direct product, metacyclic, supersoluble, monomial, A-group, 3-hyperelementary
Aliases: C3×C13⋊C9, C39⋊C9, C39.4C32, C13⋊2(C3×C9), (C3×C39).2C3, C32.2(C13⋊C3), C3.2(C3×C13⋊C3), SmallGroup(351,6)
Series: Derived ►Chief ►Lower central ►Upper central
| C13 — C3×C13⋊C9 |
Generators and relations for C3×C13⋊C9
G = < a,b,c | a3=b13=c9=1, ab=ba, ac=ca, cbc-1=b9 >
Smallest permutation representation of C3×C13⋊C9
►Regular action on 351 points
Generators in S351
(1 105 53)(2 106 54)(3 107 55)(4 108 56)(5 109 57)(6 110 58)(7 111 59)(8 112 60)(9 113 61)(10 114 62)(11 115 63)(12 116 64)(13 117 65)(14 79 66)(15 80 67)(16 81 68)(17 82 69)(18 83 70)(19 84 71)(20 85 72)(21 86 73)(22 87 74)(23 88 75)(24 89 76)(25 90 77)(26 91 78)(27 92 40)(28 93 41)(29 94 42)(30 95 43)(31 96 44)(32 97 45)(33 98 46)(34 99 47)(35 100 48)(36 101 49)(37 102 50)(38 103 51)(39 104 52)(118 234 182)(119 222 170)(120 223 171)(121 224 172)(122 225 173)(123 226 174)(124 227 175)(125 228 176)(126 229 177)(127 230 178)(128 231 179)(129 232 180)(130 233 181)(131 206 191)(132 207 192)(133 208 193)(134 196 194)(135 197 195)(136 198 183)(137 199 184)(138 200 185)(139 201 186)(140 202 187)(141 203 188)(142 204 189)(143 205 190)(144 216 162)(145 217 163)(146 218 164)(147 219 165)(148 220 166)(149 221 167)(150 209 168)(151 210 169)(152 211 157)(153 212 158)(154 213 159)(155 214 160)(156 215 161)(235 348 292)(236 349 293)(237 350 294)(238 351 295)(239 339 296)(240 340 297)(241 341 298)(242 342 299)(243 343 287)(244 344 288)(245 345 289)(246 346 290)(247 347 291)(248 320 300)(249 321 301)(250 322 302)(251 323 303)(252 324 304)(253 325 305)(254 313 306)(255 314 307)(256 315 308)(257 316 309)(258 317 310)(259 318 311)(260 319 312)(261 335 285)(262 336 286)(263 337 274)(264 338 275)(265 326 276)(266 327 277)(267 328 278)(268 329 279)(269 330 280)(270 331 281)(271 332 282)(272 333 283)(273 334 284)
(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)
(1 346 194 27 333 177 14 325 162)(2 349 190 28 336 173 15 315 158)(3 339 186 29 326 182 16 318 167)(4 342 195 30 329 178 17 321 163)(5 345 191 31 332 174 18 324 159)(6 348 187 32 335 170 19 314 168)(7 351 183 33 338 179 20 317 164)(8 341 192 34 328 175 21 320 160)(9 344 188 35 331 171 22 323 169)(10 347 184 36 334 180 23 313 165)(11 350 193 37 337 176 24 316 161)(12 340 189 38 327 172 25 319 157)(13 343 185 39 330 181 26 322 166)(40 272 229 66 253 216 53 246 196)(41 262 225 67 256 212 54 236 205)(42 265 234 68 259 221 55 239 201)(43 268 230 69 249 217 56 242 197)(44 271 226 70 252 213 57 245 206)(45 261 222 71 255 209 58 235 202)(46 264 231 72 258 218 59 238 198)(47 267 227 73 248 214 60 241 207)(48 270 223 74 251 210 61 244 203)(49 273 232 75 254 219 62 247 199)(50 263 228 76 257 215 63 237 208)(51 266 224 77 260 211 64 240 204)(52 269 233 78 250 220 65 243 200)(79 305 144 105 290 134 92 283 126)(80 308 153 106 293 143 93 286 122)(81 311 149 107 296 139 94 276 118)(82 301 145 108 299 135 95 279 127)(83 304 154 109 289 131 96 282 123)(84 307 150 110 292 140 97 285 119)(85 310 146 111 295 136 98 275 128)(86 300 155 112 298 132 99 278 124)(87 303 151 113 288 141 100 281 120)(88 306 147 114 291 137 101 284 129)(89 309 156 115 294 133 102 274 125)(90 312 152 116 297 142 103 277 121)(91 302 148 117 287 138 104 280 130)
