metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C26.7C42, C42.1D13, C26.9M4(2), C13⋊2C8⋊3C4, (C4×C52).7C2, C13⋊3(C8⋊C4), C52.45(C2×C4), (C2×C52).14C4, C4.19(C4×D13), (C2×C4).88D26, C2.3(C4×Dic13), (C2×C4).2Dic13, C2.1(C52.4C4), (C2×C52).102C22, C22.7(C2×Dic13), (C2×C13⋊2C8).7C2, (C2×C26).45(C2×C4), SmallGroup(416,10)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C26.7C42
G = < a,b,c | a26=c4=1, b4=a13, bab-1=a-1, ac=ca, cbc-1=a13b >
Smallest permutation representation of C26.7C42
►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)
(1 270 66 215 14 283 53 228)(2 269 67 214 15 282 54 227)(3 268 68 213 16 281 55 226)(4 267 69 212 17 280 56 225)(5 266 70 211 18 279 57 224)(6 265 71 210 19 278 58 223)(7 264 72 209 20 277 59 222)(8 263 73 234 21 276 60 221)(9 262 74 233 22 275 61 220)(10 261 75 232 23 274 62 219)(11 286 76 231 24 273 63 218)(12 285 77 230 25 272 64 217)(13 284 78 229 26 271 65 216)(27 300 91 242 40 287 104 255)(28 299 92 241 41 312 79 254)(29 298 93 240 42 311 80 253)(30 297 94 239 43 310 81 252)(31 296 95 238 44 309 82 251)(32 295 96 237 45 308 83 250)(33 294 97 236 46 307 84 249)(34 293 98 235 47 306 85 248)(35 292 99 260 48 305 86 247)(36 291 100 259 49 304 87 246)(37 290 101 258 50 303 88 245)(38 289 102 257 51 302 89 244)(39 288 103 256 52 301 90 243)(105 390 179 338 118 377 166 325)(106 389 180 337 119 376 167 324)(107 388 181 336 120 375 168 323)(108 387 182 335 121 374 169 322)(109 386 157 334 122 373 170 321)(110 385 158 333 123 372 171 320)(111 384 159 332 124 371 172 319)(112 383 160 331 125 370 173 318)(113 382 161 330 126 369 174 317)(114 381 162 329 127 368 175 316)(115 380 163 328 128 367 176 315)(116 379 164 327 129 366 177 314)(117 378 165 326 130 365 178 313)(131 395 199 361 144 408 186 348)(132 394 200 360 145 407 187 347)(133 393 201 359 146 406 188 346)(134 392 202 358 147 405 189 345)(135 391 203 357 148 404 190 344)(136 416 204 356 149 403 191 343)(137 415 205 355 150 402 192 342)(138 414 206 354 151 401 193 341)(139 413 207 353 152 400 194 340)(140 412 208 352 153 399 195 339)(141 411 183 351 154 398 196 364)(142 410 184 350 155 397 197 363)(143 409 185 349 156 396 198 362)
(1 152 31 129)(2 153 32 130)(3 154 33 105)(4 155 34 106)(5 156 35 107)(6 131 36 108)(7 132 37 109)(8 133 38 110)(9 134 39 111)(10 135 40 112)(11 136 41 113)(12 137 42 114)(13 138 43 115)(14 139 44 116)(15 140 45 117)(16 141 46 118)(17 142 47 119)(18 143 48 120)(19 144 49 121)(20 145 50 122)(21 146 51 123)(22 147 52 124)(23 148 27 125)(24 149 28 126)(25 150 29 127)(26 151 30 128)(53 207 82 164)(54 208 83 165)(55 183 84 166)(56 184 85 167)(57 185 86 168)(58 186 87 169)(59 187 88 170)(60 188 89 171)(61 189 90 172)(62 190 91 173)(63 191 92 174)(64 192 93 175)(65 193 94 176)(66 194 95 177)(67 195 96 178)(68 196 97 179)(69 197 98 180)(70 198 99 181)(71 199 100 182)(72 200 101 157)(73 201 102 158)(74 202 103 159)(75 203 104 160)(76 204 79 161)(77 205 80 162)(78 206 81 163)(209 347 258 321)(210 348 259 322)(211 349 260 323)(212 350 235 324)(213 351 236 325)(214 352 237 326)(215 353 238 327)(216 354 239 328)(217 355 240 329)(218 