direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C14.SD16, C14⋊1(C4.Q8), C28.15(C4⋊C4), (C2×C28).15Q8, C28.62(C2×Q8), C4⋊C4.224D14, (C2×C28).131D4, C28.57(C22×C4), (C2×C4).27Dic14, (C2×C14).39SD16, C14.65(C2×SD16), C4.27(C2×Dic14), C4.15(Dic7⋊C4), (C2×C28).316C23, (C22×C14).181D4, (C22×C4).328D14, C23.96(C7⋊D4), C22.10(Q8⋊D7), C4⋊Dic7.322C22, C22.10(D4.D7), C22.24(Dic7⋊C4), (C22×C28).131C22, (C2×C7⋊C8)⋊6C4, C7⋊2(C2×C4.Q8), C7⋊C8⋊24(C2×C4), C4.85(C2×C4×D7), (C2×C4⋊C4).5D7, C2.1(C2×Q8⋊D7), (C14×C4⋊C4).4C2, C14.33(C2×C4⋊C4), (C22×C7⋊C8).4C2, C2.1(C2×D4.D7), (C2×C28).75(C2×C4), (C2×C4).150(C4×D7), C2.8(C2×Dic7⋊C4), (C2×C14).45(C4⋊C4), (C2×C14).436(C2×D4), (C2×C7⋊C8).240C22, (C2×C4⋊Dic7).30C2, C22.55(C2×C7⋊D4), (C2×C4).123(C7⋊D4), (C7×C4⋊C4).255C22, (C2×C4).416(C22×D7), SmallGroup(448,497)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C14.SD16
G = < a,b,c,d | a2=b14=c8=1, d2=b7, ab=ba, ac=ca, ad=da, cbc-1=b-1, bd=db, dcd-1=c3 >
Subgroups: 452 in 130 conjugacy classes, 79 normal (27 characteristic)
C1, C2 [×3], C2 [×4], C4 [×2], C4 [×2], C4 [×4], C22, C22 [×6], C7, C8 [×4], C2×C4 [×2], C2×C4 [×4], C2×C4 [×8], C23, C14 [×3], C14 [×4], C4⋊C4 [×2], C4⋊C4 [×4], C2×C8 [×6], C22×C4, C22×C4 [×2], Dic7 [×2], C28 [×2], C28 [×2], C28 [×2], C2×C14, C2×C14 [×6], C4.Q8 [×4], C2×C4⋊C4, C2×C4⋊C4, C22×C8, C7⋊C8 [×4], C2×Dic7 [×4], C2×C28 [×2], C2×C28 [×4], C2×C28 [×4], C22×C14, C2×C4.Q8, C2×C7⋊C8 [×6], C4⋊Dic7 [×2], C4⋊Dic7, C7×C4⋊C4 [×2], C7×C4⋊C4, C22×Dic7, C22×C28, C22×C28, C14.SD16 [×4], C22×C7⋊C8, C2×C4⋊Dic7, C14×C4⋊C4, C2×C14.SD16
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×2], Q8 [×2], C23, D7, C4⋊C4 [×4], SD16 [×4], C22×C4, C2×D4, C2×Q8, D14 [×3], C4.Q8 [×4], C2×C4⋊C4, C2×SD16 [×2], Dic14 [×2], C4×D7 [×2], C7⋊D4 [×2], C22×D7, C2×C4.Q8, Dic7⋊C4 [×4], D4.D7 [×2], Q8⋊D7 [×2], C2×Dic14, C2×C4×D7, C2×C7⋊D4, C14.SD16 [×4], C2×Dic7⋊C4, C2×D4.D7, C2×Q8⋊D7, C2×C14.SD16
►Regular action on 448 points
Generators in S448
(1 281)(2 282)(3 283)(4 284)(5 285)(6 286)(7 287)(8 288)(9 289)(10 290)(11 291)(12 292)(13 293)(14 294)(15 327)(16 328)(17 329)(18 330)(19 331)(20 332)(21 333)(22 334)(23 335)(24 336)(25 323)(26 324)(27 325)(28 326)(29 134)(30 135)(31 136)(32 137)(33 138)(34 139)(35 140)(36 127)(37 128)(38 129)(39 130)(40 131)(41 132)(42 133)(43 126)(44 113)(45 114)(46 115)(47 116)(48 117)(49 118)(50 119)(51 120)(52 121)(53 122)(54 123)(55 124)(56 125)(57 224)(58 211)(59 212)(60 213)(61 214)(62 215)(63 216)(64 217)(65 218)(66 219)(67 220)(68 221)(69 222)(70 223)(71 235)(72 236)(73 237)(74 238)(75 225)(76 226)(77 227)(78 228)(79 229)(80 230)(81 231)(82 232)(83 233)(84 234)(85 427)(86 428)(87 429)(88 430)(89 431)(90 432)(91 433)(92 434)(93 421)(94 422)(95 423)(96 424)(97 425)(98 426)(99 192)(100 193)(101 194)(102 195)(103 196)(104 183)(105 184)(106 185)(107 186)(108 187)(109 188)(110 189)(111 190)(112 191)(141 209)(142 210)(143 197)(144 198)(145 199)(146 200)(147 201)(148 202)(149 203)(150 204)(151 205)(152 206)(153 207)(154 208)(155 179)(156 180)(157 181)(158 182)(159 169)(160 170)(161 171)(162 172)(163 173)(164 174)(165 175)(166 176)(167 177)(168 178)(239 418)(240 419)(241 420)(242 407)(243 408)(244 409)(245 410)(246 411)(247 412)(248 413)(249 414)(250 415)(251 416)(252 417)(253 385)(254 386)(255 387)(256 