direct product, abelian, monomial, 3-elementary
Aliases: C32×C39, SmallGroup(351,14)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C32×C39 |
| C1 — C32×C39 |
| C1 — C32×C39 |
Generators and relations for C32×C39
G = < a,b,c | a3=b3=c39=1, ab=ba, ac=ca, bc=cb >
Subgroups: 56, all normal (4 characteristic)
C1, C3, C32, C13, C33, C39, C3×C39, C32×C39
Quotients: C1, C3, C32, C13, C33, C39, C3×C39, C32×C39
►Regular action on 351 points
Generators in S351
(1 240 120)(2 241 121)(3 242 122)(4 243 123)(5 244 124)(6 245 125)(7 246 126)(8 247 127)(9 248 128)(10 249 129)(11 250 130)(12 251 131)(13 252 132)(14 253 133)(15 254 134)(16 255 135)(17 256 136)(18 257 137)(19 258 138)(20 259 139)(21 260 140)(22 261 141)(23 262 142)(24 263 143)(25 264 144)(26 265 145)(27 266 146)(28 267 147)(29 268 148)(30 269 149)(31 270 150)(32 271 151)(33 272 152)(34 273 153)(35 235 154)(36 236 155)(37 237 156)(38 238 118)(39 239 119)(40 275 159)(41 276 160)(42 277 161)(43 278 162)(44 279 163)(45 280 164)(46 281 165)(47 282 166)(48 283 167)(49 284 168)(50 285 169)(51 286 170)(52 287 171)(53 288 172)(54 289 173)(55 290 174)(56 291 175)(57 292 176)(58 293 177)(59 294 178)(60 295 179)(61 296 180)(62 297 181)(63 298 182)(64 299 183)(65 300 184)(66 301 185)(67 302 186)(68 303 187)(69 304 188)(70 305 189)(71 306 190)(72 307 191)(73 308 192)(74 309 193)(75 310 194)(76 311 195)(77 312 157)(78 274 158)(79 350 227)(80 351 228)(81 313 229)(82 314 230)(83 315 231)(84 316 232)(85 317 233)(86 318 234)(87 319 196)(88 320 197)(89 321 198)(90 322 199)(91 323 200)(92 324 201)(93 325 202)(94 326 203)(95 327 204)(96 328 205)(97 329 206)(98 330 207)(99 331 208)(100 332 209)(101 333 210)(102 334 211)(103 335 212)(104 336 213)(105 337 214)(106 338 215)(107 339 216)(108 340 217)(109 341 218)(110 342 219)(111 343 220)(112 344 221)(113 345 222)(114 346 223)(115 347 224)(116 348 225)(117 349 226)
(1 94 76)(2 95 77)(3 96 78)(4 97 40)(5 98 41)(6 99 42)(7 100 43)(8 101 44)(9 102 45)(10 103 46)(11 104 47)(12 105 48)(13 106 49)(14 107 50)(15 108 51)(16 109 52)(17 110 53)(18 111 54)(19 112 55)(20 113 56)(21 114 57)(22 115 58)(23 116 59)(24 117 60)(25 79 61)(26 80 62)(27 81 63)(28 82 64)(29 83 65)(30 84 66)(31 85 67)(32 86 68)(33 87 69)(34 88 70)(35 89 71)(36 90 72)(37 91 73)(38 92 74)(39 93 75)(118 201 193)(119 202 194)(120 203 195)(121 204 157)(122 205 158)(123 206 159)(124 207 160)(125 208 161)(126 209 162)(127 210 163)(128 211 164)(129 212 165)(130 213 166)(131 214 167)(132 215 168)(133 216 169)(134 217 170)(135 218 171)(136 219 172)(137 220 173)(138 221 174)(139 222 175)(140 223 176)(141 224 177)(142 225 178)(143 226 179)(144 227 180)(145 228 181)(146 229 182)(147 230 183)(148 231 184)(149 232 185)(150 233 186)(151 234 187)(152 196 188)(153 197 189)(154 198 190)(155 199 191)(156 200 192)(235 321 306)(236 322 307)(237 323 308)(238 324 309)(239 325 310)(240 326 311)(241 327 312)(242 328 274)(243 329 275)(244 330 276)(245 331 277)(246 332 278)(247 333 279)(248 334 280)(249 335 281)(250 336 282)(251 337 283)(252 338 284)(253 339 285)(254 340 286)(255 341 287)(256 342 288)(257 343 289)(258 344 290)(259 345 291)(260 346 292)(261 347 293)(262 348 294)(263 349 295)(264 350 296)(265 351 297)(266 313 298)(267 314 299)(268 315 300)(269 316 301)(270 317 302)(271 318 303)(272 319 304)(273 320 305)
(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)
