direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C13⋊2C16, C26⋊2C16, C52.6C8, C104.8C4, C8.21D26, C8.4Dic13, C104.21C22, C13⋊4(C2×C16), (C2×C26).4C8, (C2×C8).9D13, (C2×C104).9C2, C26.17(C2×C8), C52.59(C2×C4), (C2×C52).22C4, C4.3(C13⋊2C8), (C2×C4).8Dic13, C4.10(C2×Dic13), C22.2(C13⋊2C8), C2.2(C2×C13⋊2C8), SmallGroup(416,18)
Series: Derived ►Chief ►Lower central ►Upper central
| C13 — C2×C13⋊2C16 |
Generators and relations for C2×C13⋊2C16
G = < a,b,c | a2=b13=c16=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×C13⋊2C16
►Regular action on 416 points
Generators in S416
(1 228)(2 229)(3 230)(4 231)(5 232)(6 233)(7 234)(8 235)(9 236)(10 237)(11 238)(12 239)(13 240)(14 225)(15 226)(16 227)(17 311)(18 312)(19 313)(20 314)(21 315)(22 316)(23 317)(24 318)(25 319)(26 320)(27 305)(28 306)(29 307)(30 308)(31 309)(32 310)(33 274)(34 275)(35 276)(36 277)(37 278)(38 279)(39 280)(40 281)(41 282)(42 283)(43 284)(44 285)(45 286)(46 287)(47 288)(48 273)(49 202)(50 203)(51 204)(52 205)(53 206)(54 207)(55 208)(56 193)(57 194)(58 195)(59 196)(60 197)(61 198)(62 199)(63 200)(64 201)(65 297)(66 298)(67 299)(68 300)(69 301)(70 302)(71 303)(72 304)(73 289)(74 290)(75 291)(76 292)(77 293)(78 294)(79 295)(80 296)(81 362)(82 363)(83 364)(84 365)(85 366)(86 367)(87 368)(88 353)(89 354)(90 355)(91 356)(92 357)(93 358)(94 359)(95 360)(96 361)(97 386)(98 387)(99 388)(100 389)(101 390)(102 391)(103 392)(104 393)(105 394)(106 395)(107 396)(108 397)(109 398)(110 399)(111 400)(112 385)(113 372)(114 373)(115 374)(116 375)(117 376)(118 377)(119 378)(120 379)(121 380)(122 381)(123 382)(124 383)(125 384)(126 369)(127 370)(128 371)(129 173)(130 174)(131 175)(132 176)(133 161)(134 162)(135 163)(136 164)(137 165)(138 166)(139 167)(140 168)(141 169)(142 170)(143 171)(144 172)(145 410)(146 411)(147 412)(148 413)(149 414)(150 415)(151 416)(152 401)(153 402)(154 403)(155 404)(156 405)(157 406)(158 407)(159 408)(160 409)(177 259)(178 260)(179 261)(180 262)(181 263)(182 264)(183 265)(184 266)(185 267)(186 268)(187 269)(188 270)(189 271)(190 272)(191 257)(192 258)(209 346)(210 347)(211 348)(212 349)(213 350)(214 351)(215 352)(216 337)(217 338)(218 339)(219 340)(220 341)(221 342)(222 343)(223 344)(224 345)(241 331)(242 332)(243 333)(244 334)(245 335)(246 336)(247 321)(248 322)(249 323)(250 324)(251 325)(252 326)(253 327)(254 328)(255 329)(256 330)
(1 76 371 414 346 364 41 144 259 330 203 306 106)(2 107 307 204 331 260 129 42 365 347 415 372 77)(3 78 373 416 348 366 43 130 261 332 205 308 108)(4 109 309 206 333 262 131 44 367 349 401 374 79)(5 80 375 402 350 368 45 132 263 334 207 310 110)(6 111 311 208 335 264 133 46 353 351 403 376 65)(7 66 377 404 352 354 47 134 265 336 193 312 112)(8 97 313 194 321 266 135 48 355 337 405 378 67)(9 68 379 406 338 356 33 136 267 322 195 314 98)(10 99 315 196 323 268 137 34 357 339 407 380 69)(11 70 381 408 340 358 35 138 269 324 197 316 100)(12 101 317 198 325 270 139 36 359 341 409 382 71)(13 72 383 410 342 360 37 140 271 326 199 318 102)(14 103 319 200 327 272 141 38 361 343 411 384 73)(15 74 369 412 344 362 39 142 257 328 201 320 104)(16 105 305 202 329 258 143 40 363 345 413 370 75)(17 55 245 182 161 287 88 214 154 117 297 233 400)(18 385 234 298 118 155 215 89 288 162 183 246 