direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C4⋊C4×C26, C4⋊2(C2×C52), (C2×C4)⋊3C52, (C2×C52)⋊13C4, C52⋊12(C2×C4), C2.2(D4×C26), (C2×C26).8Q8, C2.1(Q8×C26), C26.65(C2×D4), (C2×C26).51D4, C26.18(C2×Q8), (C22×C4).3C26, C2.2(C22×C52), (C22×C52).5C2, C22.3(Q8×C13), C26.43(C22×C4), C23.13(C2×C26), (C2×C26).71C23, C22.11(C2×C52), C22.13(D4×C13), (C2×C52).120C22, C22.5(C22×C26), (C22×C26).49C22, (C2×C26).60(C2×C4), (C2×C4).13(C2×C26), SmallGroup(416,177)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊C4×C26
G = < a,b,c | a26=b4=c4=1, ab=ba, ac=ca, cbc-1=b-1 >
Subgroups: 108 in 92 conjugacy classes, 76 normal (16 characteristic)
C1, C2, C2, C4, C4, C22, C22, C2×C4, C2×C4, C23, C13, C4⋊C4, C22×C4, C22×C4, C26, C26, C2×C4⋊C4, C52, C52, C2×C26, C2×C26, C2×C52, C2×C52, C22×C26, C13×C4⋊C4, C22×C52, C22×C52, C4⋊C4×C26
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, C13, C4⋊C4, C22×C4, C2×D4, C2×Q8, C26, C2×C4⋊C4, C52, C2×C26, C2×C52, D4×C13, Q8×C13, C22×C26, C13×C4⋊C4, C22×C52, D4×C26, Q8×C26, C4⋊C4×C26
►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)
(1 111 168 369)(2 112 169 370)(3 113 170 371)(4 114 171 372)(5 115 172 373)(6 116 173 374)(7 117 174 375)(8 118 175 376)(9 119 176 377)(10 120 177 378)(11 121 178 379)(12 122 179 380)(13 123 180 381)(14 124 181 382)(15 125 182 383)(16 126 157 384)(17 127 158 385)(18 128 159 386)(19 129 160 387)(20 130 161 388)(21 105 162 389)(22 106 163 390)(23 107 164 365)(24 108 165 366)(25 109 166 367)(26 110 167 368)(27 276 241 144)(28 277 242 145)(29 278 243 146)(30 279 244 147)(31 280 245 148)(32 281 246 149)(33 282 247 150)(34 283 248 151)(35 284 249 152)(36 285 250 153)(37 286 251 154)(38 261 252 155)(39 262 253 156)(40 263 254 131)(41 264 255 132)(42 265 256 133)(43 266 257 134)(44 267 258 135)(45 268 259 136)(46 269 260 137)(47 270 235 138)(48 271 236 139)(49 272 237 140)(50 273 238 141)(51 274 239 142)(52 275 240 143)(53 201 324 351)(54 202 325 352)(55 203 326 353)(56 204 327 354)(57 205 328 355)(58 206 329 356)(59 207 330 357)(60 208 331 358)(61 183 332 359)(62 184 333 360)(63 185 334 361)(64 186 335 362)(65 187 336 363)(66 188 337 364)(67 189 338 339)(68 190 313 340)(69 191 314 341)(70 192 315 342)(71 193 316 343)(72 194 317 344)(73 195 318 345)(74 196 319 346)(75 197 320 347)(76 198 321 348)(77 199 322 349)(78 200 323 350)(79 287 216 401)(80 288 217 402)(81 289 218 403)(82 290 219 404)(83 291 220 405)(84 292 221 406)(85 293 222 407)(86 294 223 408)(87 295 224 409)(88 296 225 410)(89 297 226 411)(90 298 227 412)(91 299 228 413)(92 300 229 414)(93 301 230 415)(94 302 231 416)(95 303 232 391)(96 304 233 392)(97 305 234 393)(98 306 209 394)(99 307 210 395)(100 308 211 396)(101 309 212 397)(102 310 213 398)(103 311 214 399)(104 312 215 400)