356 241 330)(219 357 242 331)(220 358 243 332)(221 359 244 333)(222 360 245 334)(223 361 246 335)(224 362 247 336)(225 363 248 337)(226 364 249 338)(227 339 250 313)(228 340 251 314)(229 341 252 315)(230 342 253 316)(231 343 254 317)(232 344 255 318)(233 345 256 319)(234 346 257 320)(261 404 287 370)(262 405 288 371)(263 406 289 372)(264 407 290 373)(265 408 291 374)(266 409 292 375)(267 410 293 376)(268 411 294 377)(269 412 295 378)(270 413 296 379)(271 414 297 380)(272 415 298 381)(273 416 299 382)(274 391 300 383)(275 392 301 384)(276 393 302 385)(277 394 303 386)(278 395 304 387)(279 396 305 388)(280 397 306 389)(281 398 307 390)(282 399 308 365)(283 400 309 366)(284 401 310 367)(285 402 311 368)(286 403 312 369)
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), (1,270,66,215,14,283,53,228)(2,269,67,214,15,282,54,227)(3,268,68,213,16,281,55,226)(4,267,69,212,17,280,56,225)(5,266,70,211,18,279,57,224)(6,265,71,210,19,278,58,223)(7,264,72,209,20,277,59,222)(8,263,73,234,21,276,60,221)(9,262,74,233,22,275,61,220)(10,261,75,232,23,274,62,219)(11,286,76,231,24,273,63,218)(12,285,77,230,25,272,64,217)(13,284,78,229,26,271,65,216)(27,300,91,242,40,287,104,255)(28,299,92,241,41,312,79,254)(29,298,93,240,42,311,80,253)(30,297,94,239,43,310,81,252)(31,296,95,238,44,309,82,251)(32,295,96,237,45,308,83,250)(33,294,97,236,46,307,84,249)(34,293,98,235,47,306,85,248)(35,292,99,260,48,305,86,247)(36,291,100,259,49,304,87,246)(37,290,101,258,50,303,88,245)(38,289,102,257,51,302,89,244)(39,288,103,256,52,301,90,243)(105,390,179,338,118,377,166,325)(106,389,180,337,119,376,167,324)(107,388,181,336,120,375,168,323)(108,387,182,335,121,374,169,322)(109,386,157,334,122,373,170,321)(110,385,158,333,123,372,171,320)(111,384,159,332,124,371,172,319)(112,383,160,331,125,370,173,318)(113,382,161,330,126,369,174,317)(114,381,162,329,127,368,175,316)(115,380,163,328,128,367,176,315)(116,379,164,327,129,366,177,314)(117,378,165,326,130,365,178,313)(131,395,199,361,144,408,186,348)(132,394,200,360,145,407,187,347)(133,393,201,359,146,406,188,346)(134,392,202,358,147,405,189,345)(135,391,203,357,148,404,190,344)(136,416,204,356,149,403,191,343)(137,415,205,355,150,402,192,342)(138,414,206,354,151,401,193,341)(139,413,207,353,152,400,194,340)(140,412,208,352,153,399,195,339)(141,411,183,351,154,398,196,364)(142,410,184,350,155,397,197,363)(143,409,185,349,156,396,198,362), (1,152,31,129)(2,153,32,130)(3,154,33,105)(4,155,34,106)(5,156,35,107)(6,131,36,108)(7,132,37,109)(8,133,38,110)(9,134,39,111)(10,135,40,112)(11,136,41,113)(12,137,42,114)(13,138,43,115)(14,139,44,116)(15,140,45,117)(16,141,46,118)(17,142,47,119)(18,143,48,120)(19,144,49,121)(20,145,50,122)(21,146,51,123)(22,147,52,124)(23,148,27,125)(24,149,28,126)(25,150,29,127)(26,151,30,128)(53,207,82,164)(54,208,83,165)(55,183,84,166)(56,184,85,167)(57,185,86,168)(58,186,87,169)(59,187,88,170)(60,188,89,171)(61,189,90,172)(62,190,91,173)(63,191,92,174)(64,192,93,175)(65,193,94,176)(66,194,95,177)(67,195,96,178)(68,196,97,179)(69,197,98,180)(70,198,99,181)(71,199,100,182)(72,200,101,157)(73,201,102,158)(74,202