metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic13⋊3C8, Dic13.5Q8, C26.4M4(2), Dic13.13D4, C13⋊2(C4⋊C8), C26.4(C2×C8), (C2×C52).4C4, C26.6(C4⋊C4), C2.5(D13⋊C8), C2.2(C52⋊C4), (C4×Dic13).8C2, (C2×Dic13).11C4, C2.2(C13⋊M4(2)), (C2×Dic13).52C22, (C2×C13⋊C8).3C2, (C2×C4).4(C13⋊C4), (C2×C26).7(C2×C4), C22.12(C2×C13⋊C4), SmallGroup(416,79)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic13⋊C8
G = < a,b,c | a26=c8=1, b2=a13, bab-1=a-1, cac-1=a5, cbc-1=a13b >
Smallest permutation representation of Dic13⋊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)
(1 285 14 272)(2 284 15 271)(3 283 16 270)(4 282 17 269)(5 281 18 268)(6 280 19 267)(7 279 20 266)(8 278 21 265)(9 277 22 264)(10 276 23 263)(11 275 24 262)(12 274 25 261)(13 273 26 286)(27 354 40 341)(28 353 41 340)(29 352 42 339)(30 351 43 364)(31 350 44 363)(32 349 45 362)(33 348 46 361)(34 347 47 360)(35 346 48 359)(36 345 49 358)(37 344 50 357)(38 343 51 356)(39 342 52 355)(53 386 66 373)(54 385 67 372)(55 384 68 371)(56 383 69 370)(57 382 70 369)(58 381 71 368)(59 380 72 367)(60 379 73 366)(61 378 74 365)(62 377 75 390)(63 376 76 389)(64 375 77 388)(65 374 78 387)(79 131 92 144)(80 156 93 143)(81 155 94 142)(82 154 95 141)(83 153 96 140)(84 152 97 139)(85 151 98 138)(86 150 99 137)(87 149 100 136)(88 148 101 135)(89 147 102 134)(90 146 103 133)(91 145 104 132)(105 230 118 217)(106 229 119 216)(107 228 120 215)(108 227 121 214)(109 226 122 213)(110 225 123 212)(111 224 124 211)(112 223 125 210)(113 222 126 209)(114 221 127 234)(115 220 128 233)(116 219 129 232)(117 218 130 231)(157 243 170 256)(158 242 171 255)(159 241 172 254)(160 240 173 253)(161 239 174 252)(162 238 175 251)(163 237 176 250)(164 236 177 249)(165 235 178 248)(166 260 179 247)(167 259 180 246)(168 258 181 245)(169 257 182 244)(183 391 196 404)(184 416 197 403)(185 415 198 402)(186 414 199 401)(187 413 200 400)(188 412 201 399)(189 411 202 398)(190 410 203 397)(191 409 204 396)(192 408 205 395)(193 407 206 394)(194 406 207 393)(195 405 208 392)(287 337 300 324)(288 336 301 323)(289 335 302 322)(290 334 303 321)(291 333 304 320)(292 332 305 319)(293 331 306 318)(294 330 307 317)(295 329 308 316)(296 328 309 315)(297 327 310 314)(298 326 311 313)(299 325 312 338)
(1 298 136 105 235 385 207 30)(2 293 135 110 236 380 206 35)(3 288 134 115 237 375 205 40)(4 309 133 120 238 370 204 45)(5 304 132 125 239 365 203 50)(6 299 131 130 240 386 202 29)(7 294 156 109 241 381 201 34)(8 289 155 114 242 376 200 39)(9 310 154 119 243 371 199 44)(10 305 153 124 244 366 198 49)(11 300 152 129 245 387 197 28)(12 295 151 108 246 382 196 33)(13 290 150 113 247 377 195 38)(14 311 149 118 248 372 194 43)(15 306 148 123 249 367 193 48)(16 301 147 128 250 388 192 27)(17 296 146 107 251 383 191 32)(18 291 145 112 252 378 190 37)(19 312 144 117 253 373 189 42)(20 307 143 122 254 368 188 47)(21 302 142 127 255 389 187 52)(22 297 141 106 256 384 186 31)(23 292 140 111 257 379 185 36)(24 287 139 116 258 374 184 41)(25 308 138 121 259 369 183 46)(26 303 137 126 260 390 208 51)(53 398 339 280 338 92 218 173)(54 393 364 285 313 87 217 178)(55 414 363 264 314 82 216 157)(56 409 362 269 315 103 215 162)(57 404 361 274 316 98 214 167)(58 399 360 279 317 93 213 172)(59 394 359 284 318 88 212 177)(60 415 358 263 319 83 211 182)(61 410 357 268 320 104 210 161)(62 405 356 273 321 99 209 166)(63 400 355 278 322 94 234 171)(64 395 354 283 323 89 233 176)(65 416 353 262 324 84 232 181)(66 411 352 267 325 79 231 160)(67 406 351 272 326 100 230 165)(68 401 350 277 327 95 229 170)(69 396 349 282 328 90 228 175)(70 391 348 261 329 85 227 180)(71 412 347 266 330 80 226 159)(72 407 346 271 331 101 225 164)(73 402 345 276 332 96 224 169)(74 397 344 281 333 91 223 174)(75 392 343 286 334 86 222 179)(76 413 342 265 335 81 221 158)(77 408 341 270 336 102 220 163)(78 403 340 275 337 97 219 168)
