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G = C26.7C42order 416 = 25·13

2nd non-split extension by C26 of C42 acting via C42/C2×C4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C26.7C42, C42.1D13, C26.9M4(2), C132C83C4, (C4×C52).7C2, C133(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×C132C8).7C2, (C2×C26).45(C2×C4), SmallGroup(416,10)

Series: Derived Chief Lower central Upper central

C1C26 — C26.7C42
C1C13C26C52C2×C52C2×C132C8 — C26.7C42
C13C26 — C26.7C42
C1C2×C4C42

Generators and relations for C26.7C42
 G = < a,b,c | a26=c4=1, b4=a13, bab-1=a-1, ac=ca, cbc-1=a13b >

2C4
2C4
13C8
13C8
13C8
13C8
2C52
2C52
13C2×C8
13C2×C8
13C8⋊C4

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

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

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

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

116 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H8A···8H13A···13F26A···26R52A···52BT
order1222444444448···813···1326···2652···52
size11111111222226···262···22···22···2

116 irreducible representations

dim11111222222
type++++-+
imageC1C2C2C4C4M4(2)D13Dic13D26C4×D13C52.4C4
kernelC26.7C42C2×C132C8C4×C52C132C8C2×C52C26C42C2×C4C2×C4C4C2
# reps12184461262448

Matrix representation of C26.7C42 in GL4(𝔽313) generated by

5730000
21728000
001313
00300276
,
2185100
19500
003271
00285281
,
288000
028800
0022793
0022086
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

Export

Subgroup lattice of C26.7C42 in TeX

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