(1 355 43 300)(2 356 44 301)(3 357 45 302)(4 358 46 303)(5 359 47 304)(6 360 48 305)(7 361 49 306)(8 362 50 307)(9 363 51 308)(10 364 52 309)(11 339 27 310)(12 340 28 311)(13 341 29 312)(14 342 30 287)(15 343 31 288)(16 344 32 289)(17 345 33 290)(18 346 34 291)(19 347 35 292)(20 348 36 293)(21 349 37 294)(22 350 38 295)(23 351 39 296)(24 352 40 297)(25 353 41 298)(26 354 42 299)(53 156 225 365)(54 131 226 366)(55 132 227 367)(56 133 228 368)(57 134 229 369)(58 135 230 370)(59 136 231 371)(60 137 232 372)(61 138 233 373)(62 139 234 374)(63 140 209 375)(64 141 210 376)(65 142 211 377)(66 143 212 378)(67 144 213 379)(68 145 214 380)(69 146 215 381)(70 147 216 382)(71 148 217 383)(72 149 218 384)(73 150 219 385)(74 151 220 386)(75 152 221 387)(76 153 222 388)(77 154 223 389)(78 155 224 390)(79 124 315 279)(80 125 316 280)(81 126 317 281)(82 127 318 282)(83 128 319 283)(84 129 320 284)(85 130 321 285)(86 105 322 286)(87 106 323 261)(88 107 324 262)(89 108 325 263)(90 109 326 264)(91 110 327 265)(92 111 328 266)(93 112 329 267)(94 113 330 268)(95 114 331 269)(96 115 332 270)(97 116 333 271)(98 117 334 272)(99 118 335 273)(100 119 336 274)(101 120 337 275)(102 121 338 276)(103 122 313 277)(104 123 314 278)(157 194 246 403)(158 195 247 404)(159 196 248 405)(160 197 249 406)(161 198 250 407)(162 199 251 408)(163 200 252 409)(164 201 253 410)(165 202 254 411)(166 203 255 412)(167 204 256 413)(168 205 257 414)(169 206 258 415)(170 207 259 416)(171 208 260 391)(172 183 235 392)(173 184 236 393)(174 185 237 394)(175 186 238 395)(176 187 239 396)(177 188 240 397)(178 189 241 398)(179 190 242 399)(180 191 243 400)(181 192 244 401)(182 193 245 402)
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), (1,111,168,369)(2,112,169,370)(3,113,170,371)(4,114,171,372)(5,115,172,373)(6,116,173,374)(7,117,174,375)(8,118,175,376)(9,119,176,377)(10,120,177,378)(11,121,178,379)(12,122,179,380)(13,123,180,381)(14,124,181,382)(15,125,182,383)(16,126,157,384)(17,127,158,385)(18,128,159,386)(19,129,160,387)(20,130,161,388)(21,105,162,389)(22,106,163,390)(23,107,164,365)(24,108,165,366)(25,109,166,367)(26,110,167,368)(27,276,241,144)(28,277,242,145)(29,278,243,146)(30,279,244,147)(31,280,245,148)(32,281,246,149)(33,282,247,150)(34,283,248,151)(35,284,249,152)(36,285,250,153)(37,286,251,154)(38,261,252,155)(39,262,253,156)(40,263,254,131)(41,264,255,132)(42,265,256,133)(43,266,257,134)(44,267,258,135)(45,268,259,136)(46,269,260,137)(47,270,235,138)(48,271,236,139)(49,272,237,140)(50,273,238,141)(51,274,239,142)(52,275,240,143)(53,201,324,351)(54,202,325,352)(55,203,326,353)(56,204,327,354)(57,205,328,355)(58,206,329,356)(59,207,330,357)(60,208,331,358)(61,183,332,359)(62,184,333,360)(63,185,334,361)(64,186,335,362)(65,187,336,363)(66,188,337,364)(67,189,338,339)(68,190,313,340)(69,191,314,341)(70,192,315,342)(71,193,316,343)(72,194,317,344)(73,195,318,345)(74,196,319,346)(75,197,320,347)(76,198,321,348)(77,199,322,349)(78,200,323,350)(79,287,216,401)(80,288,217,402)(81,289,218,403)(82,290,219,404)(83,291,220,405)(84,292,221,406)(85,293,222,407)(86,294,223,408)(87,295,224,409)(88,296,225,410)(89,297,226,411)(90,298,227,412)(91,299,228,413)(92,300,229,414)(93,301,230,415)(94,302,231,416)(95,303,232,391)(96,304,233,392)(97,305,234,393)(98,306,209,394)(99,307,210,395)(100,308,211,396)(101,309,212,397)(102,310,213,398)(103,311,214,399)(104,312,215,400), (1,355,43,300)(2,356,44,301)(3,357,45,302)(4,358,46,303)(5,359,47,304)(6,360,48,305)(7,361,49,306)(8,362,50,307)(9,363,51,308)(10,364,52,309)(11,339,27,310)(12,340,28,311)(13,341,29,312)(14,342,30,287)(15,343,31,288)(16,344,32,289)(17,345,33,290)(18,346,34,291)(19,347,35,292)(20,348,36,293)(21,349,37,294)(22,350,38,