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), (1,285,14,272)(2,284,15,271)(3,283,16,270)(4,282,17,269)(5,281,18,268)(6,280,19,267)(7,279,20,266)(8,278,21,265)(9,277,22,264)(10,276,23,263)(11,275,24,262)(12,274,25,261)(13,273,26,286)(27,354,40,341)(28,353,41,340)(29,352,42,339)(30,351,43,364)(31,350,44,363)(32,349,45,362)(33,348,46,361)(34,347,47,360)(35,346,48,359)(36,345,49,358)(37,344,50,357)(38,343,51,356)(39,342,52,355)(53,386,66,373)(54,385,67,372)(55,384,68,371)(56,383,69,370)(57,382,70,369)(58,381,71,368)(59,380,72,367)(60,379,73,366)(61,378,74,365)(62,377,75,390)(63,376,76,389)(64,375,77,388)(65,374,78,387)(79,131,92,144)(80,156,93,143)(81,155,94,142)(82,154,95,141)(83,153,96,140)(84,152,97,139)(85,151,98,138)(86,150,99,137)(87,149,100,136)(88,148,101,135)(89,147,102,134)(90,146,103,133)(91,145,104,132)(105,230,118,217)(106,229,119,216)(107,228,120,215)(108,227,121,214)(109,226,122,213)(110,225,123,212)(111,224,124,211)(112,223,125,210)(113,222,126,209)(114,221,127,234)(115,220,128,233)(116,219,129,232)(117,218,130,231)(157,243,170,256)(158,242,171,255)(159,241,172,254)(160,240,173,253)(161,239,174,252)(162,238,175,251)(163,237,176,250)(164,236,177,249)(165,235,178,248)(166,260,179,247)(167,259,180,246)(168,258,181,245)(169,257,182,244)(183,391,196,404)(184,416,197,403)(185,415,198,402)(186,414,199,401)(187,413,200,400)(188,412,201,399)(189,411,202,398)(190,410,203,397)(191,409,204,396)(192,408,205,395)(193,407,206,394)(194,406,207,393)(195,405,208,392)(287,337,300,324)(288,336,301,323)(289,335,302,322)(290,334,303,321)(291,333,304,320)(292,332,305,319)(293,331,306,318)(294,330,307,317)(295,329,308,316)(296,328,309,315)(297,327,310,314)(298,326,311,313)(299,325,312,338), (1,298,136,105,235,385,207,30)(2,293,135,110,236,380,206,35)(3,288,134,115,237,375,205,40)(4,309,133,120,238,370,204,45)(5,304,132,125,239,365,203,50)(6,299,131,130,240,386,202,29)(7,294,156,109,241,381,201,34)(8,289,155,114,242,376,200,39)(9,310,154,119,243,371,199,44)(10,305,153,124,244,366,198,49)(11,300,152,129,245,387,197,28)(12,295,151,108,246,382,196,33)(13,290,150,113,247,377,195,38)(14,311,149,118,248,372,194,43)(15,306,148,123,249,367,193,48)(16,301,147,128,250,388,192,27)(17,296,146,107,251,383,191,32)(18,291,145,112,252,378,190,37)(19,312,144,117,253,373,189,42)(20,307,143,122,254,368,188,47)(21,302,142,127,255,389,187,52)(22,297,141,106,256,384,186,31)(23,292,140,111,257,379,185,36)(24,287,139,116,258,374,184,41)(25,308,138,121,259,369,183,46)(26,303,137,126,260,390,208,51)(53,398,339,280,338,92,218,173)(54,393,364,285,313,87,217,178)(55,414,363,264,314,82,216,157)(56,409,362,269,315,103,215,162)(57,404,361,274,316,98,214,167)(58,399,360,279,317,93,213,172)(59,394,359,284,318,88,212,177)(60,415,358,263,319,83,211,182)(61,410,357,268,320,104,210,161)(62,405,356,273,321,99,209,166)(63,400,355,278,322,94,234,171)(64,395,354,283,323,89,233,176)(65,416,353,262,324,84,232,181)(66,411,352,267,325,79,231,160)(67,406,351,272,326,100,230,165)(68,401,350,277,327,95,229,170)(69,396,349,282,328,90,228,175)(70,391,348,261,329,85,227,180)(71,412,347,266,330,80,226,159)(72,407,346,271,331,101,225,164)(73,402,345,276,332,96,224,169)(74,397,344,281,333,91,223,174)(75,392,343,286,334,86,222,179)(76,413,342,265,335,81,221,158)(77,408,341,270,336,102,220,163)(78,403,340,275,337,97,219,168)>;
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), (1,285,14,272)(2,284,15,271)(3,283,16,270)(4,282,17,269)(5,281,18,268)(6,280,19,267)(7,279,20,266)(8,278,21,265)(9,277,22,264)(10,276,23,263)(11,275,24,262)(12,274,25,261)(13,273,26,286)(27,354,40,341)(28,353,41,340)(29,352,42,339)(30,351,43,364)(31,350,44,363)(32,349,45,362)(33,348,46,361)(34,347,47,360)(35,346,48,359)(36,345,49,358)(37,344,50,357)(38,343,51,356)(39,342,52,355)(53,386,66,373)(54,385,67,372)(55,384,68,371)(56,383,69,370)(57,382,70,369)(58,381,71,368)(59,380,72,367)(60,379,73,366)(61,378,74,365)(62,377,75,390)(63,376,76,389)(64,375,77,388)(65,374,78,387)(79,131,92,144)(80,156,93,143)(81,155,94,142)(82,154,95,141)(83,153,96,140)(84,152,97,139)(85,151,98,138)(86,150,99,137)(87,149,100,136)(88,148,101,135)(89,147,102,134)(90,146,103,133)(91,145,104,132)(105,230,118,217)(106,229,119,216)(107,228,120,215)(108,227,121,214)(109,226,122,213)(110,225,123,212)(111,224,124,211)(112,223,125,210)(113,222,126,209)(114,221,127,234)(115,220,128,233)(116,219,129,232)(117,218,130,231)(157,243,170,256)(158,242,171,255)(159,241,172,254)(160,240,173,253)(161,239,174,252)(162,238,175,251)(163,237,176,250)(164,236,177,249)(165,235,178,248)(166,260,179,247)(167,259,180,246)(168,258,181,245)(169,257,182,244)(183,391,196,404)(184,416,197,403)(185,415,198,402)(186,414,199,401)(187,413,200,400)(188,412,201,399)(189,411,202,398)(190,410,203,397)(191,409,204,396)(192,408,205,395)(193,407,206,394)(194,406,207,393)(195,405,208,392)(287,337,300,324)(288,336,301,323)(289,335,302,322)(290,334,303,321)(291,333,304,320)(292,332,305,319)(293,331,306,318)(294,330,307,317)(295,329,308,316)(296,328,309,315)(297,327,310,314)(298,326,311,313)(299,325,312,338), (1,298,136,105,235,385,207,30)(2,293,135,110,236,380,206,35)(3,288,134,115,237,375,205,40)(4,309,133,120,238,370,204,45)(5,304,132,125,239,365,203,50)(6,299,131,130,240,386,202,29)(7,294,156,109,241,381,201,34)(8,289,155,114,242,376,200,39)(9,310,154,119,243,371,199,44)(10,305,153,124,244,366,198,49)(11,300,152,129,245,387,197,28)(12,295,151,108,246,382,196,33)(13,290,150,113,247,377,195,38)(14,311,149,118,248,372,194,43)(15,306,148,123,249,367,193,48)(16,301,147,128,250,388,192,27)(17,296,146,107,251,383,191,32)(18,291,145,112,252,378,190,37)(19,312,144,117,253,373,189,42)(20,307,143,122,254,368,188,47)(21,302,142,127,255,389,187,52)(22,297,141,106,256,384,186,31)(23,292,140,111,257,379,185,36)(24,287,139,116,258,374,184,41)(25,308,138,121,259,369,183,46)(26,303,137,126,260,390,208,51)(53,398,339,280,338,92,218,173)(54,393,364,285,313,87,217,178)(55,414,363,264,314,82,216,157)(56,409,362,269,315,103,215,162)(57,404,361,274,316,98,214,167)(58,399,360,279,317,93,213,172)(59,394,359,284,318,88,212,177)(60,415,358,263,319,83,211,182)(61,410,357,268,320,104,210,161)(62,405,356,273,321,99,209,166)(63,400,355,278,322,94,234,171)(64,395,354,283,323,89,233,176)(65,416,353,262,324,84,232,181)(66,411,352,267,325,79,231,160)(67,406,351,272,326,100,230,165)(68,401,350,277,327,95,229,170)(69,396,349,282,328,90,228,175)(70,391,348,261,329,85,227,180)(71,412,347,266,330,80,226,159)(72,407,346,271,331,101,225,164)(73,402,345,276,332,96,224,169)(74,397,344,281,333,91,223,174)(75,392,343,286,334,86,222,179)(76,413,342,265,335,81,221,158)(77,408,341,270,336,102,220,163)(78,403,340,275,337,97,219,168) );