G:=sub<Sym(351)| (1,105,53)(2,106,54)(3,107,55)(4,108,56)(5,109,57)(6,110,58)(7,111,59)(8,112,60)(9,113,61)(10,114,62)(11,115,63)(12,116,64)(13,117,65)(14,79,66)(15,80,67)(16,81,68)(17,82,69)(18,83,70)(19,84,71)(20,85,72)(21,86,73)(22,87,74)(23,88,75)(24,89,76)(25,90,77)(26,91,78)(27,92,40)(28,93,41)(29,94,42)(30,95,43)(31,96,44)(32,97,45)(33,98,46)(34,99,47)(35,100,48)(36,101,49)(37,102,50)(38,103,51)(39,104,52)(118,234,182)(119,222,170)(120,223,171)(121,224,172)(122,225,173)(123,226,174)(124,227,175)(125,228,176)(126,229,177)(127,230,178)(128,231,179)(129,232,180)(130,233,181)(131,206,191)(132,207,192)(133,208,193)(134,196,194)(135,197,195)(136,198,183)(137,199,184)(138,200,185)(139,201,186)(140,202,187)(141,203,188)(142,204,189)(143,205,190)(144,216,162)(145,217,163)(146,218,164)(147,219,165)(148,220,166)(149,221,167)(150,209,168)(151,210,169)(152,211,157)(153,212,158)(154,213,159)(155,214,160)(156,215,161)(235,348,292)(236,349,293)(237,350,294)(238,351,295)(239,339,296)(240,340,297)(241,341,298)(242,342,299)(243,343,287)(244,344,288)(245,345,289)(246,346,290)(247,347,291)(248,320,300)(249,321,301)(250,322,302)(251,323,303)(252,324,304)(253,325,305)(254,313,306)(255,314,307)(256,315,308)(257,316,309)(258,317,310)(259,318,311)(260,319,312)(261,335,285)(262,336,286)(263,337,274)(264,338,275)(265,326,276)(266,327,277)(267,328,278)(268,329,279)(269,330,280)(270,331,281)(271,332,282)(272,333,283)(273,334,284), (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), (1,346,194,27,333,177,14,325,162)(2,349,190,28,336,173,15,315,158)(3,339,186,29,326,182,16,318,167)(4,342,195,30,329,178,17,321,163)(5,345,191,31,332,174,18,324,159)(6,348,187,32,335,170,19,314,168)(7,351,183,33,338,179,20,317,164)(8,341,192,34,328,175,21,320,160)(9,344,188,35,331,171,22,323,169)(10,347,184,36,334,180,23,313,165)(11,350,193,37,337,176,24,316,161)(12,340,189,38,327,172,25,319,157)(13,343,185,39,330,181,26,322,166)(40,272,229,66,253,216,53,246,196)(41,262,225,67,256,212,54,236,205)(42,265,234,68,259,221,55,239,201)(43,268,230,69,249,217,56,242,197)(44,271,226,70,252,213,57,245,206)(45,261,222,71,255,209,58,235,202)(46,264,231,72,258,218,59,238,198)(47,267,227,73,248,214,60,241,207)(48,270,223,74,251,210,61,244,203)(49,273,232,75,254,219,62,247,199)(50,263,228,76,257,215,63,237,208)(51,266,224,77,260,211,64,240,204)(52,269,233,78,250,220,65,243,200)(79,305,144,105,290,134,92,283,126)(80,308,153,106,293,143,93,286,122)(81,311,149,107,296,139,94,276,118)(82,301,145,108,299,135,95,279,127)(83,304,154,109,289,131,96,282,123)(84,307,150,110,292,140,97,285,119)(85,310,146,111,295,136,98,275,128)(86,300,155,112,298,132,99,278,124)(87,303,151,113,288,141,100,281,120)(88,306,147,114,291,137,101,284,129)(89,309,156,115,294,133,102,274,125)(90,312,152,116,297,142,103,277,121)(91,302,148,117,287,138,104,280,130)>;
G:=Group( (1,105,53)(2,106,54)(3,107,55)(4,108,56)(5,109,57)(6,110,58)(7,111,59)(8,112,60)(9,113,61)(10,114,62)(11,115,63)(12,116,64)(13,117,65)(14,79,66)(15,80,67)(16,81,68)(17,82,69)(18,83,70)(19,84,71)(20,85,72)(21,86,73)(22,87,74)(23,88,75)(24,89,76)(25,90,77)(26,91,78)(27,92,40)(28,93,41)(29,94,42)(30,95,43)(31,96,44)(32,97,45)(33,98,46)(34,99,47)(35,100,48)(36,101,49)(37,102,50)(38,103,51)(39,104,52)(118,234,182)(119,222,170)(120,223,171)(121,224,172)(122,225,173)(123,226,174)(124,227,175)(125,228,176)(126,229,177)(127,230,178)(128,231,179)(129,232,180)(130,233,181)(131,206,191)(132