56)(19 57 247 184 163 273 90 216 156 119 299 235 386)(20 387 236 300 120 157 217 91 274 164 185 248 58)(21 59 249 186 165 275 92 218 158 121 301 237 388)(22 389 238 302 122 159 219 93 276 166 187 250 60)(23 61 251 188 167 277 94 220 160 123 303 239 390)(24 391 240 304 124 145 221 95 278 168 189 252 62)(25 63 253 190 169 279 96 222 146 125 289 225 392)(26 393 226 290 126 147 223 81 280 170 191 254 64)(27 49 255 192 171 281 82 224 148 127 291 227 394)(28 395 228 292 128 149 209 83 282 172 177 256 50)(29 51 241 178 173 283 84 210 150 113 293 229 396)(30 397 230 294 114 151 211 85 284 174 179 242 52)(31 53 243 180 175 285 86 212 152 115 295 231 398)(32 399 232 296 116 153 213 87 286 176 181 244 54)
(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)
G:=sub<Sym(416)| (1,228)(2,229)(3,230)(4,231)(5,232)(6,233)(7,234)(8,235)(9,236)(10,237)(11,238)(12,239)(13,240)(14,225)(15,226)(16,227)(17,311)(18,312)(19,313)(20,314)(21,315)(22,316)(23,317)(24,318)(25,319)(26,320)(27,305)(28,306)(29,307)(30,308)(31,309)(32,310)(33,274)(34,275)(35,276)(36,277)(37,278)(38,279)(39,280)(40,281)(41,282)(42,283)(43,284)(44,285)(45,286)(46,287)(47,288)(48,273)(49,202)(50,203)(51,204)(52,205)(53,206)(54,207)(55,208)(56,193)(57,194)(58,195)(59,196)(60,197)(61,198)(62,199)(63,200)(64,201)(65,297)(66,298)(67,299)(68,300)(69,301)(70,302)(71,303)(72,304)(73,289)(74,290)(75,291)(76,292)(77,293)(78,294)(79,295)(80,296)(81,362)(82,363)(83,364)(84,365)(85,366)(86,367)(87,368)(88,353)(89,354)(90,355)(91,356)(92,357)(93,358)(94,359)(95,360)(96,361)(97,386)(98,387)(99,388)(100,389)(101,390)(102,391)(103,392)(104,393)(105,394)(106,395)(107,396)(108,397)(109,398)(110,399)(111,400)(112,385)(113,372)(114,373)(115,374)(116,375)(117,376)(118,377)(119,378)(120,379)(121,380)(122,381)(123,382)(124,383)(125,384)(126,369)(127,370)(128,371)(129,173)(130,174)(131,175)(132,176)(133,161)(134,162)(135,163)(136,164)(137,165)(138,166)(139,167)(140,168)(141,169)(142,170)(143,171)(144,172)(145,410)(146,411)(147,412)(148,413)(149,414)(150,415)(151,416)(152,401)(153,402)(154,403)(155,404)(156,405)(157,406)(158,407)(159,408)(160,409)(177,259)(178,260)(179,261)(180,262)(181,263)(182,264)(183,265)(184,266)(185,267)(186,268)(187,269)(188,270)(189,271)(190,272)(191,257)(192,258)(209,346)(210,347)(211,348)(212,349)(213,350)(214,351)(215,352)(216,337)(217,338)(218,339)(219,340)(220,341)(221,342)(222,343)(223,344)(224,345)(241,331)(242,332)(243,333)(244,334)(245,335)(246,336)(247,321)(248,322)(249,323)(250,324)(251,325)(252,326)(253,327)(254,328)(255,329)(256,330), (1,76,371,414,346,364,41,144,259,330,203,306,106)(2,107,307,204,331,260,129,42,365,347,415,372,77)(3,78,373,416,348,366,43,130,261,332,205,308,108)(4,109,309,206,333,262,131,44,367,349,401,374,79)(5,80,375,402,350,368,45,132,263,334,207,310,110)(6,111,311,208,335,264,133,46,353,351,403,376,65)(7,66,377,404,352,354,47,134,265,336,193,312,112)(8,97,313,194,321,266,135,48,355,337,405,378,67)(9,68,379,406,338,356,33,136,267,322,195,314,98)(10,99,315,196,323,268,137,34,357,339,407,380,69)(11,70,381,408,340,358,35,138,269,324,197,316,100)(12,101,317,198,325,270,139,36,359,341,409,382,71)(13,72,383,410,342,360,37,140,271,326,199,318,102)(14,103,319,200,327,272,141,38,361,343,411,384,73)(15,74,369,