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G = Q16×C26order 416 = 25·13

Direct product of C26 and Q16

direct product, metabelian, nilpotent (class 3), monomial, 2-elementary

Aliases: Q16×C26, C52.43D4, C52.46C23, C104.27C22, C8.5(C2×C26), (C2×C8).4C26, C4.8(D4×C13), C2.13(D4×C26), C26.76(C2×D4), (C2×C26).54D4, Q8.1(C2×C26), (C2×Q8).4C26, (Q8×C26).9C2, (C2×C104).14C2, C4.3(C22×C26), C22.16(D4×C13), (C2×C52).131C22, (Q8×C13).12C22, (C2×C4).27(C2×C26), SmallGroup(416,195)

Series: Derived Chief Lower central Upper central

C1C4 — Q16×C26
C1C2C4C52Q8×C13C13×Q16 — Q16×C26
C1C2C4 — Q16×C26
C1C2×C26C2×C52 — Q16×C26

Generators and relations for Q16×C26
 G = < a,b,c | a26=b8=1, c2=b4, ab=ba, ac=ca, cbc-1=b-1 >

Subgroups: 76 in 60 conjugacy classes, 44 normal (16 characteristic)
C1, C2, C2 [×2], C4 [×2], C4 [×4], C22, C8 [×2], C2×C4, C2×C4 [×2], Q8 [×4], Q8 [×2], C13, C2×C8, Q16 [×4], C2×Q8 [×2], C26, C26 [×2], C2×Q16, C52 [×2], C52 [×4], C2×C26, C104 [×2], C2×C52, C2×C52 [×2], Q8×C13 [×4], Q8×C13 [×2], C2×C104, C13×Q16 [×4], Q8×C26 [×2], Q16×C26
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], C23, C13, Q16 [×2], C2×D4, C26 [×7], C2×Q16, C2×C26 [×7], D4×C13 [×2], C22×C26, C13×Q16 [×2], D4×C26, Q16×C26

