direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C3×Dic29, C87⋊4C4, C58.C6, C29⋊2C12, C6.2D29, C174.2C2, C2.(C3×D29), SmallGroup(348,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C29 — C3×Dic29 |
Generators and relations for C3×Dic29
G = < a,b,c | a3=b58=1, c2=b29, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C3×Dic29
►Regular action on 348 points
Generators in S348
(1 122 102)(2 123 103)(3 124 104)(4 125 105)(5 126 106)(6 127 107)(7 128 108)(8 129 109)(9 130 110)(10 131 111)(11 132 112)(12 133 113)(13 134 114)(14 135 115)(15 136 116)(16 137 59)(17 138 60)(18 139 61)(19 140 62)(20 141 63)(21 142 64)(22 143 65)(23 144 66)(24 145 67)(25 146 68)(26 147 69)(27 148 70)(28 149 71)(29 150 72)(30 151 73)(31 152 74)(32 153 75)(33 154 76)(34 155 77)(35 156 78)(36 157 79)(37 158 80)(38 159 81)(39 160 82)(40 161 83)(41 162 84)(42 163 85)(43 164 86)(44 165 87)(45 166 88)(46 167 89)(47 168 90)(48 169 91)(49 170 92)(50 171 93)(51 172 94)(52 173 95)(53 174 96)(54 117 97)(55 118 98)(56 119 99)(57 120 100)(58 121 101)(175 291 233)(176 292 234)(177 293 235)(178 294 236)(179 295 237)(180 296 238)(181 297 239)(182 298 240)(183 299 241)(184 300 242)(185 301 243)(186 302 244)(187 303 245)(188 304 246)(189 305 247)(190 306 248)(191 307 249)(192 308 250)(193 309 251)(194 310 252)(195 311 253)(196 312 254)(197 313 255)(198 314 256)(199 315 257)(200 316 258)(201 317 259)(202 318 260)(203 319 261)(204 320 262)(205 321 263)(206 322 264)(207 323 265)(208 324 266)(209 325 267)(210 326 268)(211 327 269)(212 328 270)(213 329 271)(214 330 272)(215 331 273)(216 332 274)(217 333 275)(218 334 276)(219 335 277)(220 336 278)(221 337 279)(222 338 280)(223 339 281)(224 340 282)(225 341 283)(226 342 284)(227 343 285)(228 344 286)(229 345 287)(230 346 288)(231 347 289)(232 348 290)
(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)
(1 175 30 204)(2 232 31 203)(3 231 32 202)(4 230 33 201)(5 229 34 200)(6 228 35 199)(7 227 36 198)(8 226 37 197)(9 225 38 196)(10 224 39 195)(11 223 40 194)(12 222 41 193)(13 221 42 192)(14 220 43 191)(15 219 44 190)(16 218 45 189)(17 217 46 188)(18 216 47 187)(19 215 48 186)(20 214 49 185)(21 213 50 184)(22 212 51 183)(23 211 52 182)(24 210 53 181)(25 209 54 180)(26 208 55 179)(27 207 56 178)(28 206 57 177)(29 205 58 176)(59 276 88 247)(60 275 89 246)(61 274 90 245)(62 273 91 244)(63 272 92 243)(64 271 93 242)(65 270 94 241)(66 269 95 240)(67 268 96 239)(68 267 97 238)(69 266 98 237)(70 265 99 236)(71 264 100 235)(72 263 101 234)(73 262 102 233)(74 261 103 290)(75 260 104 289)(76 259 105 288)(77 258 106 287)(78 257 107 286)(79 256 108 285)(80 255 109 284)(81 254 110 283)(82 253 111 282)(83 252 112 281)(84 251 113 280)(85 250 114 279)(86 249 115 278)(87 248 116 277)(117 296 146 325)(118 295 147 324)(119 294 148 323)(120 293 149 322)(121 292 150 321)(122 291 151 320)(123 348 152 319)(124 347 153 318)(125 346 154 317)(126 345 155 316)(127 344 156 315)(128 343 157 314)(129 342 158 313)(130 341 159 312)(131 340 160 311)(132 339 161 310)(133 338 162 309)(134 337 163 308)(135 336 164 307)(136 335 165 306)(137 334 166 305)(138 333 167 304)(139 332 168 303)(140 331 169 302)(141 330 170 301)(142 329 171 300)(143 328 172 299)(144 327 173 298)(145 326 174 297)
