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## G = C2×C13⋊2C16order 416 = 25·13

### Direct product of C2 and C13⋊2C16

Series: Derived Chief Lower central Upper central

 Derived series C1 — C13 — C2×C13⋊2C16
 Chief series C1 — C13 — C26 — C52 — C104 — C13⋊2C16 — C2×C13⋊2C16
 Lower central C13 — C2×C13⋊2C16
 Upper central C1 — C2×C8

Generators and relations for C2×C132C16
G = < a,b,c | a2=b13=c16=1, ab=ba, ac=ca, cbc-1=b-1 >

Smallest permutation representation of C2×C132C16
Regular action on 416 points
Generators in S416
(1 141)(2 142)(3 143)(4 144)(5 129)(6 130)(7 131)(8 132)(9 133)(10 134)(11 135)(12 136)(13 137)(14 138)(15 139)(16 140)(17 367)(18 368)(19 353)(20 354)(21 355)(22 356)(23 357)(24 358)(25 359)(26 360)(27 361)(28 362)(29 363)(30 364)(31 365)(32 366)(33 277)(34 278)(35 279)(36 280)(37 281)(38 282)(39 283)(40 284)(41 285)(42 286)(43 287)(44 288)(45 273)(46 274)(47 275)(48 276)(49 292)(50 293)(51 294)(52 295)(53 296)(54 297)(55 298)(56 299)(57 300)(58 301)(59 302)(60 303)(61 304)(62 289)(63 290)(64 291)(65 320)(66 305)(67 306)(68 307)(69 308)(70 309)(71 310)(72 311)(73 312)(74 313)(75 314)(76 315)(77 316)(78 317)(79 318)(80 319)(81 258)(82 259)(83 260)(84 261)(85 262)(86 263)(87 264)(88 265)(89 266)(90 267)(91 268)(92 269)(93 270)(94 271)(95 272)(96 257)(97 167)(98 168)(99 169)(100 170)(101 171)(102 172)(103 173)(104 174)(105 175)(106 176)(107 161)(108 162)(109 163)(110 164)(111 165)(112 166)(113 217)(114 218)(115 219)(116 220)(117 221)(118 222)(119 223)(120 224)(121 209)(122 210)(123 211)(124 212)(125 213)(126 214)(127 215)(128 216)(145 325)(146 326)(147 327)(148 328)(149 329)(150 330)(151 331)(152 332)(153 333)(154 334)(155 335)(156 336)(157 321)(158 322)(159 323)(160 324)(177 395)(178 396)(179 397)(180 398)(181 399)(182 400)(183 385)(184 386)(185 387)(186 388)(187 389)(188 390)(189 391)(190 392)(191 393)(192 394)(193 378)(194 379)(195 380)(196 381)(197 382)(198 383)(199 384)(200 369)(201 370)(202 371)(203 372)(204 373)(205 374)(206 375)(207 376)(208 377)(225 409)(226 410)(227 411)(228 412)(229 413)(230 414)(231 415)(232 416)(233 401)(234 402)(235 403)(236 404)(237 405)(238 406)(239 407)(240 408)(241 350)(242 351)(243 352)(244 337)(245 338)(246 339)(247 340)(248 341)(249 342)(250 343)(251 344)(252 345)(253 346)(254 347)(255 348)(256 349)
(1 98 180 368 220 379 280 411 88 293 346 319 145)(2 146 320 347 294 89 412 281 380 221 353 181 99)(3 100 182 354 222 381 282 413 90 295 348 305 147)(4 148 306 349 296 91 414 283 382 223 355 183 101)(5 102 184 356 224 383 284 415 92 297 350 307 149)(6 150 308 351 298 93 416 285 384 209 357 185 103)(7 104 186 358 210 369 286 401 94 299 352 309 151)(8 152 310 337 300 95 402 287 370 211 359 187 105)(9 106 188 360 212 371 288 403 96 301 338 311 153)(10 154 312 339 302 81 404 273 372 213 361 189 107)(11 108 190 362 214 373 274 405 82 303 340 313 155)(12 156 314 341 304 83 406 275 374 215 363 191 109)(13 110 192 364 