295)(23,351,39,296)(24,352,40,297)(25,353,41,298)(26,354,42,299)(53,156,225,365)(54,131,226,366)(55,132,227,367)(56,133,228,368)(57,134,229,369)(58,135,230,370)(59,136,231,371)(60,137,232,372)(61,138,233,373)(62,139,234,374)(63,140,209,375)(64,141,210,376)(65,142,211,377)(66,143,212,378)(67,144,213,379)(68,145,214,380)(69,146,215,381)(70,147,216,382)(71,148,217,383)(72,149,218,384)(73,150,219,385)(74,151,220,386)(75,152,221,387)(76,153,222,388)(77,154,223,389)(78,155,224,390)(79,124,315,279)(80,125,316,280)(81,126,317,281)(82,127,318,282)(83,128,319,283)(84,129,320,284)(85,130,321,285)(86,105,322,286)(87,106,323,261)(88,107,324,262)(89,108,325,263)(90,109,326,264)(91,110,327,265)(92,111,328,266)(93,112,329,267)(94,113,330,268)(95,114,331,269)(96,115,332,270)(97,116,333,271)(98,117,334,272)(99,118,335,273)(100,119,336,274)(101,120,337,275)(102,121,338,276)(103,122,313,277)(104,123,314,278)(157,194,246,403)(158,195,247,404)(159,196,248,405)(160,197,249,406)(161,198,250,407)(162,199,251,408)(163,200,252,409)(164,201,253,410)(165,202,254,411)(166,203,255,412)(167,204,256,413)(168,205,257,414)(169,206,258,415)(170,207,259,416)(171,208,260,391)(172,183,235,392)(173,184,236,393)(174,185,237,394)(175,186,238,395)(176,187,239,396)(177,188,240,397)(178,189,241,398)(179,190,242,399)(180,191,243,400)(181,192,244,401)(182,193,245,402)>;
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), (1,111,168,369)(2,112,169,370)(3,113,170,371)(4,114,171,372)(5,115,172,373)(6,116,173,374)(7,117,174,375)(8,118,175,376)(9,119,176,377)(10,120,177,378)(11,121,178,379)(12,122,179,380)(13,123,180,381)(14,124,181,382)(15,125,182,383)(16,126,157,384)(17,127,158,385)(18,128,159,386)(19,129,160,387)(20,130,161,388)(21,105,162,389)(22,106,163,390)(23,107,164,365)(24,108,165,366)(25,109,166,367)(26,110,167,368)(27,276,241,144)(28,277,242,145)(29,278,243,146)(30,279,244,147)(31,280,245,148)(32,281,246,149)(33,282,247,150)(34,283,248,151)(35,284,249,152)(36,285,250,153)(37,286,251,154)(38,261,252,155)(39,262,253,156)(40,263,254,131)(41,264,255,132)(42,265,256,133)(43,266,257,134)(44,267,258,135)(45,268,259,136)(46,269,260,137)(47,270,235,138)(48,271,236,139)(49,272,237,140)(50,273,238,141)(51,274,239,142)(52,275,240,143)(53,201,324,351)(54,202,325,352)(55,203,326,353)(56,204,327,354)(57,205,328,355)(58,206,329,356)(59,207,330,357)(60,208,331,358)(61,183,332,359)(62,184,333,360)(63,185,334,361)(64,186,335,362)(65,187,336,363)(66,188,337,364)(67,189,338,339)(68,190,313,340)(69,191,314,341)(70,192,315,342)(71,193,316,343)(72,194,317,344)(73,195,318,345)(74,196,319,346)(75,197,320,347)(76,198,321,348)(77,199,322,349)(78,200,323,350)(79,287,216,401)(80,288,217,402)(81,289,218,403)(82,290,219,404)(83,291,220,405)(84,292,221,406)(85,293,222,407)(86,294,223,408)(87,295,224,409)(88,296,225,410)(89,297,226,411)(90,298,227,412)(91,299,228,413)(92,300,229,414)(93,301,230,415)(94,302,231,416)(95,303,232,391)(96,304,233,392)(97,305,234,393)(98,306,209,394)(99,307,210,395)(100,308,211,396)(101,309,212,397)(102,310,213,398)(103,311,214,399)(104,312,215,400), (1,355,43,300)(2,356,44,301)(3,357,45,302)(4,358,46,303)(5,359,47,304)(6,360,48,305)(7,361,49,306)(8,362,50,307)(9,363,51,308)(10,364,52,309)(11,339,27,310)(12