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G = C26.D8order 416 = 25·13

1st non-split extension by C26 of D8 acting via D8/D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C26.6D8, C52.1Q8, C26.3Q16, C4.1Dic26, C132C81C4, C4⋊C4.1D13, C132(C2.D8), C26.9(C4⋊C4), C52.22(C2×C4), (C2×C4).33D26, C4.11(C4×D13), (C2×C26).28D4, C523C4.8C2, C2.1(D4⋊D13), (C2×C52).8C22, C2.1(C13⋊Q16), C2.3(C26.D4), C22.12(C13⋊D4), (C13×C4⋊C4).1C2, (C2×C132C8).1C2, SmallGroup(416,14)

Series: Derived Chief Lower central Upper central

C1C52 — C26.D8
C1C13C26C2×C26C2×C52C2×C132C8 — C26.D8
C13C26C52 — C26.D8
C1C22C2×C4C4⋊C4

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 >

4C4
52C4
2C2×C4
13C8
13C8
26C2×C4
4C52
4Dic13
13C2×C8
13C4⋊C4
2C2×Dic13
2C2×C52
13C2.D8

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

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

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

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

74 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F8A8B8C8D13A···13F26A···26R52A···52AJ
order1222444444888813···1326···2652···52
size111122445252262626262···22···24···4

74 irreducible representations

dim1111122222222244
type++++-++-++-+-
imageC1C2C2C2C4Q8D4D8Q16D13D26Dic26C4×D13C13⋊D4D4⋊D13C13⋊Q16
kernelC26.D8C2×C132C8C523C4C13×C4⋊C4C132C8C52C2×C26C26C26C4⋊C4C2×C4C4C4C22C2C2
# reps1111411226612121266

Matrix representation of C26.D8 in GL6(𝔽313)

31200000
03120000
0023423200
0010216400
00003120
00000312
,
991000000
712140000
0012511000
0026218800
0000253253
000060253
,
632560000
1632500000
0015831000
0018315500
000040150
0000150273

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

Export

Subgroup lattice of C26.D8 in TeX

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