388)(257 389)(258 390)(259 391)(260 392)(261 379)(262 380)(263 381)(264 382)(265 383)(266 384)(267 400)(268 401)(269 402)(270 403)(271 404)(272 405)(273 406)(274 393)(275 394)(276 395)(277 396)(278 397)(279 398)(280 399)(295 438)(296 439)(297 440)(298 441)(299 442)(300 443)(301 444)(302 445)(303 446)(304 447)(305 448)(306 435)(307 436)(308 437)(309 372)(310 373)(311 374)(312 375)(313 376)(314 377)(315 378)(316 365)(317 366)(318 367)(319 368)(320 369)(321 370)(322 371)(337 362)(338 363)(339 364)(340 351)(341 352)(342 353)(343 354)(344 355)(345 356)(346 357)(347 358)(348 359)(349 360)(350 361)
(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 73 266 201 156 133 45 414)(2 72 253 200 157 132 46 413)(3 71 254 199 158 131 47 412)(4 84 255 198 159 130 48 411)(5 83 256 197 160 129 49 410)(6 82 257 210 161 128 50 409)(7 81 258 209 162 127 51 408)(8 80 259 208 163 140 52 407)(9 79 260 207 164 139 53 420)(10 78 261 206 165 138 54 419)(11 77 262 205 166 137 55 418)(12 76 263 204 167 136 56 417)(13 75 264 203 168 135 43 416)(14 74 265 202 155 134 44 415)(15 398 436 65 350 429 374 186)(16 397 437 64 337 428 375 185)(17 396 438 63 338 427 376 184)(18 395 439 62 339 426 377 183)(19 394 440 61 340 425 378 196)(20 393 441 60 341 424 365 195)(21 406 442 59 342 423 366 194)(22 405 443 58 343 422 367 193)(23 404 444 57 344 421 368 192)(24 403 445 70 345 434 369 191)(25 402 446 69 346 433 370 190)(26 401 447 68 347 432 371 189)(27 400 448 67 348 431 372 188)(28 399 435 66 349 430 373 187)(29 113 250 294 238 383 148 179)(30 126 251 293 225 382 149 178)(31 125 252 292 226 381 150 177)(32 124 239 291 227 380 151 176)(33 123 240 290 228 379 152 175)(34 122 241 289 229 392 153 174)(35 121 242 288 230 391 154 173)(36 120 243 287 231 390 141 172)(37 119 244 286 232 389 142 171)(38 118 245 285 233 388 143 170)(39 117 246 284 234 387 144 169)(40 116 247 283 235 386 145 182)(41 115 248 282 236 385 146 181)(42 114 249 281 237 384 147 180)(85 313 105 329 277 295 216 363)(86 312 106 328 278 308 217 362)(87 311 107 327 279 307 218 361)(88 310 108 326 280 306 219 360)(89 309 109 325 267 305 220 359)(90 322 110 324 268 304 221 358)(91 321 111 323 269 303 222 357)(92 320 112 336 270 302 223 356)(93 319 99 335 271 301 224 355)(94 318 100 334 272 300 211 354)(95 317 101 333 273 299 212 353)(96 316 102 332 274 298 213 352)(97 315 103 331 275 297 214 351)(98 314 104 330 276 296 215 364)
(1 16 8 23)(2 17 9 24)(3 18 10 25)(4 19 11 26)(5 20 12 27)(6 21 13 28)(7 22 14 15)(29 107 36 100)(30 108 37 101)(31 109 38 102)(32 110 39 103)(33 111 40 104)(34 112 41 105)(35 99 42 106)(43 435 50 442)(44 436 51 443)(45 437 52 444)(46 438 53 445)(47 439 54 446)(48 440 55 447)(49 441 56 448)(57 73 64 80)(58 74 65 81)(59 75 66 82)(60 76 67 83)(61 77 68 84)(62 78 69 71)(63 79 70 72)(85 241 92 248)(86 242 93 249)(87 243 94 250)(88 244 95 251)(89 245 96 252)(90 246 97 239)(91 247 98 240)(113 307 120 300)(114 308 121 301)(115 295 122 302)(116 296 123 303)(117 297 124 304)(118 298 125 305)(119 299 126 306)(127 193 134 186)(128 194 135 187)(129 195 136 188)(130 196 137 189)(131 183 138 190)(132 184 139 191)(133 185 140 192)(141 272 148 279)(142 273 149 280)(143 274 150 267)(144 275 151 268)(145 276 152 269)(146 277 153 270)(147 278 154 271)(155 350 162 343)(156 337 163 344)(157 338 164 345)(158 339 165 346)(159 340 166 347)(160 341 167 348)(161 342 168 349)(169 351 176 358)(170 352 177 359)(171 353 178 360)(172 354 179 361)(173 355 180 362)(174 356 181 363)(175 357 182 364)(197 393 204 400)(198 394 205 401)(199 395 206 402)(200 396 207 403)(201 397 208 404)(202 398 209 405)(203 399 210 406)(211 238 218 231)(212 225 219 232)(213 226 220 233)(214 227 221 234)(215 228 222 235)(216 229 223 236)(217 230 224 237)(253 376 260 369)(254 377 261 370)(255 378 262 371)(256 365 263 372)(257 366 264 373)(258 367 265 374)(259 368 266 375)(281 328 288 335)(282 329 289 336)(283 330 290 323)(284 331 291 324)(285 332 292 325)(286 333 293 326)(287 334 294 327)(309 388 316 381)(310 389 317 382)(311 390 318 383)(312 391 319 384)(313 392 320 385)(314 379 321 386)(315 380 322 387)(407 421 414 428)(408 422 415 429)(409 423 416 430)(410 424 417 431)(411 425 418 432)(412 426 419 433)(413 427 420 434)
G:=sub<Sym(448)| (1,281)(2,282)(3,283)(4,284)(5,285)(6,286)(7,287)(8,288)(9,289)(10,290)(11,291)(12,292)(13,293)(14,294)(15,327)(16,328)(17,329)(18,330)(19,331)(20,332)(21,333)(22,334)(23,335)(24,336)(25,323)(26,324)(27,325)(28,326)(29,134)(30,135)(31,136)(32,137)(33,138)(34,139)(35,140)(36,127)(37,128)(38,129)(39,130)(40,131)(41,132)(42,133)(43,126)(44,113)(45,114)(46,115)(47,116)(48,117)(49,118)(50,119)(51,120)(52,121)(53,122)(54,123)(55,124)(56,125)(57,224)(58,211)(59,212)(60,213)(61,214)(62,215)(63,216)(64,217)(65,218)(66,219)(67,220)(68,221)(69,222)(70,223)(71,235)(72,236)(73,237)(74,238)(75,225)(76,226)(77,227)(78,228)(79,229)(80,230)(81,231)(82,232)(83,233)(84,234)(85,427)(86,428)(87,429)(88,430)(89,431)(90,432)(91,433)(92,434)(93,421)(94,422)(95,423)(96,424)(97,425)(98,426)(99,192)(100,193)(101,194)(102,195)(103,196)(104,183)(105,184)(106,185)(107,186)(108,187)(109,188)(110,189)(111,190)(112,191)(141,209)(142,210)(143,197)(144,198)(145,199)(146,200)(147,201)(148,202)(149,203)(150,204)(151,205)(152,206)(153,207)(154,208)(155,179)(156,180)(157,181)(158,182)(159,169)(160,170)(161,171)(162,172)(163,173)(164,174)(165,175)(166,176)(167,177)(168,178)(239,418)(240,419)(241,420)(242,407)(243,408)(244,409)(245,410)(246,411)(247,412)(248,413)(249,414)(250,415)(251,416)(252,417)(253,385)(254,386)(255,387)(256,388)(257,389)(258,390)(259,391)(260,392)(261,379)(262,380)(263,381)(264,382)(265,383)(266,384)(267,400)(268,401)(269,402)(270,403)(271,404)(272,405)(273,406)(274,393)(275,394)(276,395)(277,396)(278,397)(279,398)(280,399)(295,438)(296,439)(297,440)(298,441)(299,442)(300,443)(301,444)(302,445)(303,446)(304,447)(305,448)(306,435)(307,436)(308,437)(309,372)(310,373)(311,374)(312,375)(313,376)(314,377)(315,378)(316,365)(317,366)(318,367)(319,368)(320,369)(321,370)(322,371)(337,362)(338,363)(339,364)(340,351)(341,352)(342,353)(343,354)(344,355)(345,356)(346,357)(347,358)(348,359)(349,360)(350,361), (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), (1,73,266,201,156,133,45,414)(2,72,253,200,157,132,46,413)(3,71,254,199,158,131,47,412)(4,84,255,198,159,130,48,411)(5,83,256,197,160,129,49,410)(6,82,257,210,161,128,50,409)(7,81,258,209,162,127,51,408)(8,80,259,208,163,140,52,407)(9,79,260,207,164,139,53,420)(10,78,261,206,165,138,54,419)(11,77,262,205,166,137,55,418)(12,76,263,204,167,136,56,417