Smallest permutation representation of Q16×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)
(1 228 187 263 130 156 242 345)(2 229 188 264 105 131 243 346)(3 230 189 265 106 132 244 347)(4 231 190 266 107 133 245 348)(5 232 191 267 108 134 246 349)(6 233 192 268 109 135 247 350)(7 234 193 269 110 136 248 351)(8 209 194 270 111 137 249 352)(9 210 195 271 112 138 250 353)(10 211 196 272 113 139 251 354)(11 212 197 273 114 140 252 355)(12 213 198 274 115 141 253 356)(13 214 199 275 116 142 254 357)(14 215 200 276 117 143 255 358)(15 216 201 277 118 144 256 359)(16 217 202 278 119 145 257 360)(17 218 203 279 120 146 258 361)(18 219 204 280 121 147 259 362)(19 220 205 281 122 148 260 363)(20 221 206 282 123 149 235 364)(21 222 207 283 124 150 236 339)(22 223 208 284 125 151 237 340)(23 224 183 285 126 152 238 341)(24 225 184 286 127 153 239 342)(25 226 185 261 128 154 240 343)(26 227 186 262 129 155 241 344)(27 86 166 400 293 372 56 321)(28 87 167 401 294 373 57 322)(29 88 168 402 295 374 58 323)(30 89 169 403 296 375 59 324)(31 90 170 404 297 376 60 325)(32 91 171 405 298 377 61 326)(33 92 172 406 299 378 62 327)(34 93 173 407 300 379 63 328)(35 94 174 408 301 380 64 329)(36 95 175 409 302 381 65 330)(37 96 176 410 303 382 66 331)(38 97 177 411 304 383 67 332)(39 98 178 412 305 384 68 333)(40 99 179 413 306 385 69 334)(41 100 180 414 307 386 70 335)(42 101 181 415 308 387 71 336)(43 102 182 416 309 388 72 337)(44 103 157 391 310 389 73 338)(45 104 158 392 311 390 74 313)(46 79 159 393 312 365 75 314)(47 80 160 394 287 366 76 315)(48 81 161 395 288 367 77 316)(49 82 162 396 289 368 78 317)(50 83 163 397 290 369 53 318)(51 84 164 398 291 370 54 319)(52 85 165 399 292 371 55 320)
(1 373 130 87)(2 374 105 88)(3 375 106 89)(4 376 107 90)(5 377 108 91)(6 378 109 92)(7 379 110 93)(8 380 111 94)(9 381 112 95)(10 382 113 96)(11 383 114 97)(12 384 115 98)(13 385 116 99)(14 386 117 100)(15 387 118 101)(16 388 119 102)(17 389 120 103)(18 390 121 104)(19 365 122 79)(20 366 123 80)(21 367 124 81)(22 368 125 82)(23 369 126 83)(24 370 127 84)(25 371 128 85)(26 372 129 86)(27 227 293 155)(28 228 294 156)(29 229 295 131)(30 230 296 132)(31 231 297 133)(32 232 298 134)(33 233 299 135)(34 234 300 136)(35 209 301 137)(36 210 302 138)(37 211 303 139)(38 212 304 140)(39 213 305 141)(40 214 306 142)(41 215 307 143)(42 216 308 144)(43 217 309 145)(44 218 310 146)(45 219 311 147)(46 220 312 148)(47 221 287 149)(48 222 288 150)(49 223 289 151)(50 224 290 152)(51 225 291 153)(52 226 292 154)(53 285 163 341)(54 286 164 342)(55 261 165 343)(56 262 166 344)(57 263 167 345)(58 264 168 346)(59 265 169 347)(60 266 170 348)(61 267 171 349)(62 268 172 350)(63 269 173 351)(64 270 174 352)(65 271 175 353)(66 272 176 354)(67 273 177 355)(68 274 178 356)(69 275 179 357)(70 276 180 358)(71 277 181 359)(72 278 182 360)(73 279 157 361)(74 280 158 362)(75 281 159 363)(76 282 160 364)(77 283 161 339)(78 284 162 340)(183 397 238 318)(184 398 239 319)(185 399 240 320)(186 400 241 321)(187 401 242 322)(188 402 243 323)(189 403 244 324)(190 404 245 325)(191 405 246 326)(192 406 247 327)(193 407 248 328)(194 408 249 329)(195 409 250 330)(196 410 251 331)(197 411 252 332)(198 412 253 333)(199 413 254 334)(200 414 255 335)(201 415 256 336)(202 416 257 337)(203 391 258 338)(204 392 259 313)(205 393 260 314)(206 394 235 315)(207 395 236 316)(208 396 237 317)

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

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

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

182 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F8A8B8C8D13A···13L26A···26AJ52A···52X52Y···52BT104A···104AV
order1222444444888813···1326···2652···5252···52104···104
size111122444422221···11···12···24···42···2

182 irreducible representations

dim11111111222222
type++++++-
imageC1C2C2C2C13C26C26C26D4D4Q16D4×C13D4×C13C13×Q16
kernelQ16×C26C2×C104C13×Q16Q8×C26C2×Q16C2×C8Q16C2×Q8C52C2×C26C26C4C22C2
# reps114212124824114121248

Matrix representation of Q16×C26 in GL4(𝔽313) generated by

36000
03600
00270
00027
,
9223800
9222100
0025360
00253253
,
312200
0100
0010568
0068208
G:=sub<GL(4,GF(313))| [36,0,0,0,0,36,0,0,0,0,27,0,0,0,0,27],[92,92,0,0,238,221,0,0,0,0,253,253,0,0,60,253],[312,0,0,0,2,1,0,0,0,0,105,68,0,0,68,208] >;

Q16×C26 in GAP, Magma, Sage, TeX

Q_{16}\times C_{26}
% in TeX

G:=Group("Q16xC26");
// GroupNames label

G:=SmallGroup(416,195);
// by ID

G=gap.SmallGroup(416,195);
# by ID

G:=PCGroup([6,-2,-2,-2,-13,-2,-2,1248,1273,1255,9364,4690,88]);
// Polycyclic

G:=Group<a,b,c|a^26=b^8=1,c^2=b^4,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

׿
×
𝔽