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G = C26.Q16order 416 = 25·13

2nd non-split extension by C26 of Q16 acting via Q16/Q8=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C52.2D4, C4.10D52, C26.4Q16, Dic266C4, C26.5SD16, C4⋊C4.3D13, C4.2(C4×D13), C52.25(C2×C4), (C2×C26).31D4, (C2×C4).36D26, C132(Q8⋊C4), C2.2(D4.D13), (C2×C52).11C22, (C2×Dic26).6C2, C2.2(C13⋊Q16), C2.6(D26⋊C4), C26.15(C22⋊C4), C22.15(C13⋊D4), (C13×C4⋊C4).3C2, (C2×C132C8).3C2, SmallGroup(416,17)

Series: Derived Chief Lower central Upper central

C1C52 — C26.Q16
C1C13C26C2×C26C2×C52C2×Dic26 — C26.Q16
C13C26C52 — C26.Q16
C1C22C2×C4C4⋊C4

Generators and relations for C26.Q16
 G = < a,b,c | a26=b8=1, c2=a13b4, bab-1=a-1, ac=ca, cbc-1=a13b-1 >

4C4
26C4
26C4
2C2×C4
13Q8
13Q8
26C8
26Q8
26C2×C4
2Dic13
2Dic13
4C52
13C2×C8
13C2×Q8
2C132C8
2C2×C52
2C2×Dic13
2Dic26
13Q8⋊C4

Smallest permutation representation of C26.Q16
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)
(1 166 374 318 293 144 217 194)(2 165 375 317 294 143 218 193)(3 164 376 316 295 142 219 192)(4 163 377 315 296 141 220 191)(5 162 378 314 297 140 221 190)(6 161 379 313 298 139 222 189)(7 160 380 338 299 138 223 188)(8 159 381 337 300 137 224 187)(9 158 382 336 301 136 225 186)(10 157 383 335 302 135 226 185)(11 182 384 334 303 134 227 184)(12 181 385 333 304 133 228 183)(13 180 386 332 305 132 229 208)(14 179 387 331 306 131 230 207)(15 178 388 330 307 156 231 206)(16 177 389 329 308 155 232 205)(17 176 390 328 309 154 233 204)(18 175 365 327 310 153 234 203)(19 174 366 326 311 152 209 202)(20 173 367 325 312 151 210 201)(21 172 368 324 287 150 211 200)(22 171 369 323 288 149 212 199)(23 170 370 322 289 148 213 198)(24 169 371 321 290 147 214 197)(25 168 372 320 291 146 215 196)(26 167 373 319 292 145 216 195)(27 260 93 402 123 341 281 61)(28 259 94 401 124 340 282 60)(29 258 95 400 125 339 283 59)(30 257 96 399 126 364 284 58)(31 256 97 398 127 363 285 57)(32 255 98 397 128 362 286 56)(33 254 99 396 129 361 261 55)(34 253 100 395 130 360 262 54)(35 252 101 394 105 359 263 53)(36 251 102 393 106 358 264 78)(37 250 103 392 107 357 265 77)(38 249 104 391 108 356 266 76)(39 248 79 416 109 355 267 75)(40 247 80 415 110 354 268 74)(41 246 81 414 111 353 269 73)(42 245 82 413 112 352 270 72)(43 244 83 412 113 351 271 71)(44 243 84 411 114 350 272 70)(45 242 85 410 115 349 273 69)(46 241 86 409 116 348 274 68)(47 240 87 408 117 347 275 67)(48 239 88 407 118 346 276 66)(49 238 89 406 119 345 277 65)(50 237 90 405 120 344 278 64)(51 236 91 404 121 343 279 63)(52 235 92 403 122 342 280 62)
(1 74 306 402)(2 75 307 403)(3 76 308 404)(4 77 309 405)(5 78 310 406)(6 53 311 407)(7 54 312 408)(8 55 287 409)(9 56 288 410)(10 57 289 411)(11 58 290 412)(12 59 291 413)(13 60 292 414)(14 61 293 415)(15 62 294 416)(16 63 295 391)(17 64 296 392)(18 65 297 393)(19 66 298 394)(20 67 299 395)(21 68 300 396)(22 69 301 397)(23 70 302 398)(24 71 303 399)(25 72 304 400)(26 73 305 401)(27 331 110 194)(28 332 111 195)(29 333 112 196)(30 334 113 197)(31 335 114 198)(32 336 115 199)(33 337 116 200)(34 338 117 201)(35 313 118 202)(36 314 119 203)(37 315 120 204)(38 316 121 205)(39 317 122 206)(40 318 123 207)(41 319 124 208)(42 320 125 183)(43 321 126 184)(44 322 127 185)(45 323 128 186)(46 324 129 187)(47 325 130 188)(48 326 105 189)(49 327 106 190)(50 328 107 191)(51 329 108 192)(52 330 109 193)(79 165 280 156)(80 166 281 131)(81 167 282 132)(82 168 283 133)(83 169 284 134)(84 170 285 135)(85 171 286 136)(86 172 261 137)(87 173 262 138)(88 174 263 139)(89 175 264 140)(90 176 265 141)(91 177 266 142)(92 178 267 143)(93 179 268 144)(94 180 269 145)(95 181 270 146)(96 182 271 147)(97 157 272 148)(98 158 273 149)(99 159 274 150)(100 160 275 151)(101 161 276 152)(102 162 277 153)(103 163 278 154)(104 164 279 155)(209 239 379 359)(210 240 380 360)(211 241 381 361)(212 242 382 362)(213 243 383 363)(214 244 384 364)(215 245 385 339)(216 246 386 340)(217 247 387 341)(218 248 388 342)(219 249 389 343)(220 250 390 344)(221 251 365 345)(222 252 366 346)(223 253 367 347)(224 254 368 348)(225 255 369 349)(226 256 370 350)(227 257 371 351)(228 258 372 352)(229 259 373 353)(230 260 374 354)(231 235 375 355)(232 236 376 356)(233 237 377 357)(234 238 378 358)

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

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

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

74 conjugacy classes

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

74 irreducible representations

dim1111122222222244
type++++++-+++--
imageC1C2C2C2C4D4D4SD16Q16D13D26C4×D13D52C13⋊D4D4.D13C13⋊Q16
kernelC26.Q16C2×C132C8C13×C4⋊C4C2×Dic26Dic26C52C2×C26C26C26C4⋊C4C2×C4C4C4C22C2C2
# reps1111411226612121266

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

30730700
65800
0010
0001
,
290900
1502300
00061
00118120
,
15924500
6815400
0019736
0087116
G:=sub<GL(4,GF(313))| [307,6,0,0,307,58,0,0,0,0,1,0,0,0,0,1],[290,150,0,0,9,23,0,0,0,0,0,118,0,0,61,120],[159,68,0,0,245,154,0,0,0,0,197,87,0,0,36,116] >;

C26.Q16 in GAP, Magma, Sage, TeX

C_{26}.Q_{16}
% in TeX

G:=Group("C26.Q16");
// GroupNames label

G:=SmallGroup(416,17);
// by ID

G=gap.SmallGroup(416,17);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-13,96,121,31,579,297,69,13829]);
// Polycyclic

G:=Group<a,b,c|a^26=b^8=1,c^2=a^13*b^4,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=a^13*b^-1>;
// generators/relations

Export

Subgroup lattice of C26.Q16 in TeX

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