216 375 276 407 84 289 342 315 157)(14 158 316 343 290 85 408 277 376 217 365 177 111)(15 112 178 366 218 377 278 409 86 291 344 317 159)(16 160 318 345 292 87 410 279 378 219 367 179 97)(17 397 167 140 324 79 252 49 264 226 35 193 115)(18 116 194 36 227 265 50 253 80 325 141 168 398)(19 399 169 142 326 65 254 51 266 228 37 195 117)(20 118 196 38 229 267 52 255 66 327 143 170 400)(21 385 171 144 328 67 256 53 268 230 39 197 119)(22 120 198 40 231 269 54 241 68 329 129 172 386)(23 387 173 130 330 69 242 55 270 232 41 199 121)(24 122 200 42 233 271 56 243 70 331 131 174 388)(25 389 175 132 332 71 244 57 272 234 43 201 123)(26 124 202 44 235 257 58 245 72 333 133 176 390)(27 391 161 134 334 73 246 59 258 236 45 203 125)(28 126 204 46 237 259 60 247 74 335 135 162 392)(29 393 163 136 336 75 248 61 260 238 47 205 127)(30 128 206 48 239 261 62 249 76 321 137 164 394)(31 395 165 138 322 77 250 63 262 240 33 207 113)(32 114 208 34 225 263 64 251 78 323 139 166 396)
(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)| (1,141)(2,142)(3,143)(4,144)(5,129)(6,130)(7,131)(8,132)(9,133)(10,134)(11,135)(12,136)(13,137)(14,138)(15,139)(16,140)(17,367)(18,368)(19,353)(20,354)(21,355)(22,356)(23,357)(24,358)(25,359)(26,360)(27,361)(28,362)(29,363)(30,364)(31,365)(32,366)(33,277)(34,278)(35,279)(36,280)(37,281)(38,282)(39,283)(40,284)(41,285)(42,286)(43,287)(44,288)(45,273)(46,274)(47,275)(48,276)(49,292)(50,293)(51,294)(52,295)(53,296)(54,297)(55,298)(56,299)(57,300)(58,301)(59,302)(60,303)(61,304)(62,289)(63,290)(64,291)(65,320)(66,305)(67,306)(68,307)(69,308)(70,309)(71,310)(72,311)(73,312)(74,313)(75,314)(76,315)(77,316)(78,317)(79,318)(80,319)(81,258)(82,259)(83,260)(84,261)(85,262)(86,263)(87,264)(88,265)(89,266)(90,267)(91,268)(92,269)(93,270)(94,271)(95,272)(96,257)(97,167)(98,168)(99,169)(100,170)(101,171)(102,172)(103,173)(104,174)(105,175)(106,176)(107,161)(108,162)(109,163)(110,164)(111,165)(112,166)(113,217)(114,218)(115,219)(116,220)(117,221)(118,222)(119,223)(120,224)(121,209)(122,210)(123,211)(124,212)(125,213)(126,214)(127,215)(128,216)(145,325)(146,326)(147,327)(148,328)(149,329)(150,330)(151,331)(152,332)(153,333)(154,334)(155,335)(156,336)(157,321)(158,322)(159,323)(160,324)(177,395)(178,396)(179,397)(180,398)(181,399)(182,400)(183,385)(184,386)(185,387)(186,388)(187,389)(188,390)(189,391)(190,392)(191,393)(192,394)(193,378)(194,379)(195,380)(196,381)(197,382)(198,383)(199,384)(200,369)(201,370)(202,371)(203,372)(204,373)(205,374)(206,375)(207,376)(208,377)(225,409)(226,410)(227,411)(228,412)(229,413)(230,414)(231,415)(232,416)(233,401)(234,402)(235,403)(236,404)(237,405)(238,406)(239,407)(240,408)(241,350)(242,351)(243,352)(244,337)(245,338)(246,339)(247,340)(248,341)(249,342)(250,343)(251,344)(252,345)(253,346)(254,347)(255,348)(256,349), (1,98,180,368,220,379,280,411,88,293,346,319,145)(2,146,320,347,294,89,412,281,380,221,353,181,99)(3,100,182,354,222,381,282,