metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C13⋊2Q32, C8.7D26, C52.6D4, Q16.D13, C26.11D8, C104.5C22, Dic52.2C2, C13⋊2C16.1C2, C2.7(D4⋊D13), C4.4(C13⋊D4), (C13×Q16).1C2, SmallGroup(416,36)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C13⋊Q32
G = < a,b,c | a13=b16=1, c2=b8, bab-1=a-1, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C13⋊Q32
►Regular action on 416 points
Generators in S416
(1 298 54 335 117 320 378 258 189 357 101 90 395)(2 396 91 102 358 190 259 379 305 118 336 55 299)(3 300 56 321 119 306 380 260 191 359 103 92 397)(4 398 93 104 360 192 261 381 307 120 322 57 301)(5 302 58 323 121 308 382 262 177 361 105 94 399)(6 400 95 106 362 178 263 383 309 122 324 59 303)(7 304 60 325 123 310 384 264 179 363 107 96 385)(8 386 81 108 364 180 265 369 311 124 326 61 289)(9 290 62 327 125 312 370 266 181 365 109 82 387)(10 388 83 110 366 182 267 371 313 126 328 63 291)(11 292 64 329 127 314 372 268 183 367 111 84 389)(12 390 85 112 368 184 269 373 315 128 330 49 293)(13 294 50 331 113 316 374 270 185 353 97 86 391)(14 392 87 98 354 186 271 375 317 114 332 51 295)(15 296 52 333 115 318 376 272 187 355 99 88 393)(16 394 89 100 356 188 257 377 319 116 334 53 297)(17 350 248 65 234 413 34 275 134 153 173 204 224)(18 209 205 174 154 135 276 35 414 235 66 249 351)(19 352 250 67 236 415 36 277 136 155 175 206 210)(20 211 207 176 156 137 278 37 416 237 68 251 337)(21 338 252 69 238 401 38 279 138 157 161 208 212)(22 213 193 162 158 139 280 39 402 239 70 253 339)(23 340 254 71 240 403 40 281 140 159 163 194 214)(24 215 195 164 160 141 282 41 404 225 72 255 341)(25 342 256 73 226 405 42 283 142 145 165 196 216)(26 217 197 166 146 143 284 43 406 227 74 241 343)(27 344 242 75 228 407 44 285 144 147 167 198 218)(28 219 199 168 148 129 286 45 408 229 76 243 345)(29 346 244 77 230 409 46 287 130 149 169 200 220)(30 221 201 170 150 131 288 47 410 231 78 245 347)(31 348 246 79 232 411 48 273 132 151 171 202 222)(32 223 203 172 152 133 274 33 412 233 80 247 349)
(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)
(1 171 9 163)(2 170 10 162)(3 169 11 161)(4 168 12 176)(5 167 13 175)(6 166 14 174)(7 165 15 173)(8 164 16 172)(17 325 25 333)(18 324 26 332)(19 323 27 331)(20 322 28 330)(21 321 29 329)(22 336 30 328)(23 335 31 327)(24 334 32 326)(33 364 41 356)(34 363 42 355)(35 362 43 354)(36 361 44 353)(37 360 45 368)(38 359 46 367)(39 358 47 366)(40 357 48 365)(49 211 57 219)(50 210 58 218)(51 209 59 217)(52 224 60 216)(53 223 61 215)(54 222 62 214)(55 221 63 213)(56 220 64 212)(65 384 73 376)(66 383 74 375)(67 382 75 374)(68 381 76 373)(69 380 77 372)(70 379 78 371)(71 378 79 370)(72 377 80 369)(81 141 89 133)(82 140 90 132)(83 139 91 131)(84 138 92 130)(85 137 93 129)(86 136 94 144)(87 135 95 143)(88 134 96 142)(97 277 105 285)(98 276 106 284)(99 275 107 283)(100 274 108 282)(101 273 109 281)(102 288 110 280)(103 287 111 279)(104 286 112 278)(113 352 121 344)(114 351 122 343)(115 350 123 342)(116 349 124 341)(117 348 125 340)(118 347 126 339)(119 346 127 338)(120 345 128 337)(145 393 153 385)(146 392 154 400)(147 391 155 399)(148 390 156 398)(149 389 157 397)(150 388 158 396)(151 387 159 395)(152 386 160 394)(177 407 185 415)(178 406 186 414)(179 405 187 413)(180 404 188 412)(181 403 189 411)(182 402 190 410)(183 401 191 409)(184 416 192 408)(193 299 201 291)(194 298 202 290)(195 297 203 289)(196 296 204 304)(197 295 205 303)(198 294 206 302)(199 293 207 301)(200 292 208 300)(225 257 233 265)(226 272 234 264)(227 271 235 263)(228 270 236 262)(229 269 237 261)(230 268 238 260)(231 267 239 259)(232 266 240 258)(241 317 249 309)(242 316 250 308)(243 315 251 307)(244 314 252 306)(245 313 253 305)(246 312 254 320)(247 311 255 319)(248 310 256 318)
G:=sub<Sym(416)| (1,298,54,335,117,320,378,258,189,357,101,90,395)(2,396,91,102,358,190,259,379,305,118,336,55,299)(3,300,56,321,119,306,380,260,191,359,103,92,397)(4,398,93,104,360,192,261,381,307,120,322,57,301)(5,302,58,323,121,308,382,262,177,361,105,94,399)(6,400,95,106,362,178,263,383,309,122,324,59,303)(7,304,60,325,123,310,384,264,179,363,107,96,385)(8,386,81,108,364,180,265,369,311,124,326,61,289)(9,290,62,327,125,312,370,266,181,365,109,82,387)(10,388,83,110,366,182,267,371,313,126,328,63,291)(11,292,64,329,127,314,372,268,183,367,111,84,389)(12,390,85,112,368,184,269,373,315,128,330,49,293)(13,294,50,331,113,316,374,270,185,353,97,86,391)(14,392,87,98,354,186,271,375,317,114,332,51,295)(15,296,52,333,115,318,376,272,187,355,99,88,393)(16,394,89,100,356,188,257,377,319,116,334,53,297)(17,350,248,65,234,413,34,275,134,153,173,204,224)(18,209,205,174,154,135,276,35,414,235,66,249,351)(19,352,250,67,236,415,36,277,136,155,175,206,210)(20,211,207,176,156,137,278,37,416,237,68,251,337)(21,338,252,69,238,401,38,279,138,157,161,208,212)(22,213,193,162,158,139,280,39,402,239,70,253,339)(23,340,254,71,240,403,40,281,140,159,163,194,214)(24,215,195,164,160,141,282,41,404,225,72,255,341)(25,342,256,73,226,405,42,283,142,145,165,196,216)(26,217,197,166,146,143,284,43,406,227,74,241,343)(27,344,242,75,228,407,44,285,144,147,167,198,218)(28,219,199,168,148,129,286,45,408,229,76,243,345)(29,346,244,77,230,409,46,287,130,149,169,200,220)(30,221,201,170,150,131,288,47,410,231,78,245,347)(31,348,246,79,232,411,48,273,132,151,171,202,222)(32,223,203,172,152,133,274,33,412,233,80,247,349), (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), (1,171,9,163)(2,170,10,162)(3,169,11,161)(4,168,12,176)(5,167,13,175)(6,166,14,174)(7,165,15,173)(8,164,16,172)(17,325,25,333)(18,324,26,332)(19,323,27,331)(20,322,28,330)(21,321,29,329)(22,336,30,328)(23,335,31,327)(24,334,32,326)(33,364,41,356)(34,363,42,355)(35,362,43,354)(36,361,44,353)(37,360,45,368)(38,359,46,367)(39,358,47,366)(40,357,48,365)(49,211,57,219)(50,210,58,218)(51,209,59,217)(52,224,60,216)(53,223,61,215)(54,222,62,214)(55,221,63,213)(56,220,64,212)(65,384,73,376)(66,383,74,375)(67,382,75,374)(68,381,76,373)(69,380,77,372)(70,379,78,371)(71,378,79,370)(72,377,80,369)(81,141,89,133)(82,140,90,132)(83,139,91,131)(84,138,92,130)(85,137,93,129)(86,136,94,144)(87,135,95,143)(88,134,96,142)(97,277,105,285)(98,276,106,284)(99,275,107,283)(100,274,108,282)(101,273,109,281)(102,288,110,280)(103,287,111,279)(104,286,112,278)(113,352,121,344)(114,351,122,343)(115,350,123,342)(116,349,124,341)(117,348,125,340)(118,347,126,339)(119,346,127,338)(120,345,128,337)(145,393,153,385)(146,392,154,400)(147,391,155,399)(148,390,156,398)(149,389,157,397)(150,388,158,396)(151,387,159,395)(152,386,160,394)(177,407,185,415)(178,406,186,414)(179,405,187,413)(180,404,188,412)(181,403,189,411)(182,402,190,410)(183,401,191,409)(184,416,192,408)(193,299,201,291)(194,298,202,290)(195,297,203,289)(196,296,204,304)(197,295,205,303)(198,294,206,302)(199,293,207,301)(200,292,208,300)(225,257,233,265)(226,272,234,264)(227,271,235,263)(228,270,236,262)(229,269,237,261)(230,268,238,260)(231,267,239,259)(232,266,240,258)(241,317,249,309)(242,316,250,308)(243,315,251,307)(244,314,252,306)(245,313,253,305)(246,312,254,320)(247,311,255,319)(248,310,256,318)>;
G:=Group( (1,298,54,335,117,320,378,258,189,357,101,90,395)(2,396,91,102,358,190,259,379,305,118,336,55,299)(3,300,56,321,119,306,380,260,191,359,103,92,397)(4,398,93,104,360,192,261,381,307,120,322,57,301)(5,302,58,323,121,308,382,262,177,361,105,94,399)(6,400,95,106,362,178,263,383,309,122,324,59,303)(7,304,60,325,123,310,384,264,179,363,107,96,385)(8,386,81,108,364,180,265,369,311,124,326,61,289)(9,290,62,327,125,312,370,266,181,365,109,82,387)(10,388,83,110,366,182,267,371,313,126,328,63,291)(11,292,64,329,127,314,372,268,183,367,111,84,389)(12,390,85,112,368,184,269,373,315,128,330,49,293)(13,294,50,331,113,316,374,270,185,353,97,86,391)(14,392,87,98,354,186,271,375,317,114,332,51,295)(15,296,52,333,115,318,376,272,187,355,99,88,393)(16,394,89,100,356,188,257,377,319,116,334,53,297)(17,350,248,65,234,413,34,275,134,153,173,204,224)(18,209,205,174,154,135,276,35,414,235,66,249,351)(19,352,250,67,236,415,36,277,136,155,175,206,210)(20,211,207,176,156,137,278,37,416,237,68,251,337)(21,338,252,69,238,401,38,279,138,157,161,208,212)(22,213,193,162,158,139,280,39,402,239,70,253,339)(23,340,254,71,240,403,40,281,140,159,163,194,214)(24,215,195,164,160,141,282,41,404,225,72,255,341)(25,342,256,73,226,405,42,283,142,145,165,196,216)(26,217,197,166,146,143,284,43,406,227,74,241,343)(27,344,242,75,228,407,44,285,144,147,167,198,218)(28,219,199,168,148,129,286,45,408,229,76,243,345)(29,346,244,77,230,409,46,287,130,149,169,200,220)(30,221,201,170,150,131,288,47,410,231,78,245,347)(31,348,246,79,232,411,48,273,132,151,171,202,222)(32,223,203,172,152,133,274,33,412,233,80,247,349), (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), (1,171,9,163)(2,170,10,162)(3,169,11,161)(4,168,12,176)(5,167,13,175)(6,166,14,174)(7,165,15,173)(8,164,16,172)(17,325,25,333)(18,324,26,332)(19,323,27,331)(20,322,28,330)(21,321,29,329)(22,336,30,328)(23,335,31,327)(24,334,32,326)(33,364,41,356)(34,363,42,355)(35,362,43,354)(36,361,44,353)(37,360,45,368)(38,359,46,367)(39,358,47,366)(40,357,48,365)(49,211,57,219)(50,210,58,218)(51,209,59,217)(52,224,60,216)(53,223,61,215)(54,222,62,214)(55,221,63,213)(56,220,64,212)(65,384,73,376)(66,383,74,375)(67,382,75,374)(68,381,76,373)(69,380,77,372)(70,379,78,371)(71,378,79,370)(72,377,80,369)(81,141,89,133)(82,140,90,132)(83,139,91,131)(84,138,92,130)(85,137,93,129)(86,136,94,144)(87,135,95,143)(88,134,96,142)(97,277,105,285)(98,276,106,284)(99,275,107,283)(100,274,108,282)(101,273,109,281)(102,288,110,280)(103,287,111,279)(104,286,112,278)(113,352,121,344)(114,351,122,343)(115,350,123,342)(116,349,124,341)(117,348,125,340)(118,347,126,339)(119,346,127,338)(120,345,128,337)(145,393,153,385)(146,392,154,400)(147,391,155,399)(148,390,156,398)(149,389,157,397)(150,388,158,396)(151,387,159,395)(152,386,160,394)(177,407,185,415)(178,406,186,414)(179,405,187,413)(180,404,188,412)(181,403,189,411)(182,402,190,410)(183,401,191,409)(184,416,192,408)(193,299,201,291)(194,298,202,290)(195,297,203,289)(196,296,204,304)(197,295,205,303)(198,294,206,302)(199,293,207,301)(200,292,208,300)(225,257,233,265)(226,272,234,264)(227,271,235,263)(228,270,236,262)(229,269,237,261)(230,268,238,260)(231,267,239,259)(232,266,240,258)(241,317,249,309)(242,316,250,308)(243,315,251,307)(244,314,252,306)(245,313,253,305)(246,312,254,320)(247,311,255,319)(248,310,256,318) );
G=PermutationGroup([[(1,298,54,335,117,320,378,258,189,357,101,90,395),(2,396,91,102,358,190,259,379,305,118,336,55,299),(3,300,56,321,119,306,380,260,191,359,103,92,397),(4,398,93,104,360,192,261,381,307,120,322,57,301),(5,302,58,323,121,308,382,262,177,361,105,94,399),(6,400,95,106,362,178,263,383,309,122,324,59,303),(7,304,60,325,123,310,384,264,179,363,107,96,385),(8,386,81,108,364,180,265,369,311,124,326,61,289),(9,290,62,327,125,312,370,266,181,365,109,82,387),(10,388,83,110,366,182,267,371,313,126,328,63,291),(11,292,64,329,127,314,372,268,183,367,111,84,389),(12,390,85,112,368,184,269,373,315,128,330,49,293),(13,294,50,331,113,316,374,270,185,353,97,86,391),(14,392,87,98,354,186,271,375,317,114,332,51,295),(15,296,52,333,115,318,376,272,187,355,99,88,393),(16,394,89,100,356,188,257,377,319,116,334,53,297),(17,350,248,65,234,413,34,275,134,153,173,204,224),(18,209,205,174,154,135,276,35,414,235,66,249,351),(19,352,250,67,236,415,36,277,136,155,175,206,210),(20,211,207,176,156,137,278,37,416,237,68,251,337),(21,338,252,69,238,401,38,279,138,157,161,208,212),(22,213,193,162,158,139,280,39,402,239,70,253,339),(23,340,254,71,240,403,40,281,140,159,163,194,214),(24,215,195,164,160,141,282,41,404,225,72,255,341),(25,342,256,73,226,405,42,283,142,145,165,196,216),(26,217,197,166,146,143,284,43,406,227,74,241,343),(27,344,242,75,228,407,44,285,144,147,167,198,218),(28,219,199,168,148,129,286,45,408,229,76,243,345),(29,346,244,77,230,409,46,287,130,149,169,200,220),(30,221,201,170,150,131,288,47,410,231,78,245,347),(31,348,246,79,232,411,48,273,132,151,171,202,222),(32,223,203,172,152,133,274,33,412,233,80,247,349)], [(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)], [(1,171,9,163),(2,170,10,162),(3,169,11,161),(4,168,12,176),(5,167,13,175),(6,166,14,174),(7,165,15,173),(8,164,16,172),(17,325,25,333),(18,324,26,332),(19,323,27,331),(20,322,28,330),(21,321,29,329),(22,336,30,328),(23,335,31,327),(24,334,32,326),(33,364,41,356),(34,363,42,355),(35,362,43,354),(36,361,44,353),(37,360,45,368),(38,359,46,367),(39,358,47,366),(40,357,48,365),(49,211,57,219),(50,210,58,218),(51,209,59,217),(52,224,60,216),(53,223,61,215),(54,222,62,214),(55,221,63,213),(56,220,64,212),(65,384,73,376),(66,383,74,375),(67,382,75,374),(68,381,76,373),(69,380,77,372),(70,379,78,371),(71,378,79,370),(72,377,80,369),(81,141,89,133),(82,140,90,132),(83,139,91,131),(84,138,92,130),(85,137,93,129),(86,136,94,144),(87,135,95,143),(88,134,96,142),(97,277,105,285),(98,276,106,284),(99,275,107,283),(100,274,108,282),(101,273,109,281),(102,288,110,280),(103,287,111,279),(104,286,112,278),(113,352,121,344),(114,351,122,343),(115,350,123,342),(116,349,124,341),(117,348,125,340),(118,347,126,339),(119,346,127,338),(120,345,128,337),(145,393,153,385),(146,392,154,400),(147,391,155,399),(148,390,156,398),(149,389,157,397),(150,388,158,396),(151,387,159,395),(152,386,160,394),(177,407,185,415),(178,406,186,414),(179,405,187,413),(180,404,188,412),(181,403,189,411),(182,402,190,410),(183,401,191,409),(184,416,192,408),(193,299,201,291),(194,298,202,290),(195,297,203,289),(196,296,204,304),(197,295,205,303),(198,294,206,302),(199,293,207,301),(200,292,208,300),(225,257,233,265),(226,272,234,264),(227,271,235,263),(228,270,236,262),(229,269,237,261),(230,268,238,260),(231,267,239,259),(232,266,240,258),(241,317,249,309),(242,316,250,308),(243,315,251,307),(244,314,252,306),(245,313,253,305),(246,312,254,320),(247,311,255,319),(248,310,256,318)]])
53 conjugacy classes
| class | 1 | 2 | 4A | 4B | 4C | 8A | 8B | 13A | ··· | 13F | 16A | 16B | 16C | 16D | 26A | ··· | 26F | 52A | ··· | 52F | 52G | ··· | 52R | 104A | ··· | 104L |
| order | 1 | 2 | 4 | 4 | 4 | 8 | 8 | 13 | ··· | 13 | 16 | 16 | 16 | 16 | 26 | ··· | 26 | 52 | ··· | 52 | 52 | ··· | 52 | 104 | ··· | 104 |
| size | 1 | 1 | 2 | 8 | 104 | 2 | 2 | 2 | ··· | 2 | 26 | 26 | 26 | 26 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
53 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | - | |
| image | C1 | C2 | C2 | C2 | D4 | D8 | D13 | Q32 | D26 | C13⋊D4 | D4⋊D13 | C13⋊Q32 |
| kernel | C13⋊Q32 | C13⋊2C16 | Dic52 | C13×Q16 | C52 | C26 | Q16 | C13 | C8 | C4 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 2 | 6 | 4 | 6 | 12 | 6 | 12 |
Matrix representation of C13⋊Q32 ►in GL4(𝔽1249) generated by
| 789 | 1 | 0 | 0 |
| 1215 | 1040 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 488 | 862 | 0 | 0 |
| 667 | 761 | 0 | 0 |
| 0 | 0 | 536 | 1098 |
| 0 | 0 | 157 | 35 |
| 362 | 1062 | 0 | 0 |
| 113 | 887 | 0 | 0 |
| 0 | 0 | 500 | 108 |
| 0 | 0 | 241 | 749 |
G:=sub<GL(4,GF(1249))| [789,1215,0,0,1,1040,0,0,0,0,1,0,0,0,0,1],[488,667,0,0,862,761,0,0,0,0,536,157,0,0,1098,35],[362,113,0,0,1062,887,0,0,0,0,500,241,0,0,108,749] >;
C13⋊Q32 in GAP, Magma, Sage, TeX
C_{13}\rtimes Q_{32} % in TeX
G:=Group("C13:Q32"); // GroupNames label
G:=SmallGroup(416,36);
// by ID
G=gap.SmallGroup(416,36);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,96,73,103,218,116,122,579,297,69,13829]);
// Polycyclic
G:=Group<a,b,c|a^13=b^16=1,c^2=b^8,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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