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G = C4⋊C4×C26order 416 = 25·13

Direct product of C26 and C4⋊C4

direct product, metabelian, nilpotent (class 2), monomial, 2-elementary

Aliases: C4⋊C4×C26, C42(C2×C52), (C2×C4)⋊3C52, (C2×C52)⋊13C4, C5212(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

C1C2 — C4⋊C4×C26
C1C2C22C2×C26C2×C52C13×C4⋊C4 — C4⋊C4×C26
C1C2 — C4⋊C4×C26
C1C22×C26 — C4⋊C4×C26

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 [×3], C2 [×4], C4 [×4], C4 [×4], C22, C22 [×6], C2×C4 [×10], C2×C4 [×4], C23, C13, C4⋊C4 [×4], C22×C4, C22×C4 [×2], C26 [×3], C26 [×4], C2×C4⋊C4, C52 [×4], C52 [×4], C2×C26, C2×C26 [×6], C2×C52 [×10], C2×C52 [×4], C22×C26, C13×C4⋊C4 [×4], C22×C52, C22×C52 [×2], C4⋊C4×C26
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×2], Q8 [×2], C23, C13, C4⋊C4 [×4], C22×C4, C2×D4, C2×Q8, C26 [×7], C2×C4⋊C4, C52 [×4], C2×C26 [×7], C2×C52 [×6], D4×C13 [×2], Q8×C13 [×2], C22×C26, C13×C4⋊C4 [×4], C22×C52, D4×C26, Q8×C26, C4⋊C4×C26

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

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

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

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

260 conjugacy classes

class 1 2A···2G4A···4L13A···13L26A···26CF52A···52EN
order12···24···413···1326···2652···52
size11···12···21···11···12···2

260 irreducible representations

dim111111112222
type++++-
imageC1C2C2C4C13C26C26C52D4Q8D4×C13Q8×C13
kernelC4⋊C4×C26C13×C4⋊C4C22×C52C2×C52C2×C4⋊C4C4⋊C4C22×C4C2×C4C2×C26C2×C26C22C22
# reps143812483696222424

Matrix representation of C4⋊C4×C26 in GL4(𝔽53) generated by

1000
05200
00420
00042
,
1000
05200
00052
0010
,
23000
0100
002840
004025
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

׿
×
𝔽