direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C4×C13⋊2C8, C52⋊4C8, C26.6C42, C42.6D13, C13⋊3(C4×C8), (C4×C52).6C2, C52.44(C2×C4), C26.15(C2×C8), (C2×C52).21C4, C4.18(C4×D13), (C2×C4).87D26, C2.1(C4×Dic13), (C2×C4).7Dic13, (C2×C52).101C22, C22.6(C2×Dic13), C2.1(C2×C13⋊2C8), (C2×C26).44(C2×C4), (C2×C13⋊2C8).13C2, SmallGroup(416,9)
Series: Derived ►Chief ►Lower central ►Upper central
| C13 — C4×C13⋊2C8 |
Generators and relations for C4×C13⋊2C8
G = < a,b,c | a4=b13=c8=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C4×C13⋊2C8
►Regular action on 416 points
Generators in S416
(1 196 40 157)(2 197 41 158)(3 198 42 159)(4 199 43 160)(5 200 44 161)(6 201 45 162)(7 202 46 163)(8 203 47 164)(9 204 48 165)(10 205 49 166)(11 206 50 167)(12 207 51 168)(13 208 52 169)(14 183 27 170)(15 184 28 171)(16 185 29 172)(17 186 30 173)(18 187 31 174)(19 188 32 175)(20 189 33 176)(21 190 34 177)(22 191 35 178)(23 192 36 179)(24 193 37 180)(25 194 38 181)(26 195 39 182)(53 131 92 118)(54 132 93 119)(55 133 94 120)(56 134 95 121)(57 135 96 122)(58 136 97 123)(59 137 98 124)(60 138 99 125)(61 139 100 126)(62 140 101 127)(63 141 102 128)(64 142 103 129)(65 143 104 130)(66 144 79 105)(67 145 80 106)(68 146 81 107)(69 147 82 108)(70 148 83 109)(71 149 84 110)(72 150 85 111)(73 151 86 112)(74 152 87 113)(75 153 88 114)(76 154 89 115)(77 155 90 116)(78 156 91 117)(209 410 250 374)(210 411 251 375)(211 412 252 376)(212 413 253 377)(213 414 254 365)(214 415 255 366)(215 416 256 367)(216 404 257 368)(217 405 258 369)(218 406 259 370)(219 407 260 371)(220 408 248 372)(221 409 249 373)(222 400 244 380)(223 401 245 381)(224 402 246 382)(225 403 247 383)(226 391 235 384)(227 392 236 385)(228 393 237 386)(229 394 238 387)(230 395 239 388)(231 396 240 389)(232 397 241 390)(233 398 242 378)(234 399 243 379)(261 349 300 329)(262 350 301 330)(263 351 302 331)(264 339 303 332)(265 340 304 333)(266 341 305 334)(267 342 306 335)(268 343 307 336)(269 344 308 337)(270 345 309 338)(271 346 310 326)(272 347 311 327)(273 348 312 328)(274 364 299 314)(275 352 287 315)(276 353 288 316)(277 354 289 317)(278 355 290 318)(279 356 291 319)(280 357 292 320)(281 358 293 321)(282 359 294 322)(283 360 295 323)(284 361 296 324)(285 362 297 325)(286 363 298 313)
(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)
(1 277 66 232 14 273 53 211)(2 276 67 231 15 272 54 210)(3 275 68 230 16 271 55 209)(4 274 69 229 17 270 56 221)(5 286 70 228 18 269 57 220)(6 285 71 227 19 268 58 219)(7 284 72 226 20 267 59 218)(8 283 73 225 21 266 60 217)(9 282 74 224 22 265 61 216)(10 281 75 223 23 264 62 215)(11 280 76 222 24 263 63 214)(12 279 77 234 25 262 64 213)(13 278 78 233 26 261 65 212)(27 312 92 252 40 289 79 241)(28 311 93 251 41 288 80 240)(29 310 94 250 42 287 81 239)(30 309 95 249 43 299 82 238)(31 308 96 248 44 298 83 237)(32 307 97 260 45 297 84 236)(33 306 98 259 46 296 85 235)(34 305 99 258 47 295 86 247)(35 304 100 257 48 294 87 246)(36 303 101 256 49 293 88 245)(37 302 102 255 50 292 89 244)(38 301 103 254 51 291 90 243)(39 300 104 253 52 290 91 242)(105 390 170 328 118 376 157 317)(106 389 171 327 119 375 158 316)(107 388 172 326 120 374 159 315)(108 387 173 338 121 373 160 314)(109 386 174 337 122 372 161 313)(110 385 175 336 123 371 162 325)(111 384 176 335 124 370 163 324)(112 383 177 334 125 369 164 323)(113 382 178 333 126 368 165 322)(114 381 179 332 127 367 166 321)(115 380 180 331 128 366 167 320)(116 379 181 330 129 365 168 319)(117 378 182 329 130 377 169 318)(131 412 196 354 144 397 183 348)(132 411 197 353 145 396 184 347)(133 410 198 352 146 395 185 346)(134 409 199 364 147 394 186 345)(135 408 200 363 148 393 187 344)(136 407 201 362 149 392 188 343)(137 406 202 361 150 391 189 342)(138 405 203 360 151 403 190 341)(139 404 204 359 152 402 191 340)(140 416 205 358 153 401 192 339)(141 415 206 357 154 400 193 351)(142 414 207 356 155 399 194 350)(143 413 208 355 156 398 195 349)
G:=sub<Sym(416)| (1,196,40,157)(2,197,41,158)(3,198,42,159)(4,199,43,160)(5,200,44,161)(6,201,45,162)(7,202,46,163)(8,203,47,164)(9,204,48,165)(10,205,49,166)(11,206,50,167)(12,207,51,168)(13,208,52,169)(14,183,27,170)(15,184,28,171)(16,185,29,172)(17,186,30,173)(18,187,31,174)(19,188,32,175)(20,189,33,176)(21,190,34,177)(22,191,35,178)(23,192,36,179)(24,193,37,180)(25,194,38,181)(26,195,39,182)(53,131,92,118)(54,132,93,119)(55,133,94,120)(56,134,95,121)(57,135,96,122)(58,136,97,123)(59,137,98,124)(60,138,99,125)(61,139,100,126)(62,140,101,127)(63,141,102,128)(64,142,103,129)(65,143,104,130)(66,144,79,105)(67,145,80,106)(68,146,81,107)(69,147,82,108)(70,148,83,109)(71,149,84,110)(72,150,85,111)(73,151,86,112)(74,152,87,113)(75,153,88,114)(76,154,89,115)(77,155,90,116)(78,156,91,117)(209,410,250,374)(210,411,251,375)(211,412,252,376)(212,413,253,377)(213,414,254,365)(214,415,255,366)(215,416,256,367)(216,404,257,368)(217,405,258,369)(218,406,259,370)(219,407,260,371)(220,408,248,372)(221,409,249,373)(222,400,244,380)(223,401,245,381)(224,402,246,382)(225,403,247,383)(226,391,235,384)(227,392,236,385)(228,393,237,386)(229,394,238,387)(230,395,239,388)(231,396,240,389)(232,397,241,390)(233,398,242,378)(234,399,243,379)(261,349,300,329)(262,350,301,330)(263,351,302,331)(264,339,303,332)(265,340,304,333)(266,341,305,334)(267,342,306,335)(268,343,307,336)(269,344,308,337)(270,345,309,338)(271,346,310,326)(272,347,311,327)(273,348,312,328)(274,364,299,314)(275,352,287,315)(276,353,288,316)(277,354,289,317)(278,355,290,318)(279,356,291,319)(280,357,292,320)(281,358,293,321)(282,359,294,322)(283,360,295,323)(284,361,296,324)(285,362,297,325)(286,363,298,313), (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), (1,277,66,232,14,273,53,211)(2,276,67,231,15,272,54,210)(3,275,68,230,16,271,55,209)(4,274,69,229,17,270,56,221)(5,286,70,228,18,269,57,220)(6,285,71,227,19,268,58,219)(7,284,72,226,20,267,59,218)(8,283,73,225,21,266,60,217)(9,282,74,224,22,265,61,216)(10,281,75,223,23,264,62,215)(11,280,76,222,24,263,63,214)(12,279,77,234,25,262,64,213)(13,278,78,233,26,261,65,212)(27,312,92,252,40,289,79,241)(28,311,93,251,41,288,80,240)(29,310,94,250,42,287,81,239)(30,309,95,249,43,299,82,238)(31,308,96,248,44,298,83,237)(32,307,97,260,45,297,84,236)(33,306,98,259,46,296,85,235)(34,305,99,258,47,295,86,247)(35,304,100,257,48,294,87,246)(36,303,101,256,49,293,88,245)(37,302,102,255,50,292,89,244)(38,301,103,254,51,291,90,243)(39,300,104,253,52,290,91,242)(105,390,170,328,118,376,157,317)(106,389,171,327,119,375,158,316)(107,388,172,326,120,374,159,315)(108,387,173,338,121,373,160,314)(109,386,174,337,122,372,161,313)(110,385,175,336,123,371,162,325)(111,384,176,335,124,370,163,324)(112,383,177,334,125,369,164,323)(113,382,178,333,126,368,165,322)(114,381,179,332,127,367,166,321)(115,380,180,331,128,366,167,320)(116,379,181,330,129,365,168,319)(117,378,182,329,130,377,169,318)(131,412,196,354,144,397,183,348)(132,411,197,353,145,396,184,347)(133,410,198,352,146,395,185,346)(134,409,199,364,147,394,186,345)(135,408,200,363,148,393,187,344)(136,407,201,362,149,392,188,343)(137,406,202,361,150,391,189,342)(138,405,203,360,151,403,190,341)(139,404,204,359,152,402,191,340)(140,416,205,358,153,401,192,339)(141,415,206,357,154,400,193,351)(142,414,207,356,155,399,194,350)(143,413,208,355,156,398,195,349)>;
G:=Group( (1,196,40,157)(2,197,41,158)(3,198,42,159)(4,199,43,160)(5,200,44,161)(6,201,45,162)(7,202,46,163)(8,203,47,164)(9,204,48,165)(10,205,49,166)(11,206,50,167)(12,207,51,168)(13,208,52,169)(14,183,27,170)(15,184,28,171)(16,185,29,172)(17,186,30,173)(18,187,31,174)(19,188,32,175)(20,189,33,176)(21,190,34,177)(22,191,35,178)(23,192,36,179)(24,193,37,180)(25,194,38,181)(26,195,39,182)(53,131,92,118)(54,132,93,119)(55,133,94,120)(56,134,95,121)(57,135,96,122)(58,136,97,123)(59,137,98,124)(60,138,99,125)(61,139,100,126)(62,140,101,127)(63,141,102,128)(64,142,103,129)(65,143,104,130)(66,144,79,105)(67,145,80,106)(68,146,81,107)(69,147,82,108)(70,148,83,109)(71,149,84,110)(72,150,85,111)(73,151,86,112)(74,152,87,113)(75,153,88,114)(76,154,89,115)(77,155,90,116)(78,156,91,117)(209,410,250,374)(210,411,251,375)(211,412,252,376)(212,413,253,377)(213,414,254,365)(214,415,255,366)(215,416,256,367)(216,404,257,368)(217,405,258,369)(218,406,259,370)(219,407,260,371)(220,408,248,372)(221,409,249,373)(222,400,244,380)(223,401,245,381)(224,402,246,382)(225,403,247,383)(226,391,235,384)(227,392,236,385)(228,393,237,386)(229,394,238,387)(230,395,239,388)(231,396,240,389)(232,397,241,390)(233,398,242,378)(234,399,243,379)(261,349,300,329)(262,350,301,330)(263,351,302,331)(264,339,303,332)(265,340,304,333)(266,341,305,334)(267,342,306,335)(268,343,307,336)(269,344,308,337)(270,345,309,338)(271,346,310,326)(272,347,311,327)(273,348,312,328)(274,364,299,314)(275,352,287,315)(276,353,288,316)(277,354,289,317)(278,355,290,318)(279,356,291,319)(280,357,292,320)(281,358,293,321)(282,359,294,322)(283,360,295,323)(284,361,296,324)(285,362,297,325)(286,363,298,313), (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), (1,277,66,232,14,273,53,211)(2,276,67,231,15,272,54,210)(3,275,68,230,16,271,55,209)(4,274,69,229,17,270,56,221)(5,286,70,228,18,269,57,220)(6,285,71,227,19,268,58,219)(7,284,72,226,20,267,59,218)(8,283,73,225,21,266,60,217)(9,282,74,224,22,265,61,216)(10,281,75,223