,340,28,311)(13,341,29,312)(14,342,30,287)(15,343,31,288)(16,344,32,289)(17,345,33,290)(18,346,34,291)(19,347,35,292)(20,348,36,293)(21,349,37,294)(22,350,38,295)(23,351,39,296)(24,352,40,297)(25,353,41,298)(26,354,42,299)(53,156,225,365)(54,131,226,366)(55,132,227,367)(56,133,228,368)(57,134,229,369)(58,135,230,370)(59,136,231,371)(60,137,232,372)(61,138,233,373)(62,139,234,374)(63,140,209,375)(64,141,210,376)(65,142,211,377)(66,143,212,378)(67,144,213,379)(68,145,214,380)(69,146,215,381)(70,147,216,382)(71,148,217,383)(72,149,218,384)(73,150,219,385)(74,151,220,386)(75,152,221,387)(76,153,222,388)(77,154,223,389)(78,155,224,390)(79,124,315,279)(80,125,316,280)(81,126,317,281)(82,127,318,282)(83,128,319,283)(84,129,320,284)(85,130,321,285)(86,105,322,286)(87,106,323,261)(88,107,324,262)(89,108,325,263)(90,109,326,264)(91,110,327,265)(92,111,328,266)(93,112,329,267)(94,113,330,268)(95,114,331,269)(96,115,332,270)(97,116,333,271)(98,117,334,272)(99,118,335,273)(100,119,336,274)(101,120,337,275)(102,121,338,276)(103,122,313,277)(104,123,314,278)(157,194,246,403)(158,195,247,404)(159,196,248,405)(160,197,249,406)(161,198,250,407)(162,199,251,408)(163,200,252,409)(164,201,253,410)(165,202,254,411)(166,203,255,412)(167,204,256,413)(168,205,257,414)(169,206,258,415)(170,207,259,416)(171,208,260,391)(172,183,235,392)(173,184,236,393)(174,185,237,394)(175,186,238,395)(176,187,239,396)(177,188,240,397)(178,189,241,398)(179,190,242,399)(180,191,243,400)(181,192,244,401)(182,193,245,402) );
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)], [(1,111,168,369),(2,112,169,370),(3,113,170,371),(4,114,171,372),(5,115,172,373),(6,116,173,374),(7,117,174,375),(8,118,175,376),(9,119,176,377),(10,120,177,378),(11,121,178,379),(12,122,179,380),(13,123,180,381),(14,124,181,382),(15,125,182,383),(16,126,157,384),(17,127,158,385),(18,128,159,386),(19,129,160,387),(20,130,161,388),(21,105,162,389),(22,106,163,390),(23,107,164,365),(24,108,165,366),(25,109,166,367),(26,110,167,368),(27,276,241,144),(28,277,242,145),(29,278,243,146),(30,279,244,147),(31,280,245,148),(32,281,246,149),(33,282,247,150),(34,283,248,151),(35,284,249,152),(36,285,250,153),(37,286,251,154),(38,261,252,155),(39,262,253,156),(40,263,254,131),(41,264,255,132),(42,265,256,133),(43,266,257,134),(44,267,258,135),(45,268,259,136),(46,269,260,137),(47,270,235,138),(48,271,236,139),(49,272,237,140),(50,273,238,141),(51,274,239,142),(52,275,240,143),(53,201,324,351),(54,202,325,352),(55,203,326,353),(56,204,327,354),(57,205,328,355),(58,206,329,356),(59,207,330,357),(60,208,331,358),(61,183,332,359),(62,184,333,360),(63,185,334,361),(64,186,335,362),(65,187,336,363),(66,188,337,364),(67,189,338,339),(68,190,313,340),(69,191,314,341),(70,192,315,342),(71,193,316,343),(72,194,317,344),(73,195,318,345),(74,196,319,346),(75,197,320,347),(76,198,321,348),(77,199,322,349),(78,200,323,350),(79,287,216,401),(80,288,217,402),(81,289,218,403),(82,290,219,404),(83,291,220,405),(84,292,221,406),(85,293,222,407),(86,294,223,408),(87,295,224,409),(88,296,225,410),(89,297,226,411),(90,298,227,412),(91,299,228,413),(92,300,229,414),(93,301,230,415),(94,302,231,416),(95,303,232,391),(96,304,233,392),(97,305,234,393),(98,306,209,394),