,103,159)(75,203,104,160)(76,204,79,161)(77,205,80,162)(78,206,81,163)(209,347,258,321)(210,348,259,322)(211,349,260,323)(212,350,235,324)(213,351,236,325)(214,352,237,326)(215,353,238,327)(216,354,239,328)(217,355,240,329)(218,356,241,330)(219,357,242,331)(220,358,243,332)(221,359,244,333)(222,360,245,334)(223,361,246,335)(224,362,247,336)(225,363,248,337)(226,364,249,338)(227,339,250,313)(228,340,251,314)(229,341,252,315)(230,342,253,316)(231,343,254,317)(232,344,255,318)(233,345,256,319)(234,346,257,320)(261,404,287,370)(262,405,288,371)(263,406,289,372)(264,407,290,373)(265,408,291,374)(266,409,292,375)(267,410,293,376)(268,411,294,377)(269,412,295,378)(270,413,296,379)(271,414,297,380)(272,415,298,381)(273,416,299,382)(274,391,300,383)(275,392,301,384)(276,393,302,385)(277,394,303,386)(278,395,304,387)(279,396,305,388)(280,397,306,389)(281,398,307,390)(282,399,308,365)(283,400,309,366)(284,401,310,367)(285,402,311,368)(286,403,312,369)>;
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), (1,270,66,215,14,283,53,228)(2,269,67,214,15,282,54,227)(3,268,68,213,16,281,55,226)(4,267,69,212,17,280,56,225)(5,266,70,211,18,279,57,224)(6,265,71,210,19,278,58,223)(7,264,72,209,20,277,59,222)(8,263,73,234,21,276,60,221)(9,262,74,233,22,275,61,220)(10,261,75,232,23,274,62,219)(11,286,76,231,24,273,63,218)(12,285,77,230,25,272,64,217)(13,284,78,229,26,271,65,216)(27,300,91,242,40,287,104,255)(28,299,92,241,41,312,79,254)(29,298,93,240,42,311,80,253)(30,297,94,239,43,310,81,252)(31,296,95,238,44,309,82,251)(32,295,96,237,45,308,83,250)(33,294,97,236,46,307,84,249)(34,293,98,235,47,306,85,248)(35,292,99,260,48,305,86,247)(36,291,100,259,49,304,87,246)(37,290,101,258,50,303,88,245)(38,289,102,257,51,302,89,244)(39,288,103,256,52,301,90,243)(105,390,179,338,118,377,166,325)(106,389,180,337,119,376,167,324)(107,388,181,336,120,375,168,323)(108,387,182,335,121,374,169,322)(109,386,157,334,122,373,170,321)(110,385,158,333,123,372,171,320)(111,384,159,332,124,371,172,319)(112,383,160,331,125,370,173,318)(113,382,161,330,126,369,174,317)(114,381,162,329,127,368,175,316)(115,380,163,328,128,367,176,315)(116,379,164,327,129,366,177,314)(117,378,165,326,130,365,178,313)(131,395,199,361,144,408,186,348)(132,394,200,360,145,407,187,347)(133,393,201,359,146,406,188,346)(134,392,202,358,147,405,189,345)(135,391,203,357,148,404,190,344)(136,416,204,356,149,403,191,343)(137,415,205,355,150,402,192,342)(138,414,206,354,151,401,193,341)(139,413,207,353,152,400,194,340)(140,412,208,352,153,399,195,339)(141,411,183,351,154,398,196,364)(142,410,184,350,155,397,197,363)(143,409,185,349,156,396,198,362), (1,152,31,129)(2,153,32,130)(3,154,33,105)(4,155,34,106)(5,156,35,107)(6,131,36,108)(7,132,37,109)(8,133,38,110)(9,134,39,111)(10,135,40,112)(11,136,41,113)(12,137,42,114)(13,138,43,115)(14,139,44,116)(15,140,45,117)(16,141,46,118)(17,142,47,119)(18,143,48,120)(19,144,49,121)(20,145,50,122)(21,146,51,123)(22,147,52,124)(23,148,27,125)(24,149,28,126)(25,150,29,127)(26,151,30,128)(53,207,82,164)(54,208,83,165)(55,183,84,166)(56,184,85,167)(57,185,86,168)(58,186,87,169)(59