direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: Dic3×C31, C3⋊C124, C93⋊3C4, C6.C62, C62.2S3, C186.3C2, C2.(S3×C31), SmallGroup(372,3)
Series: Derived ►Chief ►Lower central ►Upper central
| C3 — Dic3×C31 |
Generators and relations for Dic3×C31
G = < a,b,c | a31=b6=1, c2=b3, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of Dic3×C31
►Regular action on 372 points
Generators in S372
(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)
(1 369 173 273 196 281)(2 370 174 274 197 282)(3 371 175 275 198 283)(4 372 176 276 199 284)(5 342 177 277 200 285)(6 343 178 278 201 286)(7 344 179 279 202 287)(8 345 180 249 203 288)(9 346 181 250 204 289)(10 347 182 251 205 290)(11 348 183 252 206 291)(12 349 184 253 207 292)(13 350 185 254 208 293)(14 351 186 255 209 294)(15 352 156 256 210 295)(16 353 157 257 211 296)(17 354 158 258 212 297)(18 355 159 259 213 298)(19 356 160 260 214 299)(20 357 161 261 215 300)(21 358 162 262 216 301)(22 359 163 263 217 302)(23 360 164 264 187 303)(24 361 165 265 188 304)(25 362 166 266 189 305)(26 363 167 267 190 306)(27 364 168 268 191 307)(28 365 169 269 192 308)(29 366 170 270 193 309)(30 367 171 271 194 310)(31 368 172 272 195 280)(32 245 325 88 148 116)(33 246 326 89 149 117)(34 247 327 90 150 118)(35 248 328 91 151 119)(36 218 329 92 152 120)(37 219 330 93 153 121)(38 220 331 63 154 122)(39 221 332 64 155 123)(40 222 333 65 125 124)(41 223 334 66 126 94)(42 224 335 67 127 95)(43 225 336 68 128 96)(44 226 337 69 129 97)(45 227 338 70 130 98)(46 228 339 71 131 99)(47 229 340 72 132 100)(48 230 341 73 133 101)(49 231 311 74 134 102)(50 232 312 75 135 103)(51 233 313 76 136 104)(52 234 314 77 137 105)(53 235 315 78 138 106)(54 236 316 79 139 107)(55 237 317 80 140 108)(56 238 318 81 141 109)(57 239 319 82 142 110)(58 240 320 83 143 111)(59 241 321 84 144 112)(60 242 322 85 145 113)(61 243 323 86 146 114)(62 244 324 87 147 115)
(1 112 273 321)(2 113 274 322)(3 114 275 323)(4 115 276 324)(5 116 277 325)(6 117 278 326)(7 118 279 327)(8 119 249 328)(9 120 250 329)(10 121 251 330)(11 122 252 331)(12 123 253 332)(13 124 254 333)(14 94 255 334)(15 95 256 335)(16 96 257 336)(17 97 258 337)(18 98 259 338)(19 99 260 339)(20 100 261 340)(21 101 262 341)(22 102 263 311)(23 103 264 312)(24 104 265 313)(25 105 266 314)(26 106 267 315)(27 107 268 316)(28 108 269 317)(29 109 270 318)(30 110 271 319)(31 111 272 320)(32 177 88 285)(33 178 89 286)(34 179 90 287)(35 180 91 288)(36 181 92 289)(37 182 93 290)(38 183 63 291)(39 184 64 292)(40 185 65 293)(41 186 66 294)(42 156 67 295)(43 157 68 296)(44 158 69 297)(45 159 70 298)(46 160 71 299)(47 161 72 300)(48 162 73 301)(49 163 74 302)(50 164 75 303)(51 165 76 304)(52 166 77 305)(53 167 78 306)(54 168 79 307)(55 169 80 308)(56 170 81 309)(57 171 82 310)(58 172 83 280)(59 173 84 281)(60 174 85 282)(61 175 86 283)(62 176 87 284)(125 208 222 350)(126 209 223 351)(127 210 224 352)(128 211 225 353)(129 212 226 354)(130 213 227 355)(131 214 228 356)(132 215 229 357)(133 216 230 358)(134 217 231 359)(135 187 232 360)(136 188 233 361)(137 189 234 362)(138 190 235 363)(139 191 236 364)(140 192 237 365)(141 193 238 366)(142 194 239 367)(143 195 240 368)(144 196 241 369)(145 197 242 370)(146 198 243 371)(147 199 244 372)(148 200 245 342)(149 201 246 343)(150 202 247 344)(151 203 248 345)(152 204 218 346)(153 205 219 347)(154 206 220 348)(155 207 221 349)
