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G = Dic3×C31order 372 = 22·3·31

Direct product of C31 and Dic3

direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: Dic3×C31, C3⋊C124, C933C4, C6.C62, C62.2S3, C186.3C2, C2.(S3×C31), SmallGroup(372,3)

Series: Derived Chief Lower central Upper central

C1C3 — Dic3×C31
C1C3C6C186 — Dic3×C31
C3 — Dic3×C31
C1C62

Generators and relations for Dic3×C31
 G = < a,b,c | a31=b6=1, c2=b3, ab=ba, ac=ca, cbc-1=b-1 >

3C4
3C124

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

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

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

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

186 conjugacy classes

class 1  2  3 4A4B 6 31A···31AD62A···62AD93A···93AD124A···124BH186A···186AD
order12344631···3162···6293···93124···124186···186
size1123321···11···12···23···32···2

186 irreducible representations

dim1111112222
type+++-
imageC1C2C4C31C62C124S3Dic3S3×C31Dic3×C31
kernelDic3×C31C186C93Dic3C6C3C62C31C2C1
# reps112303060113030

Matrix representation of Dic3×C31 in GL2(𝔽373) generated by

2170
0217
,
1372
10
,
250313
190123
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

Subgroup lattice of Dic3×C31 in TeX

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