G:=sub<Sym(351)| (1,240,120)(2,241,121)(3,242,122)(4,243,123)(5,244,124)(6,245,125)(7,246,126)(8,247,127)(9,248,128)(10,249,129)(11,250,130)(12,251,131)(13,252,132)(14,253,133)(15,254,134)(16,255,135)(17,256,136)(18,257,137)(19,258,138)(20,259,139)(21,260,140)(22,261,141)(23,262,142)(24,263,143)(25,264,144)(26,265,145)(27,266,146)(28,267,147)(29,268,148)(30,269,149)(31,270,150)(32,271,151)(33,272,152)(34,273,153)(35,235,154)(36,236,155)(37,237,156)(38,238,118)(39,239,119)(40,275,159)(41,276,160)(42,277,161)(43,278,162)(44,279,163)(45,280,164)(46,281,165)(47,282,166)(48,283,167)(49,284,168)(50,285,169)(51,286,170)(52,287,171)(53,288,172)(54,289,173)(55,290,174)(56,291,175)(57,292,176)(58,293,177)(59,294,178)(60,295,179)(61,296,180)(62,297,181)(63,298,182)(64,299,183)(65,300,184)(66,301,185)(67,302,186)(68,303,187)(69,304,188)(70,305,189)(71,306,190)(72,307,191)(73,308,192)(74,309,193)(75,310,194)(76,311,195)(77,312,157)(78,274,158)(79,350,227)(80,351,228)(81,313,229)(82,314,230)(83,315,231)(84,316,232)(85,317,233)(86,318,234)(87,319,196)(88,320,197)(89,321,198)(90,322,199)(91,323,200)(92,324,201)(93,325,202)(94,326,203)(95,327,204)(96,328,205)(97,329,206)(98,330,207)(99,331,208)(100,332,209)(101,333,210)(102,334,211)(103,335,212)(104,336,213)(105,337,214)(106,338,215)(107,339,216)(108,340,217)(109,341,218)(110,342,219)(111,343,220)(112,344,221)(113,345,222)(114,346,223)(115,347,224)(116,348,225)(117,349,226), (1,94,76)(2,95,77)(3,96,78)(4,97,40)(5,98,41)(6,99,42)(7,100,43)(8,101,44)(9,102,45)(10,103,46)(11,104,47)(12,105,48)(13,106,49)(14,107,50)(15,108,51)(16,109,52)(17,110,53)(18,111,54)(19,112,55)(20,113,56)(21,114,57)(22,115,58)(23,116,59)(24,117,60)(25,79,61)(26,80,62)(27,81,63)(28,82,64)(29,83,65)(30,84,66)(31,85,67)(32,86,68)(33,87,69)(34,88,70)(35,89,71)(36,90,72)(37,91,73)(38,92,74)(39,93,75)(118,201,193)(119,202,194)(120,203,195)(121,204,157)(122,205,158)(123,206,159)(124,207,160)(125,208,161)(126,209,162)(127,210,163)(128,211,164)(129,212,165)(130,213,166)(131,214,167)(132,215,168)(133,216,169)(134,217,170)(135,218,171)(136,219,172)(137,220,173)(138,221,174)(139,222,175)(140,223,176)(141,224,177)(142,225,178)(143,226,179)(144,227,180)(145,228,181)(146,229,182)(147,230,183)(148,231,184)(149,232,185)(150,233,186)(151,234,187)(152,196,188)(153,197,189)(154,198,190)(155,199,191)(156,200,192)(235,321,306)(236,322,307)(237,323,308)(238,324,309)(239,325,310)(240,326,311)(241,327,312)(242,328,274)(243,329,275)(244,330,276)(245,331,277)(246,332,278)(247,333,279)(248,334,280)(249,335,281)(250,336,282)(251,337,283)(252,338,284)(253,339,285)(254,340,286)(255,341,287)(256,342,288)(257,343,289)(258,344,290)(259,345,291)(260,346,292)(261,347,293)(262,348,294)(263,349,295)(264,350,296)(265,351,297)(266,313,298)(267,314,299)(268,315,300)(269,316,301)(270,317,302)(271,318,303)(272,319,304)(273,320,305), (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)>;
