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G = C3×Dic31order 372 = 22·3·31

Direct product of C3 and Dic31

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

Aliases: C3×Dic31, C932C4, C313C12, C62.3C6, C6.2D31, C186.2C2, C2.(C3×D31), SmallGroup(372,4)

Series: Derived Chief Lower central Upper central

C1C31 — C3×Dic31
C1C31C62C186 — C3×Dic31
C31 — C3×Dic31
C1C6

Generators and relations for C3×Dic31
 G = < a,b,c | a3=b62=1, c2=b31, ab=ba, ac=ca, cbc-1=b-1 >

31C4
31C12

Smallest permutation representation of C3×Dic31
Regular action on 372 points
Generators in S372
(1 182 123)(2 183 124)(3 184 63)(4 185 64)(5 186 65)(6 125 66)(7 126 67)(8 127 68)(9 128 69)(10 129 70)(11 130 71)(12 131 72)(13 132 73)(14 133 74)(15 134 75)(16 135 76)(17 136 77)(18 137 78)(19 138 79)(20 139 80)(21 140 81)(22 141 82)(23 142 83)(24 143 84)(25 144 85)(26 145 86)(27 146 87)(28 147 88)(29 148 89)(30 149 90)(31 150 91)(32 151 92)(33 152 93)(34 153 94)(35 154 95)(36 155 96)(37 156 97)(38 157 98)(39 158 99)(40 159 100)(41 160 101)(42 161 102)(43 162 103)(44 163 104)(45 164 105)(46 165 106)(47 166 107)(48 167 108)(49 168 109)(50 169 110)(51 170 111)(52 171 112)(53 172 113)(54 173 114)(55 174 115)(56 175 116)(57 176 117)(58 177 118)(59 178 119)(60 179 120)(61 180 121)(62 181 122)(187 311 249)(188 312 250)(189 313 251)(190 314 252)(191 315 253)(192 316 254)(193 317 255)(194 318 256)(195 319 257)(196 320 258)(197 321 259)(198 322 260)(199 323 261)(200 324 262)(201 325 263)(202 326 264)(203 327 265)(204 328 266)(205 329 267)(206 330 268)(207 331 269)(208 332 270)(209 333 271)(210 334 272)(211 335 273)(212 336 274)(213 337 275)(214 338 276)(215 339 277)(216 340 278)(217 341 279)(218 342 280)(219 343 281)(220 344 282)(221 345 283)(222 346 284)(223 347 285)(224 348 286)(225 349 287)(226 350 288)(227 351 289)(228 352 290)(229 353 291)(230 354 292)(231 355 293)(232 356 294)(233 357 295)(234 358 296)(235 359 297)(236 360 298)(237 361 299)(238 362 300)(239 363 301)(240 364 302)(241 365 303)(242 366 304)(243 367 305)(244 368 306)(245 369 307)(246 370 308)(247 371 309)(248 372 310)
(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)
(1 218 32 187)(2 217 33 248)(3 216 34 247)(4 215 35 246)(5 214 36 245)(6 213 37 244)(7 212 38 243)(8 211 39 242)(9 210 40 241)(10 209 41 240)(11 208 42 239)(12 207 43 238)(13 206 44 237)(14 205 45 236)(15 204 46 235)(16 203 47 234)(17 202 48 233)(18 201 49 232)(19 200 50 231)(20 199 51 230)(21 198 52 229)(22 197 53 228)(23 196 54 227)(24 195 55 226)(25 194 56 225)(26 193 57 224)(27 192 58 223)(28 191 59 222)(29 190 60 221)(30 189 61 220)(31 188 62 219)(63 278 94 309)(64 277 95 308)(65 276 96 307)(66 275 97 306)(67 274 98 305)(68 273 99 304)(69 272 100 303)(70 271 101 302)(71 270 102 301)(72 269 103 300)(73 268 104 299)(74 267 105 298)(75 266 106 297)(76 265 107 296)(77 264 108 295)(78 263 109 294)(79 262 110 293)(80 261 111 292)(81 260 112 291)(82 259 113 290)(83 258 114 289)(84 257 115 288)(85 256 116 287)(86 255 117 286)(87 254 118 285)(88 253 119 284)(89 252 120 283)(90 251 121 282)(91 250 122 281)(92 249 123 280)(93 310 124 279)(125 337 156 368)(126 336 157 367)(127 335 158 366)(128 334 159 365)(129 333 160 364)(130 332 161 363)(131 331 162 362)(132 330 163 361)(133 329 164 360)(134 328 165 359)(135 327 166 358)(136 326 167 357)(137 325 168 356)(138 324 169 355)(139 323 170 354)(140 322 171 353)(141 321 172 352)(142 320 173 351)(143 319 174 350)(144 318 175 349)(145 317 176 348)(146 316 177 347)(147 315 178 346)(148 314 179 345)(149 313 180 344)(150 312 181 343)(151 311 182 342)(152 372 183 341)(153 371 184 340)(154 370 185 339)(155 369 186 338)

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

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

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

102 conjugacy classes

class 1  2 3A3B4A4B6A6B12A12B12C12D31A···31O62A···62O93A···93AD186A···186AD
order123344661212121231···3162···6293···93186···186
size1111313111313131312···22···22···22···2

102 irreducible representations

dim1111112222
type+++-
imageC1C2C3C4C6C12D31Dic31C3×D31C3×Dic31
kernelC3×Dic31C186Dic31C93C62C31C6C3C2C1
# reps11222415153030

Matrix representation of C3×Dic31 in GL2(𝔽373) generated by

880
088
,
0372
1241
,
42300
249331
G:=sub<GL(2,GF(373))| [88,0,0,88],[0,1,372,241],[42,249,300,331] >;

C3×Dic31 in GAP, Magma, Sage, TeX

C_3\times {\rm Dic}_{31}
% in TeX

G:=Group("C3xDic31");
// GroupNames label

G:=SmallGroup(372,4);
// by ID

G=gap.SmallGroup(372,4);
# by ID

G:=PCGroup([4,-2,-3,-2,-31,24,5763]);
// Polycyclic

G:=Group<a,b,c|a^3=b^62=1,c^2=b^31,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C3×Dic31 in TeX

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