G:=sub<Sym(372)| (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), (1,369,173,273,196,281)(2,370,174,274,197,282)(3,371,175,275,198,283)(4,372,176,276,199,284)(5,342,177,277,200,285)(6,343,178,278,201,286)(7,344,179,279,202,287)(8,345,180,249,203,288)(9,346,181,250,204,289)(10,347,182,251,205,290)(11,348,183,252,206,291)(12,349,184,253,207,292)(13,350,185,254,208,293)(14,351,186,255,209,294)(15,352,156,256,210,295)(16,353,157,257,211,296)(17,354,158,258,212,297)(18,355,159,259,213,298)(19,356,160,260,214,299)(20,357,161,261,215,300)(21,358,162,262,216,301)(22,359,163,263,217,302)(23,360,164,264,187,303)(24,361,165,265,188,304)(25,362,166,266,189,305)(26,363,167,267,190,306)(27,364,168,268,191,307)(28,365,169,269,192,308)(29,366,170,270,193,309)(30,367,171,271,194,310)(31,368,172,272,195,280)(32,245,325,88,148,116)(33,246,326,89,149,117)(34,247,327,90,150,118)(35,248,328,91,151,119)(36,218,329,92,152,120)(37,219,330,93,153,121)(38,220,331,63,154,122)(39,221,332,64,155,123)(40,222,333,65,125,124)(41,223,334,66,126,94)(42,224,335,67,127,95)(43,225,336,68,128,96)(44,226,337,69,129,97)(45,227,338,70,130,98)(46,228,339,71,131,99)(47,229,340,72,132,100)(48,230,341,73,133,101)(49,231,311,74,134,102)(50,232,312,75,135,103)(51,233,313,76,136,104)(52,234,314,77,137,105)(53,235,315,78,138,106)(54,236,316,79,139,107)(55,237,317,80,140,108)(56,238,318,81,141,109)(57,239,319,82,142,110)(58,240,320,83,143,111)(59,241,321,84,144,112)(60,242,322,85,145,113)(61,243,323,86,146,114)(62,244,324,87,147,115), (1,112,273,321)(2,113,274,322)(3,114,275,323)(4,115,276,324)(5,116,277,325)(6,117,278,326)(7,118,279,327)(8,119,249,328)(9,120,250,329)(10,121,251,330)(11,122,252,331)(12,123,253,332)(13,124,254,333)(14,94,255,334)(15,95,256,335)(16,96,257,336)(17,97,258,337)(18,98,259,338)(19,99,260,339)(20,100,261,340)(21,101,262,341)(22,102,263,311)(23,103,264,312)(24,104,265,313)(25,105,266,314)(26,106,267,315)(27,107,268,316)(28,108,269,317)(29,109,270,318)(30,110,271,319)(31,111,272,320)(32,177,88,285)(33,178,89,286)(34,179,90,287)(35,180,91,288)(36,181,92,289)(37,182,93,290)(38,183,63,291)(39,184,64,292)(40,185,65,293)(41,186,66,294)(42,156,67,295)(43,157,68,296)(44,158,69,297)(45,159,70,298)(46,160,71,299)(47,161,72,300)(48,162,73,301)(49,163,74,302)(50,164,75,303)(51,165,76,304)(52,166,77,305)(53,167,78,306)(54,168,79,307)(55,169,80,308)(56,170,81,309)(57,171,82,310)(58,172,83,280)(59,173,84,281)(60,174,85,282)(61,175,86,283)(62,176,87,284)(125,208,222,350)(126,209,223,351)(127,210,224,352)(128,211,225,353)(129,212,226,354)(130,213,227,355)(131,214,228,356)(132,215,229,357)(133,216,230,358)(134,217,231,359)(135,187,232,360)(136,188,233,361)(137,189,234,362)(138,190,235,363)(139,191,236,364)(140,192,237,365)(141,193,238,366)(142,194,239,367)(143,195,240,368)(144,196,241,369)(145,197,242,370)(146,198,243,371)(147,199,244,372)(148,200,245,342)(149,201,246,343)(150,202,247,344)(151,203,248,345)(152,204,218,346)(153,205,219,347)(154,206,220,348)(155,207,221,349)>;
G:=Group( (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), (1,369,173,273,196,281)(2,370,174,274,197,282)(3,371,175,275,198,283)(4,372,176,276,199,284)(5,342,177,277,200,285)(6,343,178,278,201,286)(7,344,179,279,202,287)(8,345,180,249,203,288)(9,346,181,250,204,289)(10,347,182,251,205,290)(11,348,183,252,206,291)(12,349,184,253,207,292)(13,350,185,254,208,293)(14,351,186,255,209,294)(15,352,156,256,210,295)(16,353,157,257,211,296)(17,354,158,258,212,297)(18,355,159,259,213,298)(19,356,160,260,214,299)(20,357,161,261,215,300)(21,358,162,262,216,301)(22,359,163,263,217,302)(23,360,164,264,187,303)(24,361,165,265,188,304)(25,362,166,266,189,305)(26,363,167,267,190,306)(27,364,168,268,191,307)(28,365,169,269,192,308)(29,366,170,270,193,309)(30,367,171,271,194,310)(31,368,172,272,195,280)(32,245,325,88,148,116)(33,246,326,89,149,117)(34,247,327,90,150,118)(35,248,328,91,151,119)(36,218,329,92,152,120)(37,219,330,93,153,121)(38,220,331,63,154,122)(39,221,332,64,155,123)(40,222,333,65,125,124)(41,223,334,66,126,94)(42,224,335,67,127,95)(43,225,336,68,128,96)(44,226,337,69,129,97)(45,227,338,70,130,98)(46,228,339,71,131,99)(47,229,340,72,132,100)(48,230,341,73,133,101)(49,231,311,74,134,102)(50,232,312,75,135,103)(51,233,313,76,136,104)(52,234,314,77,137,105)(53,235,315,78,138,106)(54,236,316,79,139,107)(55,237,317,80,140,108)(56,238,318,81,141,109)(57,239,319,82,142,110)(58,240,320,83,143,111)(59,241,321,84,144,112)(60,242,322,85,145,113)(61,243,323,86,146,114)(62,244,324,87,147,115), (1,112,273,321)(2,113,274,322)(3,114,275,323)(4,115,276,324)(5,116,277,325)(6,117,278,326)(7,118,279,327)(8,119,249,328)(9,120,250,329)(10,121,251,330)(11,122,252,331)(12,123,253,332)(13,124,254,333)(14,94,255,334)(15,95,256,335)(16,96,257,336)(17,97,258,337)(18,98,259,338)(19,99,260,339)(20,100,261,340)(21,101,262,341)(22,102,263,311)(23,103,264,312)(24,104,265,313)(25,105,266,314)(26,106,267,315)(27,107,268,316)(28,108,269,317)(29,109,270,318)(30,110,271,319)(31,111,272,320)(32,177,88,285)(33,178,89,286)(34,179,90,287)(35,180,91,288)(36,181,92,289)(37,182,93,290)(38,183,63,291)(39,184,64,292)(40,185,65,293)(41,186,66,294)(42,156,67,295)(43,157,68,296)(44,158,69,297)(45,159,70,298)(46,160,71,299)(47,161,72,300)(48,162,73,301)(49,163,74,302)(50,164,75,303)(51,165,76,304)(52,166,77,305)(53,167,78,306)(54,168,79,307)(55,169,80,308)(56,170,81,309)(57,171,82,310)(58,172,83,280)(59,173,84,281)(60,174,85,282)(61,175,86,283)(62,176,87,284)(125,208,222,350)(126,209,223,351)(127,210,224,352)(128,211,225,353)(129,212,226,354)(130,213,227,355)(131,214,228,356)(132,215,229,357)(133,216,230,358)(134,217,231,359)(135,187,232,360)(136,188,233,361)(137,189,234,362)(138,190,235,363)(139,191,236,364)(140,192,237,365)(141,193,238,366)(142,194,239,367)(143,195,240,368)(144,196,241,369)(145,197,242,370)(146,198,243,371)(147,199,244,372)(148,200,245,342)(149,201,246,343)(150,202,247,344)(151,203,248,345)(152,204,218,346)(153,205,219,347)(154,206,220,348)(155,207,221,349) );
G=PermutationGroup([[(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)], [(1,369,173,273,196,281),(2,370,174,274,197,282),(3,371,175,275,198,283),(4,372,176,276,199,284),(5,342,177,277,200,285),(6,343,178,278,201,286),(7,344,179,279,202,287),(8,345,180,249,203,288),(9,346,181,250,204,289),(10,347,182,251,205,290),(11,348,183,252,206,291),(12,349,184,253,207,292),(13,350,185,254,208,293),(14,351,186,255,209,294),(15,352,156,256,210,295),(16,353,157,257,211,296),(17,354,158,258,212,297),(18,355,159,259,213,298),(19,356,160,260,214,299),(20,357,161,261,215,300),(21,358,162,262,216,301),(22,359,163,263,217,302),(23,360,164,264,187,303),(24,361,165,265,188,304),(25,362,166,266,189,305),(26,363,167,267,190,306),(27,364,168,268,191,307),(28,365,169,269,192,308),(29,366,170,270,193,309),(30,367,171,271,194,310),(31,368,172,272,195,280),(32,245,325,88,148,116),(33,246,326,89,149,117),(34,247,327,90,150,118),(35,248,328,91,151,119),(36,218,329,92,152,120),(37,219,330,93,153,121),(38,220,331,63,154,122),(39,221,332,64,155,123),(40,222,333,65,125,124),(41,223,334,66,126,94),(42,224,335,67,127,95),(43,225,336,68,128,96),(44,226,337,69,129,97),(45,227,338,70,130,98),(46,228,339,71,131,99),(47,229,340,72,132,100),(48,230,341,73,133,101),(49,231,311,74,134,102),(50,232,312,75,135,103),(51,233,313,76,136,104),(52,234,314,77,137,105),(53,235,315,78,138,106),(54,236,316,79,139,107),(55,237,317,80,140,108),(56,238,318,81,141,109),(57,239,319,82,142,110),(58,240,320,83,143,111),(59,241,321,84,144,112),(60,242,322,85,145,113),(61,243,323,86,146,114),(62,244,324,87,147,115)], [(1,112,273,321),(2,113,274,322),(3,114,275,323),(4,115,276,324),(5,116,277,325),(6,117,278,326),(7,118,279,327),(8,119,249,328),(9,120,250,329),(10,121,251,330),(11,122,252,331),(12,123,253,332),(13,124,254,333),(14,94,255,334),(15,95,256,335),(16,96,257,336),(17,97,258,337),(18,98,259,338),(19,99,260,339),(20,100,261,340),(21,101,262,341),(22,102,263,311),(23,103,264,312),(24,104,265,313),(25,105,266,314),(26,106,267,315),(27,107,268,316),(28,108,269,317),(29,109,270,318),(30,110,271,319),(31,111,272,320),(32,177,88,285),(33,178,89,286),(34,179,90,287),(35,180,91,288),(36,181,92,289),(37,182,93,290),(38,183,63,291),(39,184,64,292),(40,185,65,293),(41,186,66,294),(42,156,67,295),(43,157,68,296),(44,158,69,297),(45,159,70,298),(46,160,71,299),(47,161,72,300),(48,162,73,301),(49,163,74,302),(50,164,75,303),(51,165,76,304),(52,166,77,305),(53,167,78,306),(54,168,79,307),(55,169,80,308),(56,170,81,309),(57,171,82,310),(58,172,83,280),(59,173,84,281),(60,174,85,282),(61,175,86,283),(62,176,87,284),(125,208,222,350),(126,209,223,351),(127,210,224,352),(128,211,225,353),(129,212,226,354),(130,213,227,355),(131,214,228,356),(132,215,229,357),(133,216,230,358),(134,217,231,359),(135,187,232,360),(136,188,233,361),(137,189,234,362),(138,190,235,363),(139,191,236,364),(140,192,237,365),(141,193,238,366),(142,194,239,367),(143,195,240,368),(144,196,241,369),(145,197,242,370),(146,198,243,371),(147,199,244,372),(148,200,245,342),(149,201,246,343),(150,202,247,344),(151,203,248,345),(152,204,218,346),(153,205,219,347),(154,206,220,348),(155,207,221,349)]])
186 conjugacy classes
| class | 1 | 2 | 3 | 4A | 4B | 6 | 31A | ··· | 31AD | 62A | ··· | 62AD | 93A | ··· | 93AD | 124A | ··· | 124BH | 186A | ··· | 186AD |
| order | 1 | 2 | 3 | 4 | 4 | 6 | 31 | ··· | 31 | 62 | ··· | 62 | 93 | ··· | 93 | 124 | ··· | 124 | 186 | ··· | 186 |
| size | 1 | 1 | 2 | 3 | 3 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 3 | ··· | 3 | 2 | ··· | 2 |
186 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||
| image | C1 | C2 | C4 | C31 | C62 | C124 | S3 | Dic3 | S3×C31 | Dic3×C31 |
| kernel | Dic3×C31 | C186 | C93 | Dic3 | C6 | C3 | C62 | C31 | C2 | C1 |
| # reps | 1 | 1 | 2 | 30 | 30 | 60 | 1 | 1 | 30 | 30 |
Matrix representation of Dic3×C31 ►in GL2(𝔽373) generated by
| 217 | 0 |
| 0 | 217 |
| 1 | 372 |
| 1 | 0 |
| 250 | 313 |
| 190 | 123 |
G:=sub<GL(2,GF(373))| [217,0,0,217],[1,1,372,0],[250,190,313,123] >;
Dic3×C31 in GAP, Magma, Sage, TeX
{\rm Dic}_3\times C_{31} % in TeX
G:=Group("Dic3xC31"); // GroupNames label
G:=SmallGroup(372,3);
// by ID
G=gap.SmallGroup(372,3);
# by ID
G:=PCGroup([4,-2,-31,-2,-3,248,3971]);
// Polycyclic
G:=Group<a,b,c|a^31=b^6=1,c^2=b^3,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export