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)], [(1,285,14,272),(2,284,15,271),(3,283,16,270),(4,282,17,269),(5,281,18,268),(6,280,19,267),(7,279,20,266),(8,278,21,265),(9,277,22,264),(10,276,23,263),(11,275,24,262),(12,274,25,261),(13,273,26,286),(27,354,40,341),(28,353,41,340),(29,352,42,339),(30,351,43,364),(31,350,44,363),(32,349,45,362),(33,348,46,361),(34,347,47,360),(35,346,48,359),(36,345,49,358),(37,344,50,357),(38,343,51,356),(39,342,52,355),(53,386,66,373),(54,385,67,372),(55,384,68,371),(56,383,69,370),(57,382,70,369),(58,381,71,368),(59,380,72,367),(60,379,73,366),(61,378,74,365),(62,377,75,390),(63,376,76,389),(64,375,77,388),(65,374,78,387),(79,131,92,144),(80,156,93,143),(81,155,94,142),(82,154,95,141),(83,153,96,140),(84,152,97,139),(85,151,98,138),(86,150,99,137),(87,149,100,136),(88,148,101,135),(89,147,102,134),(90,146,103,133),(91,145,104,132),(105,230,118,217),(106,229,119,216),(107,228,120,215),(108,227,121,214),(109,226,122,213),(110,225,123,212),(111,224,124,211),(112,223,125,210),(113,222,126,209),(114,221,127,234),(115,220,128,233),(116,219,129,232),(117,218,130,231),(157,243,170,256),(158,242,171,255),(159,241,172,254),(160,240,173,253),(161,239,174,252),(162,238,175,251),(163,237,176,250),(164,236,177,249),(165,235,178,248),(166,260,179,247),(167,259,180,246),(168,258,181,245),(169,257,182,244),(183,391,196,404),(184,416,197,403),(185,415,198,402),(186,414,199,401),(187,413,200,400),(188,412,201,399),(189,411,202,398),(190,410,203,397),(191,409,204,396),(192,408,205,395),(193,407,206,394),(194,406,207,393),(195,405,208,392),(287,337,300,324),(288,336,301,323),(289,335,302,322),(290,334,303,321),(291,333,304,320),(292,332,305,319),(293,331,306,318),(294,330,307,317),(295,329,308,316),(296,328,309,315),(297,327,310,314),(298,326,311,313),(299,325,312,338)], [(1,298,136,105,235,385,207,30),(2,293,135,110,236,380,206,35),(3,288,134,115,237,375,205,40),(4,309,133,120,238,370,204,45),(5,304,132,125,239,365,203,50),(6,299,131,130,240,386,202,29),(7,294,156,109,241,381,201,34),(8,289,155,114,242,376,200,39),(9,310,154,119,243,371,199,44),(10,305,153,124,244,366,198,49),(11,300,152,129,245,387,197,28),(12,295,151,108,246,382,196,33),(13,290,150,113,247,377,195,38),(14,311,149,118,248,372,194,43),(15,306,148,123,249,367,193,48),(16,301,147,128,250,388,192,27),(17,296,146,107,251,383,191,32),(18,291,145,112,252,378,190,37),(19,312,144,117,253,373,189,42),(20,307,143,122,254,368,188,47),(21,302,142,127,255,389,187,52),(22,297,141,106,256,384,186,31),(23,292,140,111,257,379,185,36),(24,287,139,116,258,374,184,41),(25,308,138,121,259,369,183,46),(26,303,137,126,260,390,208,51),(53,398,339,280,338,92,218,173),(54,393,364,285,313,87,217,178),(55,414,363,264,314,82,216,157),(56,409,362,269,315,103,215,162),(57,404,361,274,316,98,214,167),(58,399,360,279,317,93,213,172),(59,394,359,284,318,88,212,177),(60,415,358,263,319,83,211,182),(61,410,357,268,320,104,210,161),(62,405,356,273,321,99,209,166),(63,400,355,278,322,94,234,171),(64,395,354,283,323,89,233,176),(65,416,353,262,324,84,232,181),(66,411,352,267,325,79,231,160),(67,406,351,272,326,100,230,165),(68,401,350,277,327,95,229,170),(69,396,349,282,328,90,228,175),(70,391,348,261,329,85,227,180),(71,412,347,266,330,80,226,159),(72,407,346,271,331,101,225,164),(73,402,345,276,332,96,224,169),(74,397,344,281,333,91,223,174),(75,392,343,286,334,86,222,179),(76,413,342,265,335,81,221,158),(77,408,341,270,336,102,220,163),(78,403,340,275,337,97,219,168)]])
44 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 8A | ··· | 8H | 13A | 13B | 13C | 26A | ··· | 26I | 52A | ··· | 52L |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 13 | 13 | 13 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 13 | 13 | 13 | 13 | 26 | 26 | 26 | ··· | 26 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 |
44 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | - | + | + | - | ||||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | D4 | Q8 | M4(2) | C13⋊C4 | C2×C13⋊C4 | D13⋊C8 | C52⋊C4 | C13⋊M4(2) |
| kernel | Dic13⋊C8 | C4×Dic13 | C2×C13⋊C8 | C2×Dic13 | C2×C52 | Dic13 | Dic13 | Dic13 | C26 | C2×C4 | C22 | C2 | C2 | C2 |
| # reps | 1 | 1 | 2 | 2 | 2 | 8 | 1 | 1 | 2 | 3 | 3 | 6 | 6 | 6 |
Matrix representation of Dic13⋊C8 ►in GL8(𝔽313)
| 312 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 312 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 312 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 312 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 312 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 312 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 312 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 70 | 31 | 282 | 242 |
| 312 | 311 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 258 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 155 | 55 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 129 | 133 | 72 | 1 |
| 0 | 0 | 0 | 0 | 5 | 149 | 76 | 292 |
| 0 | 0 | 0 | 0 | 184 | 303 | 236 | 105 |
| 0 | 0 | 0 | 0 | 121 | 54 | 233 | 112 |
| 244 | 131 | 0 | 0 | 0 | 0 | 0 | 0 |
| 291 | 69 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 224 | 245 | 0 | 0 | 0 | 0 |
| 0 | 0 | 245 | 89 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 307 | 35 | 61 | 117 |
| 0 | 0 | 0 | 0 | 4 | 189 | 17 | 185 |
| 0 | 0 | 0 | 0 | 249 | 19 | 204 | 232 |
| 0 | 0 | 0 | 0 | 210 | 76 | 287 | 239 |
G:=sub<GL(8,GF(313))| [312,0,0,0,0,0,0,0,0,312,0,0,0,0,0,0,0,0,312,0,0,0,0,0,0,0,0,312,0,0,0,0,0,0,0,0,312,312,312,70,0,0,0,0,1,0,0,31,0,0,0,0,0,1,0,282,0,0,0,0,0,0,1,242],[312,1,0,0,0,0,0,0,311,1,0,0,0,0,0,0,0,0,258,155,0,0,0,0,0,0,35,55,0,0,0,0,0,0,0,0,129,5,184,121,0,0,0,0,133,149,303,54,0,0,0,0,72,76,236,233,0,0,0,0,1,292,105,112],[244,291,0,0,0,0,0,0,131,69,0,0,0,0,0,0,0,0,224,245,0,0,0,0,0,0,245,89,0,0,0,0,0,0,0,0,307,4,249,210,0,0,0,0,35,189,19,76,0,0,0,0,61,17,204,287,0,0,0,0,117,185,232,239] >;
Dic13⋊C8 in GAP, Magma, Sage, TeX
{\rm Dic}_{13}\rtimes C_8 % in TeX
G:=Group("Dic13:C8"); // GroupNames label
G:=SmallGroup(416,79);
// by ID
G=gap.SmallGroup(416,79);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,24,121,151,86,9221,3473]);
// Polycyclic
G:=Group<a,b,c|a^26=c^8=1,b^2=a^13,b*a*b^-1=a^-1,c*a*c^-1=a^5,c*b*c^-1=a^13*b>;
// generators/relations
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