,187,88,170)(60,188,89,171)(61,189,90,172)(62,190,91,173)(63,191,92,174)(64,192,93,175)(65,193,94,176)(66,194,95,177)(67,195,96,178)(68,196,97,179)(69,197,98,180)(70,198,99,181)(71,199,100,182)(72,200,101,157)(73,201,102,158)(74,202,103,159)(75,203,104,160)(76,204,79,161)(77,205,80,162)(78,206,81,163)(209,347,258,321)(210,348,259,322)(211,349,260,323)(212,350,235,324)(213,351,236,325)(214,352,237,326)(215,353,238,327)(216,354,239,328)(217,355,240,329)(218,356,241,330)(219,357,242,331)(220,358,243,332)(221,359,244,333)(222,360,245,334)(223,361,246,335)(224,362,247,336)(225,363,248,337)(226,364,249,338)(227,339,250,313)(228,340,251,314)(229,341,252,315)(230,342,253,316)(231,343,254,317)(232,344,255,318)(233,345,256,319)(234,346,257,320)(261,404,287,370)(262,405,288,371)(263,406,289,372)(264,407,290,373)(265,408,291,374)(266,409,292,375)(267,410,293,376)(268,411,294,377)(269,412,295,378)(270,413,296,379)(271,414,297,380)(272,415,298,381)(273,416,299,382)(274,391,300,383)(275,392,301,384)(276,393,302,385)(277,394,303,386)(278,395,304,387)(279,396,305,388)(280,397,306,389)(281,398,307,390)(282,399,308,365)(283,400,309,366)(284,401,310,367)(285,402,311,368)(286,403,312,369) );
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)], [(1,270,66,215,14,283,53,228),(2,269,67,214,15,282,54,227),(3,268,68,213,16,281,55,226),(4,267,69,212,17,280,56,225),(5,266,70,211,18,279,57,224),(6,265,71,210,19,278,58,223),(7,264,72,209,20,277,59,222),(8,263,73,234,21,276,60,221),(9,262,74,233,22,275,61,220),(10,261,75,232,23,274,62,219),(11,286,76,231,24,273,63,218),(12,285,77,230,25,272,64,217),(13,284,78,229,26,271,65,216),(27,300,91,242,40,287,104,255),(28,299,92,241,41,312,79,254),(29,298,93,240,42,311,80,253),(30,297,94,239,43,310,81,252),(31,296,95,238,44,309,82,251),(32,295,96,237,45,308,83,250),(33,294,97,236,46,307,84,249),(34,293,98,235,47,306,85,248),(35,292,99,260,48,305,86,247),(36,291,100,259,49,304,87,246),(37,290,101,258,50,303,88,245),(38,289,102,257,51,302,89,244),(39,288,103,256,52,301,90,243),(105,390,179,338,118,377,166,325),(106,389,180,337,119,376,167,324),(107,388,181,336,120,375,168,323),(108,387,182,335,121,374,169,322),(109,386,157,334,122,373,170,321),(110,385,158,333,123,372,171,320),(111,384,159,332,124,371,172,319),(112,383,160,331,125,370,173,318),(113,382,161,330,126,369,174,317),(114,381,162,329,127,368,175,316),(115,380,163,328,128,367,176,315),(116,379,164,327,129,366,177,314),(117,378,165,326,130,365,178,313),(131,395,199,361,144,408,186,348),(132,394,200,360,145,407,187,347),(133,393,201,359,146,406,188,346),(134,392,202,358,147,405,189,345),(135,391,203,357,148,404,190,344),(136,416,204,356,149,403,191,343),(137,415,205,355,150,402,192,342),(138,414,206,354,151,401,193,341),(139,413,207,353,152,400,194,340),(140,412,208,352,153,399,195,339),(141,411,183,351,154,398,196,364),(142,410,184,350,155,397,197,363),(143,409,185,349,156,396,198,362)], [(1,152,31,129),(2,153,32,130),(3,154,33,105),(4,155,34,106),(5,156,35,107),(6,131,36,108),(7,132,37,109),(8,133,38,110),(9,134,39,111),(10,135,40,112),(11,136,41,113),(12,137,42,114),(13