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G = C13×C4⋊C8order 416 = 25·13

Direct product of C13 and C4⋊C8

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

Aliases: C13×C4⋊C8, C4⋊C104, C525C8, C52.67D4, C52.12Q8, C42.2C26, C26.14M4(2), (C2×C4).4C52, (C4×C52).8C2, (C2×C8).2C26, C4.4(Q8×C13), C26.21(C2×C8), (C2×C52).24C4, (C2×C104).4C2, C2.2(C2×C104), C4.18(D4×C13), C26.18(C4⋊C4), C22.10(C2×C52), C2.3(C13×M4(2)), (C2×C52).136C22, C2.2(C13×C4⋊C4), (C2×C4).32(C2×C26), (C2×C26).59(C2×C4), SmallGroup(416,55)

Series: Derived Chief Lower central Upper central

C1C2 — C13×C4⋊C8
C1C2C4C2×C4C2×C52C2×C104 — C13×C4⋊C8
C1C2 — C13×C4⋊C8
C1C2×C52 — C13×C4⋊C8

Generators and relations for C13×C4⋊C8
 G = < a,b,c | a13=b4=c8=1, ab=ba, ac=ca, cbc-1=b-1 >

2C4
2C8
2C8
2C52
2C104
2C104

Smallest permutation representation of C13×C4⋊C8
Regular action on 416 points
Generators in S416
(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)
(1 288 34 277)(2 289 35 278)(3 290 36 279)(4 291 37 280)(5 292 38 281)(6 293 39 282)(7 294 27 283)(8 295 28 284)(9 296 29 285)(10 297 30 286)(11 298 31 274)(12 299 32 275)(13 287 33 276)(14 185 345 46)(15 186 346 47)(16 187 347 48)(17 188 348 49)(18 189 349 50)(19 190 350 51)(20 191 351 52)(21 192 339 40)(22 193 340 41)(23 194 341 42)(24 195 342 43)(25 183 343 44)(26 184 344 45)(53 409 208 253)(54 410 196 254)(55 411 197 255)(56 412 198 256)(57 413 199 257)(58 414 200 258)(59 415 201 259)(60 416 202 260)(61 404 203 248)(62 405 204 249)(63 406 205 250)(64 407 206 251)(65 408 207 252)(66 176 327 325)(67 177 328 313)(68 178 329 314)(69 179 330 315)(70 180 331 316)(71 181 332 317)(72 182 333 318)(73 170 334 319)(74 171 335 320)(75 172 336 321)(76 173 337 322)(77 174 338 323)(78 175 326 324)(79 361 369 101)(80 362 370 102)(81 363 371 103)(82 364 372 104)(83 352 373 92)(84 353 374 93)(85 354 375 94)(86 355 376 95)(87 356 377 96)(88 357 365 97)(89 358 366 98)(90 359 367 99)(91 360 368 100)(105 234 221 166)(106 222 209 167)(107 223 210 168)(108 224 211 169)(109 225 212 157)(110 226 213 158)(111 227 214 159)(112 228 215 160)(113 229 216 161)(114 230 217 162)(115 231 218 163)(116 232 219 164)(117 233 220 165)(118 394 308 150)(119 395 309 151)(120 396 310 152)(121 397 311 153)(122 398 312 154)(123 399 300 155)(124 400 301 156)(125 401 302 144)(126 402 303 145)(127 403 304 146)(128 391 305 147)(129 392 306 148)(130 393 307 149)(131 263 386 241)(132 264 387 242)(133 265 388 243)(134 266 389 244)(135 267 390 245)(136 268 378 246)(137 269 379 247)(138 270 380 235)(139 271 381 236)(140 272 382 237)(141 273 383 238)(142 261 384 239)(143 262 385 240)
(1 231 72 242 95 348 127 256)(2 232 73 243 96 349 128 257)(3 233 74 244 97 350 129 258)(4 234 75 245 98 351 130 259)(5 222 76 246 99 339 118 260)(6 223 77 247 100 340 119 248)(7 224 78 235 101 341 120 249)(8 225 66 236 102 342 121 250)(9 226 67 237 103 343 122 251)(10 227 68 238 104 344 123 252)(11 228 69 239 92 345 124 253)(12 229 70 240 93 346 125 254)(13 230 71 241 94 347 126 255)(14 301 409 31 160 330 261 352)(15 302 410 32 161 331 262 353)(16 303 411 33 162 332 263 354)(17 304 412 34 163 333 264 355)(18 305 413 35 164 334 265 356)(19 306 414 36 165 335 266 357)(20 307 415 37 166 336 267 358)(21 308 416 38 167 337 268 359)(22 309 404 39 168 338 269 360)(23 310 405 27 169 326 270 361)(24 311 406 28 157 327 271 362)(25 312 407 29 158 328 272 363)(26 300 408 30 159 329 273 364)(40 150 60 281 209 322 136 367)(41 151 61 282 210 323 137 368)(42 152 62 283 211 324 138 369)(43 153 63 284 212 325 139 370)(44 154 64 285 213 313 140 371)(45 155 65 286 214 314 141 372)(46 156 53 274 215 315 142 373)(47 144 54 275 216 316 143 374)(48 145 55 276 217 317 131 375)(49 146 56 277 218 318 132 376)(50 147 57 278 219 319 133 377)(51 148 58 279 220 320 134 365)(52 149 59 280 221 321 135 366)(79 194 396 204 294 108 175 380)(80 195 397 205 295 109 176 381)(81 183 398 206 296 110 177 382)(82 184 399 207 297 111 178 383)(83 185 400 208 298 112 179 384)(84 186 401 196 299 113 180 385)(85 187 402 197 287 114 181 386)(86 188 403 198 288 115 182 387)(87 189 391 199 289 116 170 388)(88 190 392 200 290 117 171 389)(89 191 393 201 291 105 172 390)(90 192 394 202 292 106 173 378)(91 193 395 203 293 107 174 379)

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

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

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

260 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H8A···8H13A···13L26A···26AJ52A···52AV52AW···52CR104A···104CR
order1222444444448···813···1326···2652···5252···52104···104
size1111111122222···21···11···11···12···22···2

260 irreducible representations

dim1111111111222222
type++++-
imageC1C2C2C4C8C13C26C26C52C104D4Q8M4(2)D4×C13Q8×C13C13×M4(2)
kernelC13×C4⋊C8C4×C52C2×C104C2×C52C52C4⋊C8C42C2×C8C2×C4C4C52C52C26C4C4C2
# reps112481212244896112121224

Matrix representation of C13×C4⋊C8 in GL3(𝔽313) generated by

100
0270
0027
,
31200
01972
01116
,
12500
0185102
0125128
G:=sub<GL(3,GF(313))| [1,0,0,0,27,0,0,0,27],[312,0,0,0,197,1,0,2,116],[125,0,0,0,185,125,0,102,128] >;

C13×C4⋊C8 in GAP, Magma, Sage, TeX

C_{13}\times C_4\rtimes C_8
% in TeX

G:=Group("C13xC4:C8");
// GroupNames label

G:=SmallGroup(416,55);
// by ID

G=gap.SmallGroup(416,55);
# by ID

G:=PCGroup([6,-2,-2,-13,-2,-2,-2,624,649,319,88]);
// Polycyclic

G:=Group<a,b,c|a^13=b^4=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C13×C4⋊C8 in TeX

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