e^7=1,d^2=a*c^2,f^2=a,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,f*c*f^-1=b*c=c*b,f*d*f^-1=b*d=d*b,b*e=e*b,b*f=f*b,d*c*d^-1=c^-1,c*e=e*c,d*e=e*d,f*e*f^-1=e^-1>;
// generators/relations

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