,138,43,115),(14,139,44,116),(15,140,45,117),(16,141,46,118),(17,142,47,119),(18,143,48,120),(19,144,49,121),(20,145,50,122),(21,146,51,123),(22,147,52,124),(23,148,27,125),(24,149,28,126),(25,150,29,127),(26,151,30,128),(53,207,82,164),(54,208,83,165),(55,183,84,166),(56,184,85,167),(57,185,86,168),(58,186,87,169),(59,187,88,170),(60,188,89,171),(61,189,90,172),(62,190,91,173),(63,191,92,174),(64,192,93,175),(65,193,94,176),(66,194,95,177),(67,195,96,178),(68,196,97,179),(69,197,98,180),(70,198,99,181),(71,199,100,182),(72,200,101,157),(73,201,102,158),(74,202,103,159),(75,203,104,160),(76,204,79,161),(77,205,80,162),(78,206,81,163),(209,347,258,321),(210,348,259,322),(211,349,260,323),(212,350,235,324),(213,351,236,325),(214,352,237,326),(215,353,238,327),(216,354,239,328),(217,355,240,329),(218,356,241,330),(219,357,242,331),(220,358,243,332),(221,359,244,333),(222,360,245,334),(223,361,246,335),(224,362,247,336),(225,363,248,337),(226,364,249,338),(227,339,250,313),(228,340,251,314),(229,341,252,315),(230,342,253,316),(231,343,254,317),(232,344,255,318),(233,345,256,319),(234,346,257,320),(261,404,287,370),(262,405,288,371),(263,406,289,372),(264,407,290,373),(265,408,291,374),(266,409,292,375),(267,410,293,376),(268,411,294,377),(269,412,295,378),(270,413,296,379),(271,414,297,380),(272,415,298,381),(273,416,299,382),(274,391,300,383),(275,392,301,384),(276,393,302,385),(277,394,303,386),(278,395,304,387),(279,396,305,388),(280,397,306,389),(281,398,307,390),(282,399,308,365),(283,400,309,366),(284,401,310,367),(285,402,311,368),(286,403,312,369)]])
116 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 8A | ··· | 8H | 13A | ··· | 13F | 26A | ··· | 26R | 52A | ··· | 52BT |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 13 | ··· | 13 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 26 | ··· | 26 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
116 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | |||||
| image | C1 | C2 | C2 | C4 | C4 | M4(2) | D13 | Dic13 | D26 | C4×D13 | C52.4C4 |
| kernel | C26.7C42 | C2×C13⋊2C8 | C4×C52 | C13⋊2C8 | C2×C52 | C26 | C42 | C2×C4 | C2×C4 | C4 | C2 |
| # reps | 1 | 2 | 1 | 8 | 4 | 4 | 6 | 12 | 6 | 24 | 48 |
Matrix representation of C26.7C42 ►in GL4(𝔽313) generated by
| 57 | 300 | 0 | 0 |
| 217 | 280 | 0 | 0 |
| 0 | 0 | 13 | 13 |
| 0 | 0 | 300 | 276 |
| 218 | 51 | 0 | 0 |
| 1 | 95 | 0 | 0 |
| 0 | 0 | 32 | 71 |
| 0 | 0 | 285 | 281 |
| 288 | 0 | 0 | 0 |
| 0 | 288 | 0 | 0 |
| 0 | 0 | 227 | 93 |
| 0 | 0 | 220 | 86 |
G:=sub<GL(4,GF(313))| [57,217,0,0,300,280,0,0,0,0,13,300,0,0,13,276],[218,1,0,0,51,95,0,0,0,0,32,285,0,0,71,281],[288,0,0,0,0,288,0,0,0,0,227,220,0,0,93,86] >;
C26.7C42 in GAP, Magma, Sage, TeX
C_{26}._7C_4^2 % in TeX
G:=Group("C26.7C4^2"); // GroupNames label
G:=SmallGroup(416,10);
// by ID
G=gap.SmallGroup(416,10);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,24,217,55,86,13829]);
// Polycyclic
G:=Group<a,b,c|a^26=c^4=1,b^4=a^13,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=a^13*b>;
// generators/relations
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