G:=sub<Sym(348)| (1,122,102)(2,123,103)(3,124,104)(4,125,105)(5,126,106)(6,127,107)(7,128,108)(8,129,109)(9,130,110)(10,131,111)(11,132,112)(12,133,113)(13,134,114)(14,135,115)(15,136,116)(16,137,59)(17,138,60)(18,139,61)(19,140,62)(20,141,63)(21,142,64)(22,143,65)(23,144,66)(24,145,67)(25,146,68)(26,147,69)(27,148,70)(28,149,71)(29,150,72)(30,151,73)(31,152,74)(32,153,75)(33,154,76)(34,155,77)(35,156,78)(36,157,79)(37,158,80)(38,159,81)(39,160,82)(40,161,83)(41,162,84)(42,163,85)(43,164,86)(44,165,87)(45,166,88)(46,167,89)(47,168,90)(48,169,91)(49,170,92)(50,171,93)(51,172,94)(52,173,95)(53,174,96)(54,117,97)(55,118,98)(56,119,99)(57,120,100)(58,121,101)(175,291,233)(176,292,234)(177,293,235)(178,294,236)(179,295,237)(180,296,238)(181,297,239)(182,298,240)(183,299,241)(184,300,242)(185,301,243)(186,302,244)(187,303,245)(188,304,246)(189,305,247)(190,306,248)(191,307,249)(192,308,250)(193,309,251)(194,310,252)(195,311,253)(196,312,254)(197,313,255)(198,314,256)(199,315,257)(200,316,258)(201,317,259)(202,318,260)(203,319,261)(204,320,262)(205,321,263)(206,322,264)(207,323,265)(208,324,266)(209,325,267)(210,326,268)(211,327,269)(212,328,270)(213,329,271)(214,330,272)(215,331,273)(216,332,274)(217,333,275)(218,334,276)(219,335,277)(220,336,278)(221,337,279)(222,338,280)(223,339,281)(224,340,282)(225,341,283)(226,342,284)(227,343,285)(228,344,286)(229,345,287)(230,346,288)(231,347,289)(232,348,290), (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), (1,175,30,204)(2,232,31,203)(3,231,32,202)(4,230,33,201)(5,229,34,200)(6,228,35,199)(7,227,36,198)(8,226,37,197)(9,225,38,196)(10,224,39,195)(11,223,40,194)(12,222,41,193)(13,221,42,192)(14,220,43,191)(15,219,44,190)(16,218,45,189)(17,217,46,188)(18,216,47,187)(19,215,48,186)(20,214,49,185)(21,213,50,184)(22,212,51,183)(23,211,52,182)(24,210,53,181)(25,209,54,180)(26,208,55,179)(27,207,56,178)(28,206,57,177)(29,205,58,176)(59,276,88,247)(60,275,89,246)(61,274,90,245)(62,273,91,244)(63,272,92,243)(64,271,93,242)(65,270,94,241)(66,269,95,240)(67,268,96,239)(68,267,97,238)(69,266,98,237)(70,265,99,236)(71,264,100,235)(72,263,101,234)(73,262,102,233)(74,261,103,290)(75,260,104,289)(76,259,105,288)(77,258,106,287)(78,257,107,286)(79,256,108,285)(80,255,109,284)(81,254,110,283)(82,253,111,282)(83,252,112,281)(84,251,113,280)(85,250,114,279)(86,249,115,278)(87,248,116,277)(117,296,146,325)(118,295,147,324)(119,294,148,323)(120,293,149,322)(121,292,150,321)(122,291,151,320)(123,348,152,319)(124,347,153,318)(125,346,154,317)(126,345,155,316)(127,344,156,315)(128,343,157,314)(129,342,158,313)(130,341,159,312)(131,340,160,311)(132,339,161,310)(133,338,162,309)(134,337,163,308)(135,336,164,307)(136,335,165,306)(137,334,166,305)(138,333,167,304)(139,332,168,303)(140,331,169,302)(141,330,170,301)(142,329,171,300)(143,328,172,299)(144,327,173,298)(145,326,174,297)>;
G:=Group( (1,122,102)(2,123,103)(3,124,104)(4,125,105)(5,126,106)(6,127,107)(7,128,108)(8,129,109)(9,130,110)(10,131,111)(11,132,112)(12,133,113)(13,134,114)(14,135,115)(15,136,116)(16,137,59)(17,138,60)(18,139,61)(19,140,62)(20,141,63)(21,142,64)(22,143,65)(23,144,66)(24,145,67)(25,146,68)(26,147,69)(27,148,70)(28,149,71)(29,150,72)(30,151,73)(31,152,74)(32,153,75)(33,154,76)(34,155,77)(35,156,78)(36,157,79)(37,158,80)(38,159,81)(39,160,82)(40,161,83)(41,162,84)(42,163,85)(43,164,86)(44,165,87)(45,166,88)(46,167,89)(47,168,90)(48,169,91)(49,170,92)(50,171,93)(51,172,94)(52,173,95)(53,174,96)(54,117,97)(55,118,98)(56,119,99)(57,120,100)(58,121,101)(175,291,233)(176,292,234)(177,293,235)(178,294,236)(179,295,237)(180,296,238)(181,297,239)(182,298,240)(183,299,241)(184,300,242)(185,301,243)(186,302,244)(187,303,245)(188,304,246)(189,305,247)(190,306,248)(191,307,249)(192,308,250)(193,309,251)(194,310,252)(195,311,253)(196,312,254)(197,313,255)(198,314,256)(199,315,257)(200,316,258)(201,317,259)(202,318,260)(203,319,261)(204,320,262)(205,321,263)(206,322,264)(207,323,265)(208,324,266)(209,325,267)(210,326,268)(211,327,269)(212,328,270)(213,329,271)(214,330,272)(215,331,273)(216,332,274)(217,333,275)(218,334,276)(219,335,277)(220,336,278)(221,337,279)(222,338,280)(223,339,281)(224,340,282)(225,341,283)(226,342,284)(227,343,285)(228,344,286)(229,345,287)(230,346,288)(231,347,289)(232,348,290), (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), (1,175,30,204)(2,232,31,203)(3,231,32,202)(4,230,33,201)(5,229,34,200)(6,228,35,199)(7,227,36,198)(8,226,37,197)(9,225,38,196)(10,224,39,195)(11,223,40,194)(12,222,41,193)(13,221,42,192)(14,220,43,191)(15,219,44,190)(16,218,45,189)(17,217,46,188)(18,216,47,187)(19,215,48,186)(20,214,49,185)(21,213,50,184)(22,212,51,183)(23,211,52,182)(24,210,53,181)(25,209,54,180)(26,208,55,179)(27,207,56,178)(28,206,57,177)(29,205,58,176)(59,276,88,247)(60,275,89,246)(61,274,90,245)(62,273,91,244)(63,272,92,243)(64,271,93,242)(65,270,94,241)(66,269,95,240)(67,268,96,239)(68,267,97,238)(69,266,98,237)(70,265,99,236)(71,264,100,235)(72,263,101,234)(73,262,102,233)(74,261,103,290)(75,260,104,289)(76,259,105,288)(77,258,106,287)(78,257,107,286)(79,256,108,285)(80,255,109,284)(81,254,110,283)(82,253,111,282)(83,252,112,281)(84,251,113,280)(85,250,114,279)(86,249,115,278)(87,248,116,277)(117,296,146,325)(118,295,147,324)(119,294,148,323)(120,293,149,322)(121,292,150,321)(122,291,151,320)(123,348,152,319)(124,347,153,318)(125,346,154,317)(126,345,155,316)(127,344,156,315)(128,343,157,314)(129,342,158,313)(130,341,159,312)(131,340,160,311)(132,339,161,310)(133,338,162,309)(134,337,163,308)(135,336,164,307)(136,335,165,306)(137,334,166,305)(138,333,167,304)(139,332,168,303)(140,331,169,302)(141,330,170,301)(142,329,171,300)(143,328,172,299)(144,327,173,298)(145,326,174,297) );
G=PermutationGroup([[(1,122,102),(2,123,103),(3,124,104),(4,125,105),(5,126,106),(6,127,107),(7,128,108),(8,129,109),(9,130,110),(10,131,111),(11,132,112),(12,133,113),(13,134,114),(14,135,115),(15,136,116),(16,137,59),(17,138,60),(18,139,61),(19,140,62),(20,141,63),(21,142,64),(22,143,65),(23,144,66),(24,145,67),(25,146,68),(26,147,69),(27,148,70),(28,149,71),(29,150,72),(30,151,73),(31,152,74),(32,153,75),(33,154,76),(34,155,77),(35,156,78),(36,157,79),(37,158,80),(38,159,81),(39,160,82),(40,161,83),(41,162,84),(42,163,85),(43,164,86),(44,165,87),(45,166,88),(46,167,89),(47,168,90),(48,169,91),(49,170,92),(50,171,93),(51,172,94),(52,173,95),(53,174,96),(54,117,97),(55,118,98),(56,119,99),(57,120,100),(58,121,101),(175,291,233),(176,292,234),(177,293,235),(178,294,236),(179,295,237),(180,296,238),(181,297,239),(182,298,240),(183,299,241),(184,300,242),(185,301,243),(186,302,244),(187,303,245),(188,304,246),(189,305,247),(190,306,248),(191,307,249),(192,308,250),(193,309,251),(194,310,252),(195,311,253),(196,312,254),(197,313,255),(198,314,256),(199,315,257),(200,316,258),(201,317,259),(202,318,260),(203,319,261),(204,320,262),(205,321,263),(206,322,264),(207,323,265),(208,324,266),(209,325,267),(210,326,268),(211,327,269),(212,328,270),(213,329,271),(214,330,272),(215,331,273),(216,332,274),(217,333,275),(218,334,276),(219,335,277),(220,336,278),(221,337,279),(222,338,280),(223,339,281),(224,340,282),(225,341,283),(226,342,284),(227,343,285),(228,344,286),(229,345,287),(230,346,288),(231,347,289),(232,348,290)], [(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)], [(1,175,30,204),(2,232,31,203),(3,231,32,202),(4,230,33,201),(5,229,34,200),(6,228,35,199),(7,227,36,198),(8,226,37,197),(9,225,38,196),(10,224,39,195),(11,223,40,194),(12,222,41,193),(13,221,42,192),(14,220,43,191),(15,219,44,190),(16,218,45,189),(17,217,46,188),(18,216,47,187),(19,215,48,186),(20,214,49,185),(21,213,50,184),(22,212,51,183),(23,211,52,182),(24,210,53,181),(25,209,54,180),(26,208,55,179),(27,207,56,178),(28,206,57,177),(29,205,58,176),(59,276,88,247),(60,275,89,246),(61,274,90,245),(62,273,91,244),(63,272,92,243),(64,271,93,242),(65,270,94,241),(66,269,95,240),(67,268,96,239),(68,267,97,238),(69,266,98,237),(70,265,99,236),(71,264,100,235),(72,263,101,234),(73,262,102,233),(74,261,103,290),(75,260,104,289),(76,259,105,288),(77,258,106,287),(78,257,107,286),(79,256,108,285),(80,255,109,284),(81,254,110,283),(82,253,111,282),(83,252,112,281),(84,251,113,280),(85,250,114,279),(86,249,115,278),(87,248,116,277),(117,296,146,325),(118,295,147,324),(119,294,148,323),(120,293,149,322),(121,292,150,321),(122,291,151,320),(123,348,152,319),(124,347,153,318),(125,346,154,317),(126,345,155,316),(127,344,156,315),(128,343,157,314),(129,342,158,313),(130,341,159,312),(131,340,160,311),(132,339,161,310),(133,338,162,309),(134,337,163,308),(135,336,164,307),(136,335,165,306),(137,334,166,305),(138,333,167,304),(139,332,168,303),(140,331,169,302),(141,330,170,301),(142,329,171,300),(143,328,172,299),(144,327,173,298),(145,326,174,297)]])
96 conjugacy classes
| class | 1 | 2 | 3A | 3B | 4A | 4B | 6A | 6B | 12A | 12B | 12C | 12D | 29A | ··· | 29N | 58A | ··· | 58N | 87A | ··· | 87AB | 174A | ··· | 174AB |
| order | 1 | 2 | 3 | 3 | 4 | 4 | 6 | 6 | 12 | 12 | 12 | 12 | 29 | ··· | 29 | 58 | ··· | 58 | 87 | ··· | 87 | 174 | ··· | 174 |
| size | 1 | 1 | 1 | 1 | 29 | 29 | 1 | 1 | 29 | 29 | 29 | 29 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
96 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||
| image | C1 | C2 | C3 | C4 | C6 | C12 | D29 | Dic29 | C3×D29 | C3×Dic29 |
| kernel | C3×Dic29 | C174 | Dic29 | C87 | C58 | C29 | C6 | C3 | C2 | C1 |
| # reps | 1 | 1 | 2 | 2 | 2 | 4 | 14 | 14 | 28 | 28 |
Matrix representation of C3×Dic29 ►in GL4(𝔽349) generated by
| 1 | 0 | 0 | 0 |
| 0 | 226 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 348 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 348 | 18 |
| 213 | 0 | 0 | 0 |
| 0 | 348 | 0 | 0 |
| 0 | 0 | 301 | 90 |
| 0 | 0 | 273 | 48 |
G:=sub<GL(4,GF(349))| [1,0,0,0,0,226,0,0,0,0,1,0,0,0,0,1],[348,0,0,0,0,1,0,0,0,0,0,348,0,0,1,18],[213,0,0,0,0,348,0,0,0,0,301,273,0,0,90,48] >;
C3×Dic29 in GAP, Magma, Sage, TeX
C_3\times {\rm Dic}_{29} % in TeX
G:=Group("C3xDic29"); // GroupNames label
G:=SmallGroup(348,2);
// by ID
G=gap.SmallGroup(348,2);
# by ID
G:=PCGroup([4,-2,-3,-2,-29,24,5379]);
// Polycyclic
G:=Group<a,b,c|a^3=b^58=1,c^2=b^29,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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