(99,307,210,395),(100,308,211,396),(101,309,212,397),(102,310,213,398),(103,311,214,399),(104,312,215,400)], [(1,355,43,300),(2,356,44,301),(3,357,45,302),(4,358,46,303),(5,359,47,304),(6,360,48,305),(7,361,49,306),(8,362,50,307),(9,363,51,308),(10,364,52,309),(11,339,27,310),(12,340,28,311),(13,341,29,312),(14,342,30,287),(15,343,31,288),(16,344,32,289),(17,345,33,290),(18,346,34,291),(19,347,35,292),(20,348,36,293),(21,349,37,294),(22,350,38,295),(23,351,39,296),(24,352,40,297),(25,353,41,298),(26,354,42,299),(53,156,225,365),(54,131,226,366),(55,132,227,367),(56,133,228,368),(57,134,229,369),(58,135,230,370),(59,136,231,371),(60,137,232,372),(61,138,233,373),(62,139,234,374),(63,140,209,375),(64,141,210,376),(65,142,211,377),(66,143,212,378),(67,144,213,379),(68,145,214,380),(69,146,215,381),(70,147,216,382),(71,148,217,383),(72,149,218,384),(73,150,219,385),(74,151,220,386),(75,152,221,387),(76,153,222,388),(77,154,223,389),(78,155,224,390),(79,124,315,279),(80,125,316,280),(81,126,317,281),(82,127,318,282),(83,128,319,283),(84,129,320,284),(85,130,321,285),(86,105,322,286),(87,106,323,261),(88,107,324,262),(89,108,325,263),(90,109,326,264),(91,110,327,265),(92,111,328,266),(93,112,329,267),(94,113,330,268),(95,114,331,269),(96,115,332,270),(97,116,333,271),(98,117,334,272),(99,118,335,273),(100,119,336,274),(101,120,337,275),(102,121,338,276),(103,122,313,277),(104,123,314,278),(157,194,246,403),(158,195,247,404),(159,196,248,405),(160,197,249,406),(161,198,250,407),(162,199,251,408),(163,200,252,409),(164,201,253,410),(165,202,254,411),(166,203,255,412),(167,204,256,413),(168,205,257,414),(169,206,258,415),(170,207,259,416),(171,208,260,391),(172,183,235,392),(173,184,236,393),(174,185,237,394),(175,186,238,395),(176,187,239,396),(177,188,240,397),(178,189,241,398),(179,190,242,399),(180,191,243,400),(181,192,244,401),(182,193,245,402)]])
260 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4L | 13A | ··· | 13L | 26A | ··· | 26CF | 52A | ··· | 52EN |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 13 | ··· | 13 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 |
260 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | |||||||
| image | C1 | C2 | C2 | C4 | C13 | C26 | C26 | C52 | D4 | Q8 | D4×C13 | Q8×C13 |
| kernel | C4⋊C4×C26 | C13×C4⋊C4 | C22×C52 | C2×C52 | C2×C4⋊C4 | C4⋊C4 | C22×C4 | C2×C4 | C2×C26 | C2×C26 | C22 | C22 |
| # reps | 1 | 4 | 3 | 8 | 12 | 48 | 36 | 96 | 2 | 2 | 24 | 24 |
Matrix representation of C4⋊C4×C26 ►in GL4(𝔽53) generated by
| 1 | 0 | 0 | 0 |
| 0 | 52 | 0 | 0 |
| 0 | 0 | 42 | 0 |
| 0 | 0 | 0 | 42 |
| 1 | 0 | 0 | 0 |
| 0 | 52 | 0 | 0 |
| 0 | 0 | 0 | 52 |
| 0 | 0 | 1 | 0 |
| 23 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 28 | 40 |
| 0 | 0 | 40 | 25 |
G:=sub<GL(4,GF(53))| [1,0,0,0,0,52,0,0,0,0,42,0,0,0,0,42],[1,0,0,0,0,52,0,0,0,0,0,1,0,0,52,0],[23,0,0,0,0,1,0,0,0,0,28,40,0,0,40,25] >;
C4⋊C4×C26 in GAP, Magma, Sage, TeX
C_4\rtimes C_4\times C_{26} % in TeX
G:=Group("C4:C4xC26"); // GroupNames label
G:=SmallGroup(416,177);
// by ID
G=gap.SmallGroup(416,177);
# by ID
G:=PCGroup([6,-2,-2,-2,-13,-2,-2,1248,1273,631]);
// Polycyclic
G:=Group<a,b,c|a^26=b^4=c^4=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations