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G = C13⋊Q32order 416 = 25·13

The semidirect product of C13 and Q32 acting via Q32/Q16=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C132Q32, C8.7D26, C52.6D4, Q16.D13, C26.11D8, C104.5C22, Dic52.2C2, C132C16.1C2, C2.7(D4⋊D13), C4.4(C13⋊D4), (C13×Q16).1C2, SmallGroup(416,36)

Series: Derived Chief Lower central Upper central

C1C104 — C13⋊Q32
C1C13C26C52C104Dic52 — C13⋊Q32
C13C26C52C104 — C13⋊Q32
C1C2C4C8Q16

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 >

4C4
52C4
2Q8
26Q8
4Dic13
4C52
13C16
13Q16
2Dic26
2Q8×C13
13Q32

Smallest permutation representation of C13⋊Q32
Regular action on 416 points
Generators in S416
(1 103 367 20 405 400 263 374 279 249 305 227 302)(2 303 228 306 250 280 375 264 385 406 21 368 104)(3 105 353 22 407 386 265 376 281 251 307 229 304)(4 289 230 308 252 282 377 266 387 408 23 354 106)(5 107 355 24 409 388 267 378 283 253 309 231 290)(6 291 232 310 254 284 379 268 389 410 25 356 108)(7 109 357 26 411 390 269 380 285 255 311 233 292)(8 293 234 312 256 286 381 270 391 412 27 358 110)(9 111 359 28 413 392 271 382 287 241 313 235 294)(10 295 236 314 242 288 383 272 393 414 29 360 112)(11 97 361 30 415 394 257 384 273 243 315 237 296)(12 297 238 316 244 274 369 258 395 416 31 362 98)(13 99 363 32 401 396 259 370 275 245 317 239 298)(14 299 240 318 246 276 371 260 397 402 17 364 100)(15 101 365 18 403 398 261 372 277 247 319 225 300)(16 301 226 320 248 278 373 262 399 404 19 366 102)(33 218 194 345 72 53 183 170 144 81 153 325 122)(34 123 326 154 82 129 171 184 54 73 346 195 219)(35 220 196 347 74 55 185 172 130 83 155 327 124)(36 125 328 156 84 131 173 186 56 75 348 197 221)(37 222 198 349 76 57 187 174 132 85 157 329 126)(38 127 330 158 86 133 175 188 58 77 350 199 223)(39 224 200 351 78 59 189 176 134 87 159 331 128)(40 113 332 160 88 135 161 190 60 79 352 201 209)(41 210 202 337 80 61 191 162 136 89 145 333 114)(42 115 334 146 90 137 163 192 62 65 338 203 211)(43 212 204 339 66 63 177 164 138 91 147 335 116)(44 117 336 148 92 139 165 178 64 67 340 205 213)(45 214 206 341 68 49 179 166 140 93 149 321 118)(46 119 322 150 94 141 167 180 50 69 342 207 215)(47 216 208 343 70 51 181 168 142 95 151 323 120)(48 121 324 152 96 143 169 182 52 71 344 193 217)
(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)
(1 214 9 222)(2 213 10 221)(3 212 11 220)(4 211 12 219)(5 210 13 218)(6 209 14 217)(7 224 15 216)(8 223 16 215)(17 71 25 79)(18 70 26 78)(19 69 27 77)(20 68 28 76)(21 67 29 75)(22 66 30 74)(23 65 31 73)(24 80 32 72)(33 290 41 298)(34 289 42 297)(35 304 43 296)(36 303 44 295)(37 302 45 294)(38 301 46 293)(39 300 47 292)(40 299 48 291)(49 413 57 405)(50 412 58 404)(51 411 59 403)(52 410 60 402)(53 409 61 401)(54 408 62 416)(55 407 63 415)(56 406 64 414)(81 283 89 275)(82 282 90 274)(83 281 91 273)(84 280 92 288)(85 279 93 287)(86 278 94 286)(87 277 95 285)(88 276 96 284)(97 196 105 204)(98 195 106 203)(99 194 107 202)(100 193 108 201)(101 208 109 200)(102 207 110 199)(103 206 111 198)(104 205 112 197)(113 240 121 232)(114 239 122 231)(115 238 123 230)(116 237 124 229)(117 236 125 228)(118 235 126 227)(119 234 127 226)(120 233 128 225)(129 377 137 369)(130 376 138 384)(131 375 139 383)(132 374 140 382)(133 373 141 381)(134 372 142 380)(135 371 143 379)(136 370 144 378)(145 245 153 253)(146 244 154 252)(147 243 155 251)(148 242 156 250)(149 241 157 249)(150 256 158 248)(151 255 159 247)(152 254 160 246)(161 260 169 268)(162 259 170 267)(163 258 171 266)(164 257 172 265)(165 272 173 264)(166 271 174 263)(167 270 175 262)(168 269 176 261)(177 394 185 386)(178 393 186 385)(179 392 187 400)(180 391 188 399)(181 390 189 398)(182 389 190 397)(183 388 191 396)(184 387 192 395)(305 321 313 329)(306 336 314 328)(307 335 315 327)(308 334 316 326)(309 333 317 325)(310 332 318 324)(311 331 319 323)(312 330 320 322)(337 363 345 355)(338 362 346 354)(339 361 347 353)(340 360 348 368)(341 359 349 367)(342 358 350 366)(343 357 351 365)(344 356 352 364)

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

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

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

53 conjugacy classes

class 1  2 4A4B4C8A8B13A···13F16A16B16C16D26A···26F52A···52F52G···52R104A···104L
order124448813···131616161626···2652···5252···52104···104
size1128104222···2262626262···24···48···84···4

53 irreducible representations

dim111122222244
type+++++++-++-
imageC1C2C2C2D4D8D13Q32D26C13⋊D4D4⋊D13C13⋊Q32
kernelC13⋊Q32C132C16Dic52C13×Q16C52C26Q16C13C8C4C2C1
# reps11111264612612

Matrix representation of C13⋊Q32 in GL4(𝔽1249) generated by

789100
1215104000
0010
0001
,
48886200
66776100
005361098
0015735
,
362106200
11388700
00500108
00241749
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

Export

Subgroup lattice of C13⋊Q32 in TeX

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