,23,264,62,215)(11,280,76,222,24,263,63,214)(12,279,77,234,25,262,64,213)(13,278,78,233,26,261,65,212)(27,312,92,252,40,289,79,241)(28,311,93,251,41,288,80,240)(29,310,94,250,42,287,81,239)(30,309,95,249,43,299,82,238)(31,308,96,248,44,298,83,237)(32,307,97,260,45,297,84,236)(33,306,98,259,46,296,85,235)(34,305,99,258,47,295,86,247)(35,304,100,257,48,294,87,246)(36,303,101,256,49,293,88,245)(37,302,102,255,50,292,89,244)(38,301,103,254,51,291,90,243)(39,300,104,253,52,290,91,242)(105,390,170,328,118,376,157,317)(106,389,171,327,119,375,158,316)(107,388,172,326,120,374,159,315)(108,387,173,338,121,373,160,314)(109,386,174,337,122,372,161,313)(110,385,175,336,123,371,162,325)(111,384,176,335,124,370,163,324)(112,383,177,334,125,369,164,323)(113,382,178,333,126,368,165,322)(114,381,179,332,127,367,166,321)(115,380,180,331,128,366,167,320)(116,379,181,330,129,365,168,319)(117,378,182,329,130,377,169,318)(131,412,196,354,144,397,183,348)(132,411,197,353,145,396,184,347)(133,410,198,352,146,395,185,346)(134,409,199,364,147,394,186,345)(135,408,200,363,148,393,187,344)(136,407,201,362,149,392,188,343)(137,406,202,361,150,391,189,342)(138,405,203,360,151,403,190,341)(139,404,204,359,152,402,191,340)(140,416,205,358,153,401,192,339)(141,415,206,357,154,400,193,351)(142,414,207,356,155,399,194,350)(143,413,208,355,156,398,195,349) );
G=PermutationGroup([[(1,196,40,157),(2,197,41,158),(3,198,42,159),(4,199,43,160),(5,200,44,161),(6,201,45,162),(7,202,46,163),(8,203,47,164),(9,204,48,165),(10,205,49,166),(11,206,50,167),(12,207,51,168),(13,208,52,169),(14,183,27,170),(15,184,28,171),(16,185,29,172),(17,186,30,173),(18,187,31,174),(19,188,32,175),(20,189,33,176),(21,190,34,177),(22,191,35,178),(23,192,36,179),(24,193,37,180),(25,194,38,181),(26,195,39,182),(53,131,92,118),(54,132,93,119),(55,133,94,120),(56,134,95,121),(57,135,96,122),(58,136,97,123),(59,137,98,124),(60,138,99,125),(61,139,100,126),(62,140,101,127),(63,141,102,128),(64,142,103,129),(65,143,104,130),(66,144,79,105),(67,145,80,106),(68,146,81,107),(69,147,82,108),(70,148,83,109),(71,149,84,110),(72,150,85,111),(73,151,86,112),(74,152,87,113),(75,153,88,114),(76,154,89,115),(77,155,90,116),(78,156,91,117),(209,410,250,374),(210,411,251,375),(211,412,252,376),(212,413,253,377),(213,414,254,365),(214,415,255,366),(215,416,256,367),(216,404,257,368),(217,405,258,369),(218,406,259,370),(219,407,260,371),(220,408,248,372),(221,409,249,373),(222,400,244,380),(223,401,245,381),(224,402,246,382),(225,403,247,383),(226,391,235,384),(227,392,236,385),(228,393,237,386),(229,394,238,387),(230,395,239,388),(231,396,240,389),(232,397,241,390),(233,398,242,378),(234,399,243,379),(261,349,300,329),(262,350,301,330),(263,351,302,331),(264,339,303,332),(265,340,304,333),(266,341,305,334),(267,342,306,335),(268,343,307,336),(269,344,308,337),(270,345,309,338),(271,346,310,326),(272,347,311,327),(273,348,312,328),(274,364,299,314),(275,352,287,315),(276,353,288,316),(277,354,289,317),(278,355,290,318),(279,356,291,319),(280,357,292,320),(281,358,293,321),(282,359,294,322),(283,360,295,323),(284,361,296