413,90,295,348,305,147)(4,148,306,349,296,91,414,283,382,223,355,183,101)(5,102,184,356,224,383,284,415,92,297,350,307,149)(6,150,308,351,298,93,416,285,384,209,357,185,103)(7,104,186,358,210,369,286,401,94,299,352,309,151)(8,152,310,337,300,95,402,287,370,211,359,187,105)(9,106,188,360,212,371,288,403,96,301,338,311,153)(10,154,312,339,302,81,404,273,372,213,361,189,107)(11,108,190,362,214,373,274,405,82,303,340,313,155)(12,156,314,341,304,83,406,275,374,215,363,191,109)(13,110,192,364,216,375,276,407,84,289,342,315,157)(14,158,316,343,290,85,408,277,376,217,365,177,111)(15,112,178,366,218,377,278,409,86,291,344,317,159)(16,160,318,345,292,87,410,279,378,219,367,179,97)(17,397,167,140,324,79,252,49,264,226,35,193,115)(18,116,194,36,227,265,50,253,80,325,141,168,398)(19,399,169,142,326,65,254,51,266,228,37,195,117)(20,118,196,38,229,267,52,255,66,327,143,170,400)(21,385,171,144,328,67,256,53,268,230,39,197,119)(22,120,198,40,231,269,54,241,68,329,129,172,386)(23,387,173,130,330,69,242,55,270,232,41,199,121)(24,122,200,42,233,271,56,243,70,331,131,174,388)(25,389,175,132,332,71,244,57,272,234,43,201,123)(26,124,202,44,235,257,58,245,72,333,133,176,390)(27,391,161,134,334,73,246,59,258,236,45,203,125)(28,126,204,46,237,259,60,247,74,335,135,162,392)(29,393,163,136,336,75,248,61,260,238,47,205,127)(30,128,206,48,239,261,62,249,76,321,137,164,394)(31,395,165,138,322,77,250,63,262,240,33,207,113)(32,114,208,34,225,263,64,251,78,323,139,166,396), (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( (1,141)(2,142)(3,143)(4,144)(5,129)(6,130)(7,131)(8,132)(9,133)(10,134)(11,135)(12,136)(13,137)(14,138)(15,139)(16,140)(17,367)(18,368)(19,353)(20,354)(21,355)(22,356)(23,357)(24,358)(25,359)(26,360)(27,361)(28,362)(29,363)(30,364)(31,365)(32,366)(33,277)(34,278)(35,279)(36,280)(37,281)(38,282)(39,283)(40,284)(41,285)(42,286)(43,287)(44,288)(45,273)(46,274)(47,275)(48,276)(49,292)(50,293)(51,294)(52,295)(53,296)(54,297)(55,298)(56,299)(57,300)(58,301)(59,302)(60,303)(61,304)(62,289)(63,290)(64,291)(65,320)(66,305)(67,306)(68,307)(69,308)(70,309)(71,310)(72,311)(73,312)(74,313)(75,314)(76,315)(77,316)(78,317)(79,318)(80,319)(81,258)(82,259)(83,260)(84,261)(85,262)(86,263)(87,264)(88,265)(89,266)(90,267)(91,268)(92,269)(93,270)(94,271)(95,272)(96,257)(97,167)(98,168)(99,169)(100,170)(101,171)(102,172)(103,173)(104,174)(105,175)(106,176)(107,161)(108,162)(109,163)(110,164)(111,165)(112,166)(113,217)(114,218)(115,219)(116,220)(117,221)(118,222)(119,223)(120,224)(121,209)(122,210)(123,211)(124,212)(125,213)(126,214)(127,215)(128,216)(145,325)(146,326)(147,327)(148,328)(149,329)(150,330)(151,331)(152,332)(153,333)(154,334)(155,335)(156,336)(157,321)(158,322)(159,323)(160,324)(177,395)(178,396)(179,397)(180,398)(181,399)(182,400)(183,385)(184,386)(185,387)(186,388)(187,389)(188,390)(189,391)(190,392)(191,393)(192,394)(193,378)(194,379)(195,380)(196,381)(197,382)(198,383)(199,384)(200,