metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C26.6D8, C52.1Q8, C26.3Q16, C4.1Dic26, C13⋊2C8⋊1C4, C4⋊C4.1D13, C13⋊2(C2.D8), C26.9(C4⋊C4), C52.22(C2×C4), (C2×C4).33D26, C4.11(C4×D13), (C2×C26).28D4, C52⋊3C4.8C2, C2.1(D4⋊D13), (C2×C52).8C22, C2.1(C13⋊Q16), C2.3(C26.D4), C22.12(C13⋊D4), (C13×C4⋊C4).1C2, (C2×C13⋊2C8).1C2, SmallGroup(416,14)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C26.D8
G = < a,b,c | a26=b8=1, c2=a13, bab-1=cac-1=a-1, cbc-1=b-1 >
Smallest permutation representation of C26.D8
►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)
(1 118 177 329 262 241 410 296)(2 117 178 328 263 240 411 295)(3 116 179 327 264 239 412 294)(4 115 180 326 265 238 413 293)(5 114 181 325 266 237 414 292)(6 113 182 324 267 236 415 291)(7 112 157 323 268 235 416 290)(8 111 158 322 269 260 391 289)(9 110 159 321 270 259 392 288)(10 109 160 320 271 258 393 287)(11 108 161 319 272 257 394 312)(12 107 162 318 273 256 395 311)(13 106 163 317 274 255 396 310)(14 105 164 316 275 254 397 309)(15 130 165 315 276 253 398 308)(16 129 166 314 277 252 399 307)(17 128 167 313 278 251 400 306)(18 127 168 338 279 250 401 305)(19 126 169 337 280 249 402 304)(20 125 170 336 281 248 403 303)(21 124 171 335 282 247 404 302)(22 123 172 334 283 246 405 301)(23 122 173 333 284 245 406 300)(24 121 174 332 285 244 407 299)(25 120 175 331 286 243 408 298)(26 119 176 330 261 242 409 297)(27 79 137 209 76 187 374 340)(28 104 138 234 77 186 375 339)(29 103 139 233 78 185 376 364)(30 102 140 232 53 184 377 363)(31 101 141 231 54 183 378 362)(32 100 142 230 55 208 379 361)(33 99 143 229 56 207 380 360)(34 98 144 228 57 206 381 359)(35 97 145 227 58 205 382 358)(36 96 146 226 59 204 383 357)(37 95 147 225 60 203 384 356)(38 94 148 224 61 202 385 355)(39 93 149 223 62 201 386 354)(40 92 150 222 63 200 387 353)(41 91 151 221 64 199 388 352)(42 90 152 220 65 198 389 351)(43 89 153 219 66 197 390 350)(44 88 154 218 67 196 365 349)(45 87 155 217 68 195 366 348)(46 86 156 216 69 194 367 347)(47 85 131 215 70 193 368 346)(48 84 132 214 71 192 369 345)(49 83 133 213 72 191 370 344)(50 82 134 212 73 190 371 343)(51 81 135 211 74 189 372 342)(52 80 136 210 75 188 373 341)
(1 56 14 69)(2 55 15 68)(3 54 16 67)(4 53 17 66)(5 78 18 65)(6 77 19 64)(7 76 20 63)(8 75 21 62)(9 74 22 61)(10 73 23 60)(11 72 24 59)(12 71 25 58)(13 70 26 57)(27 281 40 268)(28 280 41 267)(29 279 42 266)(30 278 43 265)(31 277 44 264)(32 276 45 263)(33 275 46 262)(34 274 47 261)(35 273 48 286)(36 272 49 285)(37 271 50 284)(38 270 51 283)(39 269 52 282)(79 336 92 323)(80 335 93 322)(81 334 94 321)(82 333 95 320)(83 332 96 319)(84 331 97 318)(85 330 98 317)(86 329 99 316)(87 328 100 315)(88 327 101 314)(89 326 102 313)(90 325 103 338)(91 324 104 337)(105 216 118 229)(106 215 119 228)(107 214 120 227)(108 213 121 226)(109 212 122 225)(110 211 123 224)(111 210 124 223)(112 209 125 222)(113 234 126 221)(114 233 127 220)(115 232 128 219)(116 231 129 218)(117 230 130 217)(131 176 144 163)(132 175 145 162)(133 174 146 161)(134 173 147 160)(135 172 148 159)(136 171 149 158)(137 170 150 157)(138 169 151 182)(139 168 152 181)(140 167 153 180)(141 166 154 179)(142 165 155 178)(143 164 156 177)(183 307 196 294)(184 306 197 