,324),(285,362,297,325),(286,363,298,313)], [(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)], [(1,277,66,232,14,273,53,211),(2,276,67,231,15,272,54,210),(3,275,68,230,16,271,55,209),(4,274,69,229,17,270,56,221),(5,286,70,228,18,269,57,220),(6,285,71,227,19,268,58,219),(7,284,72,226,20,267,59,218),(8,283,73,225,21,266,60,217),(9,282,74,224,22,265,61,216),(10,281,75,223,23,264,62,215),(11,280,76,222,24,263,63,214),(12,279,77,234,25,262,64,213),(13,278,78,233,26,261,65,212),(27,312,92,252,40,289,79,241),(28,311,93,251,41,288,80,240),(29,310,94,250,42,287,81,239),(30,309,95,249,43,299,82,238),(31,308,96,248,44,298,83,237),(32,307,97,260,45,297,84,236),(33,306,98,259,46,296,85,235),(34,305,99,258,47,295,86,247),(35,304,100,257,48,294,87,246),(36,303,101,256,49,293,88,245),(37,302,102,255,50,292,89,244),(38,301,103,254,51,291,90,243),(39,300,104,253,52,290,91,242),(105,390,170,328,118,376,157,317),(106,389,171,327,119,375,158,316),(107,388,172,326,120,374,159,315),(108,387,173,338,121,373,160,314),(109,386,174,337,122,372,161,313),(110,385,175,336,123,371,162,325),(111,384,176,335,124,370,163,324),(112,383,177,334,125,369,164,323),(113,382,178,333,126,368,165,322),(114,381,179,332,127,367,166,321),(115,380,180,331,128,366,167,320),(116,379,181,330,129,365,168,319),(117,378,182,329,130,377,169,318),(131,412,196,354,144,397,183,348),(132,411,197,353,145,396,184,347),(133,410,198,352,146,395,185,346),(134,409,199,364,147,394,186,345),(135,408,200,363,148,393,187,344),(136,407,201,362,149,392,188,343),(137,406,202,361,150,391,189,342),(138,405,203,360,151,403,190,341),(139,404,204,359,152,402,191,340),(140,416,205,358,153,401,192,339),(141,415,206,357,154,400,193,351),(142,414,207,356,155,399,194,350),(143,413,208,355,156,398,195,349)]])
128 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | ··· | 4L | 8A | ··· | 8P | 13A | ··· | 13F | 26A | ··· | 26R | 52A | ··· | 52BT |
| order | 1 | 2 | 2 | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 13 | ··· | 13 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 13 | ··· | 13 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
128 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | |||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | D13 | Dic13 | D26 | C13⋊2C8 | C4×D13 |
| kernel | C4×C13⋊2C8 | C2×C13⋊2C8 | C4×C52 | C13⋊2C8 | C2×C52 | C52 | C42 | C2×C4 | C2×C4 | C4 | C4 |
| # reps | 1 | 2 | 1 | 8 | 4 | 16 | 6 | 12 | 6 | 48 | 24 |
Matrix representation of C4×C13⋊2C8 ►in GL3(𝔽313) generated by
| 288 | 0 | 0 |
| 0 | 288 | 0 |
| 0 | 0 | 288 |
| 1 | 0 | 0 |
| 0 | 27 | 0 |
| 0 | 256 | 58 |
| 25 | 0 | 0 |
| 0 | 188 | 57 |
| 0 | 0 | 125 |
G:=sub<GL(3,GF(313))| [288,0,0,0,288,0,0,0,288],[1,0,0,0,27,256,0,0,58],[25,0,0,0,188,0,0,57,125] >;
C4×C13⋊2C8 in GAP, Magma, Sage, TeX
C_4\times C_{13}\rtimes_2C_8 % in TeX
G:=Group("C4xC13:2C8"); // GroupNames label
G:=SmallGroup(416,9);
// by ID
G=gap.SmallGroup(416,9);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,24,55,86,13829]);
// Polycyclic
G:=Group<a,b,c|a^4=b^13=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export