412,344,362,39,142,257,328,201,320,104)(16,105,305,202,329,258,143,40,363,345,413,370,75)(17,55,245,182,161,287,88,214,154,117,297,233,400)(18,385,234,298,118,155,215,89,288,162,183,246,56)(19,57,247,184,163,273,90,216,156,119,299,235,386)(20,387,236,300,120,157,217,91,274,164,185,248,58)(21,59,249,186,165,275,92,218,158,121,301,237,388)(22,389,238,302,122,159,219,93,276,166,187,250,60)(23,61,251,188,167,277,94,220,160,123,303,239,390)(24,391,240,304,124,145,221,95,278,168,189,252,62)(25,63,253,190,169,279,96,222,146,125,289,225,392)(26,393,226,290,126,147,223,81,280,170,191,254,64)(27,49,255,192,171,281,82,224,148,127,291,227,394)(28,395,228,292,128,149,209,83,282,172,177,256,50)(29,51,241,178,173,283,84,210,150,113,293,229,396)(30,397,230,294,114,151,211,85,284,174,179,242,52)(31,53,243,180,175,285,86,212,152,115,295,231,398)(32,399,232,296,116,153,213,87,286,176,181,244,54), (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)>;
G:=Group( (1,228)(2,229)(3,230)(4,231)(5,232)(6,233)(7,234)(8,235)(9,236)(10,237)(11,238)(12,239)(13,240)(14,225)(15,226)(16,227)(17,311)(18,312)(19,313)(20,314)(21,315)(22,316)(23,317)(24,318)(25,319)(26,320)(27,305)(28,306)(29,307)(30,308)(31,309)(32,310)(33,274)(34,275)(35,276)(36,277)(37,278)(38,279)(39,280)(40,281)(41,282)(42,283)(43,284)(44,285)(45,286)(46,287)(47,288)(48,273)(49,202)(50,203)(51,204)(52,205)(53,206)(54,207)(55,208)(56,193)(57,194)(58,195)(59,196)(60,197)(61,198)(62,199)(63,200)(64,201)(65,297)(66,298)(67,299)(68,300)(69,301)(70,302)(71,303)(72,304)(73,289)(74,290)(75,291)(76,292)(77,293)(78,294)(79,295)(80,296)(81,362)(82,363)(83,364)(84,365)(85,366)(86,367)(87,368)(88,353)(89,354)(90,355)(91,356)(92,357)(93,358)(94,359)(95,360)(96,361)(97,386)(98,387)(99,388)(100,389)(101,390)(102,391)(103,392)(104,393)(105,394)(106,395)(107,396)(108,397)(109,398)(110,399)(111,400)(112,385)(113,372)(114,373)(115,374)(116,375)(117,376)(118,377)(119,378)(120,379)(121,380)(122,381)(123,382)(124,383)(125,384)(126,369)(127,370)(128,371)(129,173)(130,174)(131,175)(132,176)(133,161)(134,162)(135,163)(136,164)(137,165)(138,166)(139,167)(140,168)(141,169)(142,170)(143,171)(144,172)(145,410)(146,411)(147,412)(148,413)(149,414)(150,415)(151,416)(152,401)(153,402)(154,403)(155,404)(156,405)(157,406)(158,407)(159,408)(160,409)(177,259)(178,260)(179,261)(180,262)(181,263)(182,264)(183,265)(184,266)(185,267)(186,268)(187,269)(188,270)(189,271)(190,272)(191,257)(192,258)(209,346)(210,347)(211,348)(212,349)(213,350)(214,351)(215,352)(216,337)(217,338)(218,339)(219,340)(220,341)(221,342)(222,343)(223,344)(224,345)(241,331)(242,332)(243,333)(244,334)(245,335)(246,336)(247,321)(248,322)(249,323)(250,324)(251,325)(252,326)(253,327)(254,328)(255,329)(256,330), (1,76,371,414,346,364,41,144,259,330,203,306,106)(2,107,307,204,331,260,129,42,365,347,415,372,77)(3,78,373,416,348,366,43,130,261,332,205,308,108)(4,109,309,206,333,262,131,44,367,349,401,374,79)(5,80,375,402,350,368,45,132,263,334,207,310,110)(6,111,311,208,335,264,133,46,353,351,403,376,65)(7,66,377,404,352,354,47,134,265,336,193,312,112)(8,97,313,194,321,266,135,48,355,337,405,378,67)(9,68,379,406,338,356,33,136,267,322,195,314,98)(10,99,315,196,323,268,137,34,357,339,407,380,69)(11,70,381,408,340,358,35,138,269,324,197,316,100)(12,101,317,198,325,270,139,36,359,341,409,382,71)(13,72,383,410,342,360,37,140,271,326,199,318,102)(14,103,319,200,327,272,141,38,361,343,411,384,73)(15,74,369,412,344,362,39,142,257,328,201,320,104)(16,105,305,202,329,258,143,40,363,345,413,370,75)(17,55,245,182,161,287,88,214,154,117,297,233,400)(18,385,234,298,118,155,215,89,288,162,183,246,56)(19,57,247,184,163,273,90,216,156,119,299,235,386)(20,387,236,300,120,157,217,91,274,164,185,248,58)(21,59,249,186,165,275,92,218,158,121,301,237,388)(22,389,238,302,122,159,219,93,276,166,187,250,60)(23,61,251,188,167,277,94,220,160,123,303,239,390)(24,391,240,304,124,145,221,95,278,168,189,252,62)(25,63,253,190,169,279,96,222,146,125,289,225,392)(26,393,226,290,126,147,223,81,280,170,191,254,64)(27,49,255,192,171,281,82,224,148,127,291,227,394)(28,395,228,292,128,149,209,83,282,172,177,256,50)(29,51,241,178,173,283,84,210,150,113,293,229,396)(30,397,230,294,114,151,211,85,284,174,179,242,52)(31,53,243,180,175,285,86,212,152,115,295,231,398)(32,399,232,296,116,153,213,87,286,176,181,244,54), (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) );
G=PermutationGroup([[(1,228),(2,229),(3,230),(4,231),(5,232),(6,233),(7,234),(8,235),(9,236),(10,237),(11,238),(12,239),(13,240),(14,225),(15,226),(16,227),(17,311),(18,312),(19,313),(20,314),(21,315),(22,316),(23,317),(24,318),(25,319),(26,320),(27,305),(28,306),(29,307),(30,308),(31,309),(32,310),(33,274),(34,275),(35,276),(36,277),(37,278),(38,279),(39,280),(40,281),(41,282),(42,283),(43,284),(44,285),(45,286),(46,287),(47,288),(48,273),(49,202),(50,203),(51,204),(52,205),(53,206),(54,207),(55,208),(56,193),(57,194),(58,195),(59,196),(60,197),(61,198),(62,199),(63,200),(64,201),(65,297),(66,298),(67,299),(68,300),(69,301),(70,302),(71,303),(72,304),(73,289),(74,290),(75,291),(76,292),(77,293),(78,294),(79,295),(80,296),(81,362),(82,363),(83,364),(84,365),(85,366),(86,367),(87,368),(88,353),(89,354),(90,355),(91,356),(92,357),(93,358),(94,359),(95,360),(96,361),(97,386),(98,387),(99,388),(100,389),(101,390),(102,391),(103,392),(104,393),(105,394),(106,395),(107,396),(108,397),(109,398),(110,399),(111,400),(112,385),(113,372),(114,373),(115,374),(116,375),(117,376),(118,377),(119,378),(120,379),(121,380),(122,381),(123,382),(124,383),(125,384),(126,369),(127,370),(128,371),(129,173),(130,174),(131,175),(132,176),(133,161),(134,162),(135,163),(136,164),(137,165),(138,166),(139,167),(140,168),(141,169),(142,170),(143,171),(144,172),(145,410),(146,411),(147,412),(148,413),(149,414),(150,415),(151,416),(152,401),(153,402),(154,403),(155,404),(156,405),(157,406),(158,407),(159,408),(160,409),(177,259),(178,260),(179,261),(180,262),(181,263),(182,264),(183,265),(184,266),(185,267),(186,268),(187,269),(188,270),(189,271),(190,272),(191,257),(192,258),(209,346),(210,347),(211,348),(212,349),(213,350),(214,351),(215,352),(216,337),(217,338),(218,339),(219,340),(220,341),(221,342),(222,343),(223,344),(224,345),(241,331),(242,332),(243,333),(244,334),(245,335),(246,336),(247,321),(248,322),(249,323),(250,324),(251,325),(252,326),(253,327),(254,328),(255,329),(256,330)], [(1,76,371,414,346,364,41,144,259,330,203,306,106),(2,107,307,204,331,260,129,42,365,347,415,372,77),(3,78,373,416,348,366,43,130,261,332,205,308,108),(4,109,309,206,333,262,131,44,367,349,401,374,79),(5,80,375,402,350,368,45,132,263,334,207,310,110),(6,111,311,208,335,264,133,46,353,351,403,376,65),(7,66,377,404,352,354,47,134,265,336,193,312,112),(8,97,313,194,321,266,135,48,355,337,405,378,67),(9,68,379,406,338,356,33,136,267,322,195,314,98),(10,99,315,196,323,268,137,34,357,339,407,380,69),(11,70,381,408,340,358,35,138,269,324,197,316,100),(12,101,317,198,325,270,139,36,359,341,409,382,71),(13,72,383,410,342,360,37,140,271,326,199,318,102),(14,103,319,200,327,272,141,38,361,343,411,384,73),(15,74,369,412,344,362,39,142,257,328,201,320,104),(16,105,305,202,329,258,143,40,363,345,413,370,75),(17,55,245,182,161,287,88,214,154,117,297,233,400),(18,385,234,298,118,155,215,89,288,162,183,246,56),(19,57,247,184,163,273,90,216,156,119,299,235,386),(20,387,236,300,120,157,217,91,274,164,185,248,58),(21,59,249,186,165,275,92,218,158,121,301,237,388),(22,389,238,302,122,159,219,93,276,166,187,250,60),(23,61,251,188,167,277,94,220,160,123,303,239,390),(24,391,240,304,124,145,221,95,278,168,189,252,62),(25,63,253,190,169,279,96,222,146,125,289,225,392),(26,393,226,290,126,147,223,81,280,170,191,254,64),(27,49,255,192,171,281,82,224,148,127,291,227,394),(28,395,228,292,128,149,209,83,282,172,177,256,50),(29,51,241,178,173,283,84,210,150,113,293,229,396),(30,397,230,294,114,151,211,85,284,174,179,242,52),(31,53,243,180,175,285,86,212,152,115,295,231,398),(32,399,232,296,116,153,213,87,286,176,181,244,54)], [(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)]])
128 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 8A | ··· | 8H | 13A | ··· | 13F | 16A | ··· | 16P | 26A | ··· | 26R | 52A | ··· | 52X | 104A | ··· | 104AV |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 13 | ··· | 13 | 16 | ··· | 16 | 26 | ··· | 26 | 52 | ··· | 52 | 104 | ··· | 104 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 13 | ··· | 13 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
128 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | ||||||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | C8 | C16 | D13 | Dic13 | D26 | Dic13 | C13⋊2C8 | C13⋊2C8 | C13⋊2C16 |
| kernel | C2×C13⋊2C16 | C13⋊2C16 | C2×C104 | C104 | C2×C52 | C52 | C2×C26 | C26 | C2×C8 | C8 | C8 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 4 | 4 | 16 | 6 | 6 | 6 | 6 | 12 | 12 | 48 |
Matrix representation of C2×C13⋊2C16 ►in GL4(𝔽1249) generated by
| 1248 | 0 | 0 | 0 |
| 0 | 1248 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1235 | 1248 |
| 0 | 0 | 1236 | 1248 |
| 1125 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 229 | 419 |
| 0 | 0 | 319 | 1020 |
G:=sub<GL(4,GF(1249))| [1248,0,0,0,0,1248,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,1235,1236,0,0,1248,1248],[1125,0,0,0,0,1,0,0,0,0,229,319,0,0,419,1020] >;
C2×C13⋊2C16 in GAP, Magma, Sage, TeX
C_2\times C_{13}\rtimes_2C_{16} % in TeX
G:=Group("C2xC13:2C16"); // GroupNames label
G:=SmallGroup(416,18);
// by ID
G=gap.SmallGroup(416,18);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,24,50,69,13829]);
// Polycyclic
G:=Group<a,b,c|a^2=b^13=c^16=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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