)(13,75,264,203,168,135,43,416)(14,74,265,202,155,134,44,415)(15,398,436,65,350,429,374,186)(16,397,437,64,337,428,375,185)(17,396,438,63,338,427,376,184)(18,395,439,62,339,426,377,183)(19,394,440,61,340,425,378,196)(20,393,441,60,341,424,365,195)(21,406,442,59,342,423,366,194)(22,405,443,58,343,422,367,193)(23,404,444,57,344,421,368,192)(24,403,445,70,345,434,369,191)(25,402,446,69,346,433,370,190)(26,401,447,68,347,432,371,189)(27,400,448,67,348,431,372,188)(28,399,435,66,349,430,373,187)(29,113,250,294,238,383,148,179)(30,126,251,293,225,382,149,178)(31,125,252,292,226,381,150,177)(32,124,239,291,227,380,151,176)(33,123,240,290,228,379,152,175)(34,122,241,289,229,392,153,174)(35,121,242,288,230,391,154,173)(36,120,243,287,231,390,141,172)(37,119,244,286,232,389,142,171)(38,118,245,285,233,388,143,170)(39,117,246,284,234,387,144,169)(40,116,247,283,235,386,145,182)(41,115,248,282,236,385,146,181)(42,114,249,281,237,384,147,180)(85,313,105,329,277,295,216,363)(86,312,106,328,278,308,217,362)(87,311,107,327,279,307,218,361)(88,310,108,326,280,306,219,360)(89,309,109,325,267,305,220,359)(90,322,110,324,268,304,221,358)(91,321,111,323,269,303,222,357)(92,320,112,336,270,302,223,356)(93,319,99,335,271,301,224,355)(94,318,100,334,272,300,211,354)(95,317,101,333,273,299,212,353)(96,316,102,332,274,298,213,352)(97,315,103,331,275,297,214,351)(98,314,104,330,276,296,215,364), (1,16,8,23)(2,17,9,24)(3,18,10,25)(4,19,11,26)(5,20,12,27)(6,21,13,28)(7,22,14,15)(29,107,36,100)(30,108,37,101)(31,109,38,102)(32,110,39,103)(33,111,40,104)(34,112,41,105)(35,99,42,106)(43,435,50,442)(44,436,51,443)(45,437,52,444)(46,438,53,445)(47,439,54,446)(48,440,55,447)(49,441,56,448)(57,73,64,80)(58,74,65,81)(59,75,66,82)(60,76,67,83)(61,77,68,84)(62,78,69,71)(63,79,70,72)(85,241,92,248)(86,242,93,249)(87,243,94,250)(88,244,95,251)(89,245,96,252)(90,246,97,239)(91,247,98,240)(113,307,120,300)(114,308,121,301)(115,295,122,302)(116,296,123,303)(117,297,124,304)(118,298,125,305)(119,299,126,306)(127,193,134,186)(128,194,135,187)(129,195,136,188)(130,196,137,189)(131,183,138,190)(132,184,139,191)(133,185,140,192)(141,272,148,279)(142,273,149,280)(143,274,150,267)(144,275,151,268)(145,276,152,269)(146,277,153,270)(147,278,154,271)(155,350,162,343)(156,337,163,344)(157,338,164,345)(158,339,165,346)(159,340,166,347)(160,341,167,348)(161,342,168,349)(169,351,176,358)(170,352,177,359)(171,353,178,360)(172,354,179,361)(173,355,180,362)(174,356,181,363)(175,357,182,364)(197,393,204,400)(198,394,205,401)(199,395,206,402)(200,396,207,403)(201,397,208,404)(202,398,209,405)(203,399,210,406)(211,238,218,231)(212,225,219,232)(213,226,220,233)(214,227,221,234)(215,228,222,235)(216,229,223,236)(217,230,224,237)(253,376,260,369)(254,377,261,370)(255,378,262,371)(256,365,263,372)(257,366,264,373)(258,367,265,374)(259,368,266,375)(281,328,288,335)(282,329,289,336)(283,330,290,323)(284,331,291,324)(285,332,292,325)(286,333,293,326)(287,334,294,327)(309,388,316,381)(310,389,317,382)(311,390,318,383)(312,391,319,384)(313,392,320,385)(314,379,321,386)(315,380,322,387)(407,421,414,428)(408,422,415,429)(409,423,416,430)(410,424,417,431)(411,425,418,432)(412,426,419,433)(413,427,420,434)>;