293)(185 305 198 292)(186 304 199 291)(187 303 200 290)(188 302 201 289)(189 301 202 288)(190 300 203 287)(191 299 204 312)(192 298 205 311)(193 297 206 310)(194 296 207 309)(195 295 208 308)(235 340 248 353)(236 339 249 352)(237 364 250 351)(238 363 251 350)(239 362 252 349)(240 361 253 348)(241 360 254 347)(242 359 255 346)(243 358 256 345)(244 357 257 344)(245 356 258 343)(246 355 259 342)(247 354 260 341)(365 412 378 399)(366 411 379 398)(367 410 380 397)(368 409 381 396)(369 408 382 395)(370 407 383 394)(371 406 384 393)(372 405 385 392)(373 404 386 391)(374 403 387 416)(375 402 388 415)(376 401 389 414)(377 400 390 413)
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), (1,118,177,329,262,241,410,296)(2,117,178,328,263,240,411,295)(3,116,179,327,264,239,412,294)(4,115,180,326,265,238,413,293)(5,114,181,325,266,237,414,292)(6,113,182,324,267,236,415,291)(7,112,157,323,268,235,416,290)(8,111,158,322,269,260,391,289)(9,110,159,321,270,259,392,288)(10,109,160,320,271,258,393,287)(11,108,161,319,272,257,394,312)(12,107,162,318,273,256,395,311)(13,106,163,317,274,255,396,310)(14,105,164,316,275,254,397,309)(15,130,165,315,276,253,398,308)(16,129,166,314,277,252,399,307)(17,128,167,313,278,251,400,306)(18,127,168,338,279,250,401,305)(19,126,169,337,280,249,402,304)(20,125,170,336,281,248,403,303)(21,124,171,335,282,247,404,302)(22,123,172,334,283,246,405,301)(23,122,173,333,284,245,406,300)(24,121,174,332,285,244,407,299)(25,120,175,331,286,243,408,298)(26,119,176,330,261,242,409,297)(27,79,137,209,76,187,374,340)(28,104,138,234,77,186,375,339)(29,103,139,233,78,185,376,364)(30,102,140,232,53,184,377,363)(31,101,141,231,54,183,378,362)(32,100,142,230,55,208,379,361)(33,99,143,229,56,207,380,360)(34,98,144,228,57,206,381,359)(35,97,145,227,58,205,382,358)(36,96,146,226,59,204,383,357)(37,95,147,225,60,203,384,356)(38,94,148,224,61,202,385,355)(39,93,149,223,62,201,386,354)(40,92,150,222,63,200,387,353)(41,91,151,221,64,199,388,352)(42,90,152,220,65,198,389,351)(43,89,153,219,66,197,390,350)(44,88,154,218,67,196,365,349)(45,87,155,217,68,195,366,348)(46,86,156,216,69,194,367,347)(47,85,131,215,70,193,368,346)(48,84,132,214,71,192,369,345)(49,83,133,213,72,191,370,344)(50,82,134,212,73,190,371,343)(51,81,135,211,74,189,372,342)(52,80,136,210,75,188,373,341), (1,56,14,69)(2,55,15,68)(3,54,16,67)(4,53,17,66)(5,78,18,65)(6,77,19,64)(7,76,20,63)(8,75,21,62)(9,74,22,61)(10,73,23,60)(11,72,24,59)(12,71,25,58)(13,70,26,57)(27,281,40,268)(28,280,41,267)(29,279,42,266)(30,278,43,265)(31,277,44,264)(32,276,45,263)(33,275,46,262)(34,274,47,261)(35,273,48,286)(36,272,49,285)(37,271,50,284)(38,270,51,283)(39,269,52,282)(79,336,92,323)(80,335,93,322)(81,334,94,321)(82,333,95,320)(83,332,96,319)(84,331,97,318)(85,330,98,317)(86,329,99,316)(87,328,100,315)(88,327,101,314)(89,326,102,313)(90,325,103,338)(91,324,104,337)(105,216,118,229)(106,215,119,228)(107,214,120,227)(108,213,121,226)(109,212,122,225)(110,211,123,224)(111,210,124,223)(112,209,125,222)(113,234,126,221)(114,233,127,220)(115,232,128,219)(116,231,129,218)(117,230,130,217)(131,176,144,163)(132,175,145,162)(133,174,146,161)(134,173,147,160)(135,172,148,159)(136,171,149,158)(137,170,150,157)(138,169,151,182)(139,168,152,181)(140,167,153,180)(141,166,154,179)(142,165,155,178)(143,164,156,177)(183,307,196,294)(184,306,197,293)(185,305,198,292)(186,304,199,291)(187,303,200,290)(188,302,201,289)(189,301,202,288)(190,300,203,287)(191,299,204,312)(192,298,205,311)(193,297,206,310)(194,296,207,309)(195,295,208,308)(235,340,248,353)(236,339,249,352)(237,364,250,351)(238,363,251,350)(239,362,252,349)(240,361,253,348)(241,360,254,347)(242,359,255,346)(243,358,256,345)(244,357,257,344)(245,356,258,343)(246,355,259,342)(247,354,260,341)(365,412,378,399)(366,411,379,398)(367,410,380,397)(368,409,381,396)(369,408,382,395)(370,407,383,394)(371,406,384,393)(372,405,385,392)(373,404,386,391)(374,403,387,416)(375,402,388,415)(376,401,389,414)(377,400,390,413)>;
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), (1,118,177,329,262,241,410,296)(2,117,178,328,263,240,411,295)(3,116,179,327,264,239,412,294)(4,115,180,326,265,238,413,293)(5,114,181,325,266,237,414,292)(6,113,182,324,267,236,415,291)(7,112,157,323,268,235,416,290)(8,111,158,322,269,260,391,289)(9,110,159,321,270,259,392,288)(10,109,160,320,271,258,393,287)(11,108,161,319,272,257,394,312)(12,107,162,318,273,256,395,311)(13,106,163,317,274,255,396,310)(14,105,164,316,275,254,397,309)(15,130,165,315,276,253,398,308)(16,129,166,314,277,252,399,307)(17,128,167,313,278,251,400,306)(18,127,168,338,279,250,401,305)(19,126,169,337,280,249,402,304)(20,125,170,336,281,248,403,303)(21,124,171,335,282,247,404,302)(22,123,172,334,283,246,405,301)(23,122,173,333,284,245,406,300)(24,121,174,332,285,244,407,299)(25,120,175,331,286,243,408,298)(26,119,176,330,261,242,409,297)(27,79,137,209,76,187,374,340)(28,104,138,234,77,186,375,339)(29,103,139,233,78,185,376,364)(30,102,140,232,53,184,377,363)(31,101,141,231,54,183,378,362)(32,100,142,230,55,208,379,361)(33,99,143,229,56,207,380,360)(34,98,144,228,57,206,381,359)(35,97,145,227,58,205,382,358)(36,96,146,226,59,204,383,357)(37,95,147,225,60,203,384,356)(38,94,148,224,61,202,385,355)(39,93,149,223,62,201,386,354)(40,92,150,222,63,200,387,353)(41,91,151,221,64,199,388,352)(42,90,152,220,65,198,389,351)(43,89,153,219,66,197,390,350)(44,88,154,218,67,196,365,349)(45,87,155,217,68,195,366,348)(46,86,156,216,69,194,367,347)(47,85,131,215,70,193,368,346)(48,84,132,214,71,192,369,345)(49,83,133,213,72,191,370,344)(50,82,134,212,73,190,371,343)(51,81,135,211,74,189,372,342)(52,80,136,210,75,188,373,341), (1,56,14,69)(2,55,15,68)(3,54,16,67)(4,53,17,66)(5,78,18,65)(6,77,19,64)(7,76,20,63)(8,75,21,62)(9,74,22,61)(10,73,23,60)(11,72,24,59)(12,71,25,58)(13,70,26,57)(27,281,40,268)(28,280,41,267)(29,279,42,266)(30,278,43,265)(31,277,44,264)(32,276,45,263)(33,275,46,262)(34,274,47,261)(35,273,48,286)(36,272,49,285)(37,271,50,284)(38,270,51,283)(39,269,52,282)(79,336,92,323)(80,335,93,322)(81,334,94,321)(82,333,95,320)(83,332,96,319)(84,331,97,318)(85,330,98,317)(86,329,99,316)(87,328,100,315)(88,327,101,314)(89,326,102,313)(90,325,103,338)(91,324,104,337)(105,216,118,229)(106,215,119,228)(107,214,120,227)(108,213,121,226)(109,212,122,225)(110,211,123,224)(111,210,124,223)(112,209,125,222)(113,234,126,221)(114,233,127,220)(115,232,128,219)(116,231,129,218)(117,230,130,217)(131,176,144,163)(132,175,145,162)(133,174,146,161)(134,173,147,160)(135,172,148,159)(136,171,149,158)(137,170,150,157)(138,169,151,182)(139,168,152,181)(140,167,153,180)(141,166,154,179)(142,165,155,178)(143,164,156,177)(183,307,196,294)(184,306,197,293)(185,305,198,292)(186,304,199,291)(187,303,200,290)(188,302,201,289)(189,301,202,288)(190,300,203,287)(191,299,204,312)(192,298,205,311)(193,297,206,310)(194,296,207,309)(195,295,208,308)(235,340,248,353)(236,339,249,352)(237,364,250,351)(238,363,251,350)(239,362,252,349)(240,361,253,348)(241,360,254,347)(242,359,255,346)(243,358,256,345)(244,357,257,344)(245,356,258,343)(246,355,259,342)(247,354,260,341)(365,412,378,399)(366,411,379,398)(367,410,380,397)(368,409,381,396)(369,408,382,395)(370,407,383,394)(371,406,384,393)(372,405,385,392)(373,404,386,391)(374,403,387,416)(375,402,388,415)(376,401,389,414)(377,400,390,413) );
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)], [(1,118,177,329,262,241,410,296),(2,117,178,328,263,240,411,295),(3,116,179,327,264,239,412,294),(4,115,180,326,265,238,413,293),(5,114,181,325,266,237,414,292),(6,113,182,324,267,236,415,291),(7,112,157,323,268,235,416,290),(8,111,158,322,269,260,391,289),(9,110,159,321,270,259,392,288),(10,109,160,320,271,258,393,287),(11,108,161,319,272,257,394,312),(12,107,162,318,273,256,395,311),(13,106,163,317,274,255,396,310),(14,105,164,316,275,254,397,309),(15,130,165,315,276,253,398,308),(16,129,166,314,277,252,399,307),(17,128,167,313,278,251,400,306),(18,127,168,338,279,250,401,305),(19,126,169,337,280,249,402,304),(20,125,170,336,281,248,403,303),(21,124,171,335,282,247,404,302),(22,123,172,334,283,246,405,301),(23,122,173,333,284,245,406,300),(24,121,174,332,285,244,407,299),(25,120,175,331,286,243,408,298),(26,119,176,330,261,242,409,297),(27,79,137,209,76,187,374,340),(28,104,138,234,77,186,375,339),(29,103,139,233,78,185,376,364),(30,102,140,232,53,184,377,363),(31,101,141,231,54,183,378,362),(32,100,142,230,55,208,379,361),(33,99,143,229,56,207,380,360),(34,98,144,228,57,206,381,359),(35,97,145,227,58,205,382,358),(36,96,146,226,59,204,383,357),(37,95,147,225,60,203,384,356),(38,94,148,224,61,202,385,355),(39,93,149,223,62,201,386,354),(40,92,150,222,63,200,387,353),(41,91,151,221,64,199,388,352),(42,90,152,220,65,198,389,351),(43,89,153,219,66,197,390,350),(44,88,154,218,67,196,365,349),(45,87,155,217,68,195,366,348),(46,86,156,216,69,194,367,347),(47,85,131,215,70,193,368,346),(48,84,132,214,71,192,369,345),(49,83,133,213,72,191,370,344),(50,82,134,212,73,190,371,343),(51,81,135,211,74,189,372,342),(52,80,136,210,75,188,373,341)], [(1,56,14,69),(2,55,15,68),(3,54,16,67),(4,53,17,66),(5,78,18,65),(6,77,19,64),(7,76,20,63),(8,75,21,62),(9,74,22,61),(10,73,23,60),(11,72,24,59),(12,71,25,58),(13,70,26,57),(27,281,40,268),(28,280,41,267),(29,279,42,266),(30,278,43,265),(31,277,44,264),(32,276,45,263),(33,275,46,262),(34,274,47,261),(35,273,48,286),(36,272,49,285),(37,271,50,284),(38,270,51,283),(39,269,52,282),(79,336,92,323),(80,335,93,322),(81,334,94,321),(82,333,95,320),(83,332,96,319),(84,331,97,318),(85,330,98,317),(86,329,99,316),(87,328,100,315),(88,327,101,314),(89,326,102,313),(90,325,103,338),(91,324,104,337),(105,216,118,229),(106,215,119,228),(107,214,120,227),(108,213,121,226),(109,212,122,225),(110,211,123,224),(111,210,124,223),(112,209,125,222),(113,234,126,221),(114,233,127,220),(115,232,128,219),(116,231,129,218),(117,230,130,217),(131,176,144,163),(132,175,145,162),(133,174,146,161),(134,173,147,160),(135,172,148,159),(136,171,149,158),(137,170,150,157),(138,169,151,182),(139,168,152,181),(140,167,153,180),(141,166,154,179),(142,165,155,178),(143,164,156,177),(183,307,196,294),(184,306,197,293),(185,305,198,292),(186,304,199,291),(187,303,200,290),(188,302,201,289),(189,301,202,288),(190,300,203,287),(191,299,204,312),(192,298,205,311),(193,297,206,310),(194,296,207,309),(195,295,208,308),(235,340,248,353),(236,339,249,352),(237,364,250,351),(238,363,251,350),(239,362,252,349),(240,361,253,348),(241,360,254,347),(242,359,255,346),(243,358,256,345),(244,357,257,344),(245,356,258,343),(246,355,259,342),(247,354,260,341),(365,412,378,399),(366,411,379,398),(367,410,380,397),(368,409,381,396),(369,408,382,395),(370,407,383,394),(371,406,384,393),(372,405,385,392),(373,404,386,391),(374,403,387,416),(375,402,388,415),(376,401,389,414),(377,400,390,413)]])
74 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 8A | 8B | 8C | 8D | 13A | ··· | 13F | 26A | ··· | 26R | 52A | ··· | 52AJ |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 13 | ··· | 13 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 52 | 52 | 26 | 26 | 26 | 26 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
74 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | - | + | + | - | + | + | - | + | - | |||
| image | C1 | C2 | C2 | C2 | C4 | Q8 | D4 | D8 | Q16 | D13 | D26 | Dic26 | C4×D13 | C13⋊D4 | D4⋊D13 | C13⋊Q16 |
| kernel | C26.D8 | C2×C13⋊2C8 | C52⋊3C4 | C13×C4⋊C4 | C13⋊2C8 | C52 | C2×C26 | C26 | C26 | C4⋊C4 | C2×C4 | C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 2 | 2 | 6 | 6 | 12 | 12 | 12 | 6 | 6 |
Matrix representation of C26.D8 ►in GL6(𝔽313)
| 312 | 0 | 0 | 0 | 0 | 0 |
| 0 | 312 | 0 | 0 | 0 | 0 |
| 0 | 0 | 234 | 232 | 0 | 0 |
| 0 | 0 | 102 | 164 | 0 | 0 |
| 0 | 0 | 0 | 0 | 312 | 0 |
| 0 | 0 | 0 | 0 | 0 | 312 |
| 99 | 100 | 0 | 0 | 0 | 0 |
| 71 | 214 | 0 | 0 | 0 | 0 |
| 0 | 0 | 125 | 110 | 0 | 0 |
| 0 | 0 | 262 | 188 | 0 | 0 |
| 0 | 0 | 0 | 0 | 253 | 253 |
| 0 | 0 | 0 | 0 | 60 | 253 |
| 63 | 256 | 0 | 0 | 0 | 0 |
| 163 | 250 | 0 | 0 | 0 | 0 |
| 0 | 0 | 158 | 310 | 0 | 0 |
| 0 | 0 | 183 | 155 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 150 |
| 0 | 0 | 0 | 0 | 150 | 273 |
G:=sub<GL(6,GF(313))| [312,0,0,0,0,0,0,312,0,0,0,0,0,0,234,102,0,0,0,0,232,164,0,0,0,0,0,0,312,0,0,0,0,0,0,312],[99,71,0,0,0,0,100,214,0,0,0,0,0,0,125,262,0,0,0,0,110,188,0,0,0,0,0,0,253,60,0,0,0,0,253,253],[63,163,0,0,0,0,256,250,0,0,0,0,0,0,158,183,0,0,0,0,310,155,0,0,0,0,0,0,40,150,0,0,0,0,150,273] >;
C26.D8 in GAP, Magma, Sage, TeX
C_{26}.D_8 % in TeX
G:=Group("C26.D8"); // GroupNames label
G:=SmallGroup(416,14);
// by ID
G=gap.SmallGroup(416,14);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,48,121,31,297,69,13829]);
// Polycyclic
G:=Group<a,b,c|a^26=b^8=1,c^2=a^13,b*a*b^-1=c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations
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