369)(201,370)(202,371)(203,372)(204,373)(205,374)(206,375)(207,376)(208,377)(225,409)(226,410)(227,411)(228,412)(229,413)(230,414)(231,415)(232,416)(233,401)(234,402)(235,403)(236,404)(237,405)(238,406)(239,407)(240,408)(241,350)(242,351)(243,352)(244,337)(245,338)(246,339)(247,340)(248,341)(249,342)(250,343)(251,344)(252,345)(253,346)(254,347)(255,348)(256,349), (1,98,180,368,220,379,280,411,88,293,346,319,145)(2,146,320,347,294,89,412,281,380,221,353,181,99)(3,100,182,354,222,381,282,413,90,295,348,305,147)(4,148,306,349,296,91,414,283,382,223,355,183,101)(5,102,184,356,224,383,284,415,92,297,350,307,149)(6,150,308,351,298,93,416,285,384,209,357,185,103)(7,104,186,358,210,369,286,401,94,299,352,309,151)(8,152,310,337,300,95,402,287,370,211,359,187,105)(9,106,188,360,212,371,288,403,96,301,338,311,153)(10,154,312,339,302,81,404,273,372,213,361,189,107)(11,108,190,362,214,373,274,405,82,303,340,313,155)(12,156,314,341,304,83,406,275,374,215,363,191,109)(13,110,192,364,216,375,276,407,84,289,342,315,157)(14,158,316,343,290,85,408,277,376,217,365,177,111)(15,112,178,366,218,377,278,409,86,291,344,317,159)(16,160,318,345,292,87,410,279,378,219,367,179,97)(17,397,167,140,324,79,252,49,264,226,35,193,115)(18,116,194,36,227,265,50,253,80,325,141,168,398)(19,399,169,142,326,65,254,51,266,228,37,195,117)(20,118,196,38,229,267,52,255,66,327,143,170,400)(21,385,171,144,328,67,256,53,268,230,39,197,119)(22,120,198,40,231,269,54,241,68,329,129,172,386)(23,387,173,130,330,69,242,55,270,232,41,199,121)(24,122,200,42,233,271,56,243,70,331,131,174,388)(25,389,175,132,332,71,244,57,272,234,43,201,123)(26,124,202,44,235,257,58,245,72,333,133,176,390)(27,391,161,134,334,73,246,59,258,236,45,203,125)(28,126,204,46,237,259,60,247,74,335,135,162,392)(29,393,163,136,336,75,248,61,260,238,47,205,127)(30,128,206,48,239,261,62,249,76,321,137,164,394)(31,395,165,138,322,77,250,63,262,240,33,207,113)(32,114,208,34,225,263,64,251,78,323,139,166,396), (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([(1,141),(2,142),(3,143),(4,144),(5,129),(6,130),(7,131),(8,132),(9,133),(10,134),(11,135),(12,136),(13,137),(14,138),(15,139),(16,140),(17,367),(18,368),(19,353),(20,354),(21,355),(22,356),(23,357),(24,358),(25,359),(26,360),(27,361),(28,362),(29,363),(30,364),(31,365),(32,366),(33,277),(34,278),(35,279),(36,280),(37,281),(38,282),(39,283),(40,284),(41,285),(42,286),(43,287),(44,288),(45,273),(46,274),(47,275),(48,276),(49,292),(50,293),(51,294),(52,295),(53,296),(54,297),(55,298),(56,299),(57,300),(58,301),(59,302),(60,303),(61,304),(62,289),(63,290),(64,291),(65,320),(66,305),(67,306),(68,307),(69,308),(70,309),(71,310),(72,311),(73,312),(74,313),(75,314),(76,315),(77,316),(78,317),(79,318),(80,319),(81,258),(82,259),(83,260),(84,261),(85,262),(86,263),(87,264),(88,265),(89,266),(90,267),(91,268),(92,269),(93,270),(94,271),(95,272),(96,257),(97,167),(98,168),(99,169),(100,170),(101,171),(102,172