,207,192)(133,208,193)(134,196,194)(135,197,195)(136,198,183)(137,199,184)(138,200,185)(139,201,186)(140,202,187)(141,203,188)(142,204,189)(143,205,190)(144,216,162)(145,217,163)(146,218,164)(147,219,165)(148,220,166)(149,221,167)(150,209,168)(151,210,169)(152,211,157)(153,212,158)(154,213,159)(155,214,160)(156,215,161)(235,348,292)(236,349,293)(237,350,294)(238,351,295)(239,339,296)(240,340,297)(241,341,298)(242,342,299)(243,343,287)(244,344,288)(245,345,289)(246,346,290)(247,347,291)(248,320,300)(249,321,301)(250,322,302)(251,323,303)(252,324,304)(253,325,305)(254,313,306)(255,314,307)(256,315,308)(257,316,309)(258,317,310)(259,318,311)(260,319,312)(261,335,285)(262,336,286)(263,337,274)(264,338,275)(265,326,276)(266,327,277)(267,328,278)(268,329,279)(269,330,280)(270,331,281)(271,332,282)(272,333,283)(273,334,284), (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), (1,346,194,27,333,177,14,325,162)(2,349,190,28,336,173,15,315,158)(3,339,186,29,326,182,16,318,167)(4,342,195,30,329,178,17,321,163)(5,345,191,31,332,174,18,324,159)(6,348,187,32,335,170,19,314,168)(7,351,183,33,338,179,20,317,164)(8,341,192,34,328,175,21,320,160)(9,344,188,35,331,171,22,323,169)(10,347,184,36,334,180,23,313,165)(11,350,193,37,337,176,24,316,161)(12,340,189,38,327,172,25,319,157)(13,343,185,39,330,181,26,322,166)(40,272,229,66,253,216,53,246,196)(41,262,225,67,256,212,54,236,205)(42,265,234,68,259,221,55,239,201)(43,268,230,69,249,217,56,242,197)(44,271,226,70,252,213,57,245,206)(45,261,222,71,255,209,58,235,202)(46,264,231,72,258,218,59,238,198)(47,267,227,73,248,214,60,241,207)(48,270,223,74,251,210,61,244,203)(49,273,232,75,254,219,62,247,199)(50,263,228,76,257,215,63,237,208)(51,266,224,77,260,211,64,240,204)(52,269,233,78,250,220,65,243,200)(79,305,144,105,290,134,92,283,126)(80,308,153,106,293,143,93,286,122)(81,311,149,107,296,139,94,276,118)(82,301,145,108,299,135,95,279,127)(83,304,154,109,289,131,96,282,123)(84,307,150,110,292,140,97,285,119)(85,310,146,111,295,136,98,275,128)(86,300,155,112,298,132,99,278,124)(87,303,151,113,288,141,100,281,120)(88,306,147,114,291,137,101,284,129)(89,309,156,115,294,133,102,274,125)(90,312,152,116,297,142,103,277,121)(91,302,148,117,287,138,104,280,130) );
G=PermutationGroup([[(1,105,53),(2,106,54),(3,107,55),(4,108,56),(5,109,57),(6,110,58),(7,111,59),(8,112,60),(9,113,61),(10,114,62),(11,115,63),(12,116,64),(13,117,65),(14,79,66),(15,80,67),(16,81,68),(17,82,69),(18,83,70),(19,84,71),(20,85,72),(21,86,73),(22,87,74),(23,88,75),(24,89,76),(25,90,77),(26,91,78),(27,92,40),(28,93,41),(29,94,42),(30,95,43),(31,96,44),(32,97,45),(33,98,46),(34,99,47),(35,100,48),(36,101,49),(37,102,50),(38,103,51),(39,104,52),(118,234,182),(119,222,170),(120,223,171),(121,224,172),(122,225,173),(123,226,174),(124,227,175),(125,228,176),(126,229,177),(127,230,178),(128,231,179),(129,232,180),(130,233,181),(131,206,191),(132,207,192),(133,208,193),(134,196,194),(135,197,195),(136,198,183),(137,199,184),(138,200,185),(139,201,186),(140,202,187),(141,203,188),(142,204,189),(143,205,190),(144,216,162),(145,217,163),(146,218,164),(147,219,165),(148,220,166),(149,221,167),(150,209,168),(151,210,169),(152,211,157),(153,212,158),(154,213,159),(155,214,160),(156,215,161),(235,348,292),(236,349,293),(237,350,294),(238,351,295),(239,339,296),(240,340,297),(241,341,298),(242,342,299),(243,343,287),(244,344,288),(245,345,289),(246,346,290),(247,347,291),(248,320,300),(249,321,301),(250,322,302),(251,323,303),(252,324,304),(253,325,305),(254,313,306),(255,314,307),(256,315,308),(257,316,309),(258,317,310),(259,318,311),(260,319,312),(261,335,285),(262,336,286),(263,337,274),(264,338,275),(265,326,276),(266,327,277),(267,328,278),(268,329,279),(269,330,280),(270,331,281),(271,332,282),(272,333,283),(273,334,284)], [(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)], [(1,346,194,27,333,177,14,325,162),(2,349,190,28,336,173,15,315,158),(3,339,186,29,326,182,16,318,167),(4,342,195,30,329,178,17,321,163),(5,345,191,31,332,174,18,324,159),(6,348,187,32,335,170,19,314,168),(7,351,183,33,338,179,20,317,164),(8,341,192,34,328,175,21,320,160),(9,344,188,35,331,171,22,323,169),(10,347,184,36,334,180,23,313,165),(11,350,193,37,337,176,24,316,161),(12,340,189,38,327,172,25,319,157),(13,343,185,39,330,181,26,322,166),(40,272,229,66,253,216,53,246,196),(41,262,225,67,256,212,54,236,205),(42,265,234,68,259,221,55,239,201),(43,268,230,69,249,217,56,242,197),(44,271,226,70,252,213,57,245,206),(45,261,222,71,255,209,58,235,202),(46,264,231,72,258,218,59,238,198),(47,267,227,73,248,214,60,241,207),(48,270,223,74,251,210,61,244,203),(49,273,232,75,254,219,62,247,199),(50,263,228,76,257,215,63,237,208),(51,266,224,77,260,211,64,240,204),(52,269,233,78,250,220,65,243,200),(79,305,144,105,290,134,92,283,126),(80,308,153,106,293,143,93,286,122),(81,311,149,107,296,139,94,276,118),(82,301,145,108,299,135,95,279,127),(83,304,154,109,289,131,96,282,123),(84,307,150,110,292,140,97,285,119),(85,310,146,111,295,136,98,275,128),(86,300,155,112,298,132,99,278,124),(87,303,151,113,288,141,100,281,120),(88,306,147,114,291,137,101,284,129),(89,309,156,115,294,133,102,274,125),(90,312,152,116,297,142,103,277,121),(91,302,148,117,287,138,104,280,130)]])
63 conjugacy classes
| class | 1 | 3A | ··· | 3H | 9A | ··· | 9R | 13A | 13B | 13C | 13D | 39A | ··· | 39AF |
| order | 1 | 3 | ··· | 3 | 9 | ··· | 9 | 13 | 13 | 13 | 13 | 39 | ··· | 39 |
| size | 1 | 1 | ··· | 1 | 13 | ··· | 13 | 3 | 3 | 3 | 3 | 3 | ··· | 3 |
63 irreducible representations
| dim | 1 | 1 | 1 | 1 | 3 | 3 | 3 |
| type | + | ||||||
| image | C1 | C3 | C3 | C9 | C13⋊C3 | C13⋊C9 | C3×C13⋊C3 |
| kernel | C3×C13⋊C9 | C13⋊C9 | C3×C39 | C39 | C32 | C3 | C3 |
| # reps | 1 | 6 | 2 | 18 | 4 | 24 | 8 |
Matrix representation of C3×C13⋊C9 ►in GL5(𝔽937)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 322 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 713 | 438 | 1 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 451 | 0 | 0 | 0 | 0 |
| 0 | 614 | 0 | 0 | 0 |
| 0 | 0 | 455 | 855 | 293 |
| 0 | 0 | 466 | 685 | 229 |
| 0 | 0 | 735 | 518 | 734 |
G:=sub<GL(5,GF(937))| [1,0,0,0,0,0,322,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,713,1,0,0,0,438,0,1,0,0,1,0,0],[451,0,0,0,0,0,614,0,0,0,0,0,455,466,735,0,0,855,685,518,0,0,293,229,734] >;
C3×C13⋊C9 in GAP, Magma, Sage, TeX
C_3\times C_{13}\rtimes C_9 % in TeX
G:=Group("C3xC13:C9"); // GroupNames label
G:=SmallGroup(351,6);
// by ID
G=gap.SmallGroup(351,6);
# by ID
G:=PCGroup([4,-3,-3,-3,-13,36,1299]);
// Polycyclic
G:=Group<a,b,c|a^3=b^13=c^9=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^9>;
// generators/relations
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