G:=Group( (1,240,120)(2,241,121)(3,242,122)(4,243,123)(5,244,124)(6,245,125)(7,246,126)(8,247,127)(9,248,128)(10,249,129)(11,250,130)(12,251,131)(13,252,132)(14,253,133)(15,254,134)(16,255,135)(17,256,136)(18,257,137)(19,258,138)(20,259,139)(21,260,140)(22,261,141)(23,262,142)(24,263,143)(25,264,144)(26,265,145)(27,266,146)(28,267,147)(29,268,148)(30,269,149)(31,270,150)(32,271,151)(33,272,152)(34,273,153)(35,235,154)(36,236,155)(37,237,156)(38,238,118)(39,239,119)(40,275,159)(41,276,160)(42,277,161)(43,278,162)(44,279,163)(45,280,164)(46,281,165)(47,282,166)(48,283,167)(49,284,168)(50,285,169)(51,286,170)(52,287,171)(53,288,172)(54,289,173)(55,290,174)(56,291,175)(57,292,176)(58,293,177)(59,294,178)(60,295,179)(61,296,180)(62,297,181)(63,298,182)(64,299,183)(65,300,184)(66,301,185)(67,302,186)(68,303,187)(69,304,188)(70,305,189)(71,306,190)(72,307,191)(73,308,192)(74,309,193)(75,310,194)(76,311,195)(77,312,157)(78,274,158)(79,350,227)(80,351,228)(81,313,229)(82,314,230)(83,315,231)(84,316,232)(85,317,233)(86,318,234)(87,319,196)(88,320,197)(89,321,198)(90,322,199)(91,323,200)(92,324,201)(93,325,202)(94,326,203)(95,327,204)(96,328,205)(97,329,206)(98,330,207)(99,331,208)(100,332,209)(101,333,210)(102,334,211)(103,335,212)(104,336,213)(105,337,214)(106,338,215)(107,339,216)(108,340,217)(109,341,218)(110,342,219)(111,343,220)(112,344,221)(113,345,222)(114,346,223)(115,347,224)(116,348,225)(117,349,226), (1,94,76)(2,95,77)(3,96,78)(4,97,40)(5,98,41)(6,99,42)(7,100,43)(8,101,44)(9,102,45)(10,103,46)(11,104,47)(12,105,48)(13,106,49)(14,107,50)(15,108,51)(16,109,52)(17,110,53)(18,111,54)(19,112,55)(20,113,56)(21,114,57)(22,115,58)(23,116,59)(24,117,60)(25,79,61)(26,80,62)(27,81,63)(28,82,64)(29,83,65)(30,84,66)(31,85,67)(32,86,68)(33,87,69)(34,88,70)(35,89,71)(36,90,72)(37,91,73)(38,92,74)(39,93,75)(118,201,193)(119,202,194)(120,203,195)(121,204,157)(122,205,158)(123,206,159)(124,207,160)(125,208,161)(126,209,162)(127,210,163)(128,211,164)(129,212,165)(130,213,166)(131,214,167)(132,215,168)(133,216,169)(134,217,170)(135,218,171)(136,219,172)(137,220,173)(138,221,174)(139,222,175)(140,223,176)(141,224,177)(142,225,178)(143,226,179)(144,227,180)(145,228,181)(146,229,182)(147,230,183)(148,231,184)(149,232,185)(150,233,186)(151,234,187)(152,196,188)(153,197,189)(154,198,190)(155,199,191)(156,200,192)(235,321,306)(236,322,307)(237,323,308)(238,324,309)(239,325,310)(240,326,311)(241,327,312)(242,328,274)(243,329,275)(244,330,276)(245,331,277)(246,332,278)(247,333,279)(248,334,280)(249,335,281)(250,336,282)(251,337,283)(252,338,284)(253,339,285)(254,340,286)(255,341,287)(256,342,288)(257,343,289)(258,344,290)(259,345,291)(260,346,292)(261,347,293)(262,348,294)(263,349,295)(264,350,296)(265,351,297)(266,313,298)(267,314,299)(268,315,300)(269,316,301)(270,317,302)(271,318,303)(272,319,304)(273,320,305), (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) );
G=PermutationGroup([[(1,240,120),(2,241,121),(3,242,122),(4,243,123),(5,244,124),(6,245,125),(7,246,126),(8,247,127),(9,248,128),(10,249,129),(11,250,130),(12,251,131),(13,252,132),(14,253,133),(15,254,134),(16,255,135),(17,256,136),(18,257,137),(19,258,138),(20,259,139),(21,260,140),(22,261,141),(23,262,142),(24,263,143),(25,264,144),(26,265,145),(27,266,146),(28,267,147),(29,268,148),(30,269,149),(31,270,150),(32,271,151),(33,272,152),(34,273,153),(35,235,154),(36,236,155),(37,237,156),(38,238,118),(39,239,119),(40,275,159),(41,276,160),(42,277,161),(43,278,162),(44,279,163),(45,280,164),(46,281,165),(47,282,166),(48,283,167),(49,284,168),(50,285,169),(51,286,170),(52,287,171),(53,288,172),(54,289,173),(55,290,174),(56,291,175),(57,292,176),(58,293,177),(59,294,178),(60,295,179),(61,296,180),(62,297