),(103,173),(104,174),(105,175),(106,176),(107,161),(108,162),(109,163),(110,164),(111,165),(112,166),(113,217),(114,218),(115,219),(116,220),(117,221),(118,222),(119,223),(120,224),(121,209),(122,210),(123,211),(124,212),(125,213),(126,214),(127,215),(128,216),(145,325),(146,326),(147,327),(148,328),(149,329),(150,330),(151,331),(152,332),(153,333),(154,334),(155,335),(156,336),(157,321),(158,322),(159,323),(160,324),(177,395),(178,396),(179,397),(180,398),(181,399),(182,400),(183,385),(184,386),(185,387),(186,388),(187,389),(188,390),(189,391),(190,392),(191,393),(192,394),(193,378),(194,379),(195,380),(196,381),(197,382),(198,383),(199,384),(200,369),(201,370),(202,371),(203,372),(204,373),(205,374),(206,375),(207,376),(208,377),(225,409),(226,410),(227,411),(228,412),(229,413),(230,414),(231,415),(232,416),(233,401),(234,402),(235,403),(236,404),(237,405),(238,406),(239,407),(240,408),(241,350),(242,351),(243,352),(244,337),(245,338),(246,339),(247,340),(248,341),(249,342),(250,343),(251,344),(252,345),(253,346),(254,347),(255,348),(256,349)], [(1,98,180,368,220,379,280,411,88,293,346,319,145),(2,146,320,347,294,89,412,281,380,221,353,181,99),(3,100,182,354,222,381,282,413,90,295,348,305,147),(4,148,306,349,296,91,414,283,382,223,355,183,101),(5,102,184,356,224,383,284,415,92,297,350,307,149),(6,150,308,351,298,93,416,285,384,209,357,185,103),(7,104,186,358,210,369,286,401,94,299,352,309,151),(8,152,310,337,300,95,402,287,370,211,359,187,105),(9,106,188,360,212,371,288,403,96,301,338,311,153),(10,154,312,339,302,81,404,273,372,213,361,189,107),(11,108,190,362,214,373,274,405,82,303,340,313,155),(12,156,314,341,304,83,406,275,374,215,363,191,109),(13,110,192,364,216,375,276,407,84,289,342,315,157),(14,158,316,343,290,85,408,277,376,217,365,177,111),(15,112,178,366,218,377,278,409,86,291,344,317,159),(16,160,318,345,292,87,410,279,378,219,367,179,97),(17,397,167,140,324,79,252,49,264,226,35,193,115),(18,116,194,36,227,265,50,253,80,325,141,168,398),(19,399,169,142,326,65,254,51,266,228,37,195,117),(20,118,196,38,229,267,52,255,66,327,143,170,400),(21,385,171,144,328,67,256,53,268,230,39,197,119),(22,120,198,40,231,269,54,241,68,329,129,172,386),(23,387,173,130,330,69,242,55,270,232,41,199,121),(24,122,200,42,233,271,56,243,70,331,131,174,388),(25,389,175,132,332,71,244,57,272,234,43,201,123),(26,124,202,44,235,257,58,245,72,333,133,176,390),(27,391,161,134,334,73,246,59,258,236,45,203,125),(28,126,204,46,237,259,60,247,74,335,135,162,392),(29,393,163,136,336,75,248,61,260,238,47,205,127),(30,128,206,48,239,261,62,249,76,321,137,164,394),(31,395,165,138,322,77,250,63,262,240,33,207,113),(32,114,208,34,225,263,64,251,78,323,139,166,396)], [(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×C132C16 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×C132C16 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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