G:=Group( (1,281)(2,282)(3,283)(4,284)(5,285)(6,286)(7,287)(8,288)(9,289)(10,290)(11,291)(12,292)(13,293)(14,294)(15,327)(16,328)(17,329)(18,330)(19,331)(20,332)(21,333)(22,334)(23,335)(24,336)(25,323)(26,324)(27,325)(28,326)(29,134)(30,135)(31,136)(32,137)(33,138)(34,139)(35,140)(36,127)(37,128)(38,129)(39,130)(40,131)(41,132)(42,133)(43,126)(44,113)(45,114)(46,115)(47,116)(48,117)(49,118)(50,119)(51,120)(52,121)(53,122)(54,123)(55,124)(56,125)(57,224)(58,211)(59,212)(60,213)(61,214)(62,215)(63,216)(64,217)(65,218)(66,219)(67,220)(68,221)(69,222)(70,223)(71,235)(72,236)(73,237)(74,238)(75,225)(76,226)(77,227)(78,228)(79,229)(80,230)(81,231)(82,232)(83,233)(84,234)(85,427)(86,428)(87,429)(88,430)(89,431)(90,432)(91,433)(92,434)(93,421)(94,422)(95,423)(96,424)(97,425)(98,426)(99,192)(100,193)(101,194)(102,195)(103,196)(104,183)(105,184)(106,185)(107,186)(108,187)(109,188)(110,189)(111,190)(112,191)(141,209)(142,210)(143,197)(144,198)(145,199)(146,200)(147,201)(148,202)(149,203)(150,204)(151,205)(152,206)(153,207)(154,208)(155,179)(156,180)(157,181)(158,182)(159,169)(160,170)(161,171)(162,172)(163,173)(164,174)(165,175)(166,176)(167,177)(168,178)(239,418)(240,419)(241,420)(242,407)(243,408)(244,409)(245,410)(246,411)(247,412)(248,413)(249,414)(250,415)(251,416)(252,417)(253,385)(254,386)(255,387)(256,388)(257,389)(258,390)(259,391)(260,392)(261,379)(262,380)(263,381)(264,382)(265,383)(266,384)(267,400)(268,401)(269,402)(270,403)(271,404)(272,405)(273,406)(274,393)(275,394)(276,395)(277,396)(278,397)(279,398)(280,399)(295,438)(296,439)(297,440)(298,441)(299,442)(300,443)(301,444)(302,445)(303,446)(304,447)(305,448)(306,435)(307,436)(308,437)(309,372)(310,373)(311,374)(312,375)(313,376)(314,377)(315,378)(316,365)(317,366)(318,367)(319,368)(320,369)(321,370)(322,371)(337,362)(338,363)(339,364)(340,351)(341,352)(342,353)(343,354)(344,355)(345,356)(346,357)(347,358)(348,359)(349,360)(350,361), (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), (1,73,266,201,156,133,45,414)(2,72,253,200,157,132,46,413)(3,71,254,199,158,131,47,412)(4,84,255,198,159,130,48,411)(5,83,256,197,160,129,49,410)(6,82,257,210,161,128,50,409)(7,81,258,209,162,127,51,408)(8,80,259,208,163,140,52,407)(9,79,260,207,164,139,53,420)(10,78,261,206,165,138,54,419)(11,77,262,205,166,137,55,418)(12,76,263,204,167,136,56,417)(13,75,264,203,168,135,43,416)(14,74,265,202,155,134,44,415)(15,398,436,65,350,429,374,186)(16,397,437,64,337,428,375,185)(17,396,438,63,338,427,376,184)(18,395,439,62,339,426,377,183)(19,394,440,61,340,425,378,196)(20,393,441,60,341,424,365,195)(21,406,442,59,342,423,366,194)(22,405,443,58,343,422,367,193)(23,404,444,57,344,421,368,192)(24,403,445,70,345,434,369,191)(25,402,446,69,346,433,370,190)(26,401,447,68,347,432,371,189)(27,400,448,67,348,431,372,188)(28,399,435,66,349,430,373,187)(29,113,250,294,238,383,148,179)(30,126,251,293,225,382,149,178)(31,125,252,292,226,381,150,177)(32,124,239,291,227,380,151,176)(33,123,240,290,228,379,152,175)(34,122,241,289,229,392,153,174)(35,121,242,288,230,391,154,173)(36,120,243,287,231,390,141,172)(37,119,244,286,232,389,142,171)(38,118,245,285,233,388,143,170)(39,117,246,284,234,387,144,169)(40,116,247,283,235,386,145,182)(41,115,248,282,236,385,146,181)(42,114,249,281,237,384,147,180)(85,313,105,329,277,295,216,363)(86,312,106,328,278,308,217,362)(87,311,107,327,279,307,218,361)(88,310,108,326,280,306,219,360)(89,309,109,325,267,305,220,359)(90,322,110,324,268,304,221,358)(91,321,111,323,269,303,222,357)(92,320,112,336,270,302,223,356)(93,319,99,335,271,301,224,355)(94,318,100,334,272,300,211,354)(95,317,101,333,273,299,212,353)(96,316,102,332,274,298,213,352)(97,315,103,331,275,297,214,351)(98,314,104,330,276,296,215,364), (1,16,8,23)(2,17,9,24)(3,18,10,25)(4,19,11,26)(5,20,12,27)(6,21,13,28)(7,22,14,15)(29,107,36,100)(30,108,37,101)(31,109,38,102)(32,110,39,103)(33,111,40,104)(34,112,41,105)(35,99,42,106)(43,435,50,442)(44,436,51,443)(45,437,52,444)(46,438,53,445)(47,439,54,446)(48,440,55,447)(49,441,56,448)(57,73,64,80)(58,74,65,81)(59,75,66,82)(60,76,67,83)(61,77,68,84)(62,78,69,71)(63,79,70,72)(85,241,92,248)(86,242,93,249)(87,243,94,250)(88,244,95,251)(89,245,96,252)(90,246,97,239)(91,247,98,240)(113,307,120,300)(114,308,121,301)(115,295,122,302)(116,296,123,303)(117,297,124,304)(118,298,125,305)(119,299,126,306)(127,193,134,186)(128,194,135,187)(129,195,136,188)(130,196,137,189)(131,183,138,190)(132,184,139,191)(133,185,140,192)(141,272,148,279)(142,273,149,280)(143,274,150,267)(144,275,151,268)(145,276,152,269)(146,277,153,270)(147,278,154,271)(155,350,162,343)(156,337,163,344)(157,338,164,345)(158,339,165,346)(159,340,166,347)(160,341,167,348)(161,342,168,349)(169,351,176,358)(170,352,177,359)(171,353,178,360)(172,354,179,361)(173,355,180,362)(174,356,181,363)(175,357,182,364)(197,393,204,400)(198,394,205,401)(199,395,206,402)(200,396,207,403)(201,397,208,404)(202,398,209,405)(203,399,210,406)(211,238,218,231)(212,225,219,232)(213,226,220,233)(214,227,221,234)(215,228,222,235)(216,229,223,236)(217,230,224,237)(253,376,260,369)(254,377,261,370)(255,378,262,371)(256,365,263,372)(257,366,264,373)(258,367,265,374)(259,368,266,375)(281,328,288,335)(282,329,289,336)(283,330,290,323)(284,331,291,324)(285,332,292,325)(286,333,293,326)(287,334,294,327)(309,388,316,381)(310,389,317,382)(311,390,318,383)(312,391,319,384)(313,392,320,385)(314,379,321,386)(315,380,322,387)(407,421,414,428)(408,422,415,429)(409,423,416,430)(410,424,417,431)(411,425,418,432)(412,426,419,433)(413,427,420,434) );
G=PermutationGroup([(1,281),(2,282),(3,283),(4,284),(5,285),(6,286),(7,287),(8,288),(9,289),(10,290),(11,291),(12,292),(13,293),(14,294),(15,327),(16,328),(17,329),(18,330),(19,331),(20,332),(21,333),(22,334),(23,335),(24,336),(25,323),(26,324),(27,325),(28,326),(29,134),(30,135),(31,136),(32,137),(33,138),(34,139),(35,140),(36,127),(37,128),(38,129),(39,130),(40,131),(41,132),(42,133),(43,126),(44,113),(45,114),(46,115),(47,116),(48,117),(49,118),(50,119),(51,120),(52,121),(53,122),(54,123),(55,124),(56,125),(57,224),(58,211),(59,212),(60,213),(61,214),(62,215),(63,216),(64,217),(65,218),(66,219),(67,220),(68,221),(69,222),(70,223),(71,235),(72,236),(73,237),(74,238),(75,225),(76,226),(77,227),(78,228),(79,229),(80,230),(81,231),(82,232),(83,233),(84,234),(85,427),(86,428),(87,429),(88,430),(89,431),(90,432),(91,433),(92,434),(93,421),(94,422),(95,423),(96,424),(97,425),(98,426),(99,192),(100,193),(101,194),(102,195),(103,196),(104,183),(105,184),(106,185),(107,186),(108,187),(109,188),(110,189),(111,190),(112,191),(141,209),(142,210),(143,197),(144,198),(145,199),(146,200),(147,201),(148,202),(149,203),(150,204),(151,205),(152,206),(153,207),(154,208),(155,179),(156,180),(157,181),(158,182),(159,169),(160,170),(161,171),(162,172),(163,173),(164,174),(165,175),(166,176),(167,177),(168,178),(239,418),(240,419),(241,420),(242,407),(243,408),(244,409),(245,410),(246,411),(247,412),(248,413),(249,414),(250,415),(251,416),(252,417),(253,385),(254,386),(255,387),(256,388),(257,389),(258,390),(259,391),(260,392),(261,379),(262,380),(263,381),(264,382),(265,383),(266,384),(267,400),(268,401),(269,402),(270,403),(271,404),(272,405),(273,406),(274,393),(275,394),(276,395),(277,396),(278,397),(279,398),(280,399),(295,438),(296,439),(297,440),(298,441),(299,442),(300,443),(301,444),(302,445),(303,446),(304,447),(305,448),(306,435),(307,436),(308,437),(309,372),(310,373),(311,374),(312,375),(313,376),(314,377),(315,378),(316,365),(317,366),(318,367),(319,368),(320,369),(321,370),(322,371),(337,362),(338,363),(339,364),(340,351),(341,352),(342,353),(343,354),(344,355),(345,356),(346,357),(347,358),(348,359),(349,360),(350,361)], [(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)], [(1,73,266,201,156,133,45,414),(2,72,253,200,157,132,46,413),(3,71,254,199,158,131,47,412),(4,84,255,198,159,130,48,411),(5,83,256,197,160,129,49,410),(6,82,257,210,161,128,50,409),(7,81,258,209,162,127,51,408),(8,80,259,208,163,140,52,407),(9,79,260,207,164,139,53,420),(10,78,261,206,165,138,54,419),(11,77,262,205,166,137,55,418),(12,76,263,204,167,136,56,417),(13,75,264,203,168,135,43,416),(14,74,265,202,155,134,44,415),(15,398,436,65,350,429,374,186),(16,397,437,64,337,428,375,185),(17,396,438,63,338,427,376,184),(18,395,439,62,339,426,377,183),(19,394,440,61,340,425,378,196),(20,393,441,60,341,424,365,195),(21,406,442,59,342,423,366,194),(22,405,443,58,343,422,367,193),(23,404,444,57,344,421,368,192),(24,403,445,70,345,434,369,191),(25,402,446,69,346,433,370,190),(26,401,447,68,347,432,371,189),(27,400,448,67,348,431,372,188),(28,399,435,66,349,430,373,187),(29,113,250,294,238,383,148,179),(30,126,251,293,225,382,149,178),(31,125,252,292,226,381,150,177),(32,124,239,291,227,380,151,176),(33,123,240,290,228,379,152,175),(34,122,241,289,229,392,153,174),(35,121,242,288,230,391,154,173),(36,120,243,287,231,390,141,172),(37,119,244,286,232,389,142,171),(38,118,245,285,233,388,143,170),(39,117,246,284,234,387,144,169),(40,116,247,283,235,386,145,182),(41,115,248,282,236,385,146,181),(42,114,249,281,237,384,147,180),(85,313,105,329,277,295,216,363),(86,312,106,328,278,308,217,362),(87,311,107,327,279,307,218,361),(88,310,108,326,280,306,219,360),(89,309,109,325,267,305,220,359),(90,322,110,324,268,304,221,358),(91,321,111,323,269,303,222,357),(92,320,112,336,270,302,223,356),(93,319,99,335,271,301,224,355),(94,318,100,334,272,300,211,354),(95,317,101,333,273,299,212,353),(96,316,102,332,274,298,213,352),(97,315,103,331,275,297,214,351),(98,314,104,330,276,296,215,364)], [(1,16,8,23),(2,17,9,24),(3,18,10,25),(4,19,11,26),(5,20,12,27),(6,21,13,28),(7,22,14,15),(29,107,36,100),(30,108,37,101),(31,109,38,102),(32,110,39,103),(33,111,40,104),(34,112,41,105),(35,99,42,106),(43,435,50,442),(44,436,51,443),(45,437,52,444),(46,438,53,445),(47,439,54,446),(48,440,55,447),(49,441,56,448),(57,73,64,80),(58,74,65,81),(59,75,66,82),(60,76,67,83),(61,77,68,84),(62,78,69,71),(63,79,70,72),(85,241,92,248),(86,242,93,249),(87,243,94,250),(88,244,95,251),(89,245,96,252),(90,246,97,239),(91,247,98,240),(113,307,120,300),(114,308,121,301),(115,295,122,302),(116,296,123,303),(117,297,124,304),(118,298,125,305),(119,299,126,306),(127,193,134,186),(128,194,135,187),(129,195,136,188),(130,196,137,189),(131,183,138,190),(132,184,139,191),(133,185,140,192),(141,272,148,279),(142,273,149,280),(143,274,150,267),(144,275,151,268),(145,276,152,269),(146,277,153,270),(147,278,154,271),(155,350,162,343),(156,337,163,344),(157,338,164,345),(158,339,165,346),(159,340,166,347),(160,341,167,348),(161,342,168,349),(169,351,176,358),(170,352,177,359),(171,353,178,360),(172,354,179,361),(173,355,180,362),(174,356,181,363),(175,357,182,364),(197,393,204,400),(198,394,205,401),(199,395,206,402),(200,396,207,403),(201,397,208,404),(202,398,209,405),(203,399,210,406),(211,238,218,231),(212,225,219,232),(213,226,220,233),(214,227,221,234),(215,228,222,235),(216,229,223,236),(217,230,224,237),(253,376,260,369),(254,377,261,370),(255,378,262,371),(256,365,263,372),(257,366,264,373),(258,367,265,374),(259,368,266,375),(281,328,288,335),(282,329,289,336),(283,330,290,323),(284,331,291,324),(285,332,292,325),(286,333,293,326),(287,334,294,327),(309,388,316,381),(310,389,317,382),(311,390,318,383),(312,391,319,384),(313,392,320,385),(314,379,321,386),(315,380,322,387),(407,421,414,428),(408,422,415,429),(409,423,416,430),(410,424,417,431),(411,425,418,432),(412,426,419,433),(413,427,420,434)])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | + | + | + | - | - | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | Q8 | D4 | D7 | SD16 | D14 | D14 | Dic14 | C4×D7 | C7⋊D4 | C7⋊D4 | D4.D7 | Q8⋊D7 |
| kernel | C2×C14.SD16 | C14.SD16 | C22×C7⋊C8 | C2×C4⋊Dic7 | C14×C4⋊C4 | C2×C7⋊C8 | C2×C28 | C2×C28 | C22×C14 | C2×C4⋊C4 | C2×C14 | C4⋊C4 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C23 | C22 | C22 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 1 | 2 | 1 | 3 | 8 | 6 | 3 | 12 | 12 | 6 | 6 | 6 | 6 |
Matrix representation of C2×C14.SD16 ►in GL5(𝔽113)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 112 |
| 112 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 104 | 88 |
| 0 | 0 | 0 | 104 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 13 | 100 | 0 | 0 |
| 0 | 13 | 13 | 0 | 0 |
| 0 | 0 | 0 | 58 | 93 |
| 0 | 0 | 0 | 27 | 55 |
| 98 | 0 | 0 | 0 | 0 |
| 0 | 14 | 101 | 0 | 0 |
| 0 | 101 | 99 | 0 | 0 |
| 0 | 0 | 0 | 58 | 46 |
| 0 | 0 | 0 | 3 | 55 |
G:=sub<GL(5,GF(113))| [1,0,0,0,0,0,112,0,0,0,0,0,112,0,0,0,0,0,112,0,0,0,0,0,112],[112,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,104,104,0,0,0,88,0],[1,0,0,0,0,0,13,13,0,0,0,100,13,0,0,0,0,0,58,27,0,0,0,93,55],[98,0,0,0,0,0,14,101,0,0,0,101,99,0,0,0,0,0,58,3,0,0,0,46,55] >;
C2×C14.SD16 in GAP, Magma, Sage, TeX
C_2\times C_{14}.{\rm SD}_{16} % in TeX
G:=Group("C2xC14.SD16"); // GroupNames label
G:=SmallGroup(448,497);
// by ID
G=gap.SmallGroup(448,497);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,1094,58,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^14=c^8=1,d^2=b^7,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=c^3>;
// generators/relations