,181),(63,298,182),(64,299,183),(65,300,184),(66,301,185),(67,302,186),(68,303,187),(69,304,188),(70,305,189),(71,306,190),(72,307,191),(73,308,192),(74,309,193),(75,310,194),(76,311,195),(77,312,157),(78,274,158),(79,350,227),(80,351,228),(81,313,229),(82,314,230),(83,315,231),(84,316,232),(85,317,233),(86,318,234),(87,319,196),(88,320,197),(89,321,198),(90,322,199),(91,323,200),(92,324,201),(93,325,202),(94,326,203),(95,327,204),(96,328,205),(97,329,206),(98,330,207),(99,331,208),(100,332,209),(101,333,210),(102,334,211),(103,335,212),(104,336,213),(105,337,214),(106,338,215),(107,339,216),(108,340,217),(109,341,218),(110,342,219),(111,343,220),(112,344,221),(113,345,222),(114,346,223),(115,347,224),(116,348,225),(117,349,226)], [(1,94,76),(2,95,77),(3,96,78),(4,97,40),(5,98,41),(6,99,42),(7,100,43),(8,101,44),(9,102,45),(10,103,46),(11,104,47),(12,105,48),(13,106,49),(14,107,50),(15,108,51),(16,109,52),(17,110,53),(18,111,54),(19,112,55),(20,113,56),(21,114,57),(22,115,58),(23,116,59),(24,117,60),(25,79,61),(26,80,62),(27,81,63),(28,82,64),(29,83,65),(30,84,66),(31,85,67),(32,86,68),(33,87,69),(34,88,70),(35,89,71),(36,90,72),(37,91,73),(38,92,74),(39,93,75),(118,201,193),(119,202,194),(120,203,195),(121,204,157),(122,205,158),(123,206,159),(124,207,160),(125,208,161),(126,209,162),(127,210,163),(128,211,164),(129,212,165),(130,213,166),(131,214,167),(132,215,168),(133,216,169),(134,217,170),(135,218,171),(136,219,172),(137,220,173),(138,221,174),(139,222,175),(140,223,176),(141,224,177),(142,225,178),(143,226,179),(144,227,180),(145,228,181),(146,229,182),(147,230,183),(148,231,184),(149,232,185),(150,233,186),(151,234,187),(152,196,188),(153,197,189),(154,198,190),(155,199,191),(156,200,192),(235,321,306),(236,322,307),(237,323,308),(238,324,309),(239,325,310),(240,326,311),(241,327,312),(242,328,274),(243,329,275),(244,330,276),(245,331,277),(246,332,278),(247,333,279),(248,334,280),(249,335,281),(250,336,282),(251,337,283),(252,338,284),(253,339,285),(254,340,286),(255,341,287),(256,342,288),(257,343,289),(258,344,290),(259,345,291),(260,346,292),(261,347,293),(262,348,294),(263,349,295),(264,350,296),(265,351,297),(266,313,298),(267,314,299),(268,315,300),(269,316,301),(270,317,302),(271,318,303),(272,319,304),(273,320,305)], [(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)]])
351 conjugacy classes
| class | 1 | 3A | ··· | 3Z | 13A | ··· | 13L | 39A | ··· | 39KZ |
| order | 1 | 3 | ··· | 3 | 13 | ··· | 13 | 39 | ··· | 39 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
351 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | |||
| image | C1 | C3 | C13 | C39 |
| kernel | C32×C39 | C3×C39 | C33 | C32 |
| # reps | 1 | 26 | 12 | 312 |
Matrix representation of C32×C39 ►in GL3(𝔽79) generated by
| 55 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 23 |
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 55 |
| 76 | 0 | 0 |
| 0 | 76 | 0 |
| 0 | 0 | 20 |
G:=sub<GL(3,GF(79))| [55,0,0,0,1,0,0,0,23],[1,0,0,0,1,0,0,0,55],[76,0,0,0,76,0,0,0,20] >;
C32×C39 in GAP, Magma, Sage, TeX
C_3^2\times C_{39} % in TeX
G:=Group("C3^2xC39"); // GroupNames label
G:=SmallGroup(351,14);
// by ID
G=gap.SmallGroup(351,14);
# by ID
G:=PCGroup([4,-3,-3,-3,-13]);
// Polycyclic
G:=Group<a,b,c|a^3=b^3=c^39=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations