direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C5×Dic19, C19⋊C20, C95⋊4C4, C38.C10, C190.2C2, C10.2D19, C2.(C5×D19), SmallGroup(380,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C19 — C5×Dic19 |
Generators and relations for C5×Dic19
G = < a,b,c | a5=b38=1, c2=b19, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C5×Dic19
►Regular action on 380 points
Generators in S380
(1 190 131 84 50)(2 153 132 85 51)(3 154 133 86 52)(4 155 134 87 53)(5 156 135 88 54)(6 157 136 89 55)(7 158 137 90 56)(8 159 138 91 57)(9 160 139 92 58)(10 161 140 93 59)(11 162 141 94 60)(12 163 142 95 61)(13 164 143 96 62)(14 165 144 97 63)(15 166 145 98 64)(16 167 146 99 65)(17 168 147 100 66)(18 169 148 101 67)(19 170 149 102 68)(20 171 150 103 69)(21 172 151 104 70)(22 173 152 105 71)(23 174 115 106 72)(24 175 116 107 73)(25 176 117 108 74)(26 177 118 109 75)(27 178 119 110 76)(28 179 120 111 39)(29 180 121 112 40)(30 181 122 113 41)(31 182 123 114 42)(32 183 124 77 43)(33 184 125 78 44)(34 185 126 79 45)(35 186 127 80 46)(36 187 128 81 47)(37 188 129 82 48)(38 189 130 83 49)(191 343 324 286 248)(192 344 325 287 249)(193 345 326 288 250)(194 346 327 289 251)(195 347 328 290 252)(196 348 329 291 253)(197 349 330 292 254)(198 350 331 293 255)(199 351 332 294 256)(200 352 333 295 257)(201 353 334 296 258)(202 354 335 297 259)(203 355 336 298 260)(204 356 337 299 261)(205 357 338 300 262)(206 358 339 301 263)(207 359 340 302 264)(208 360 341 303 265)(209 361 342 304 266)(210 362 305 267 229)(211 363 306 268 230)(212 364 307 269 231)(213 365 308 270 232)(214 366 309 271 233)(215 367 310 272 234)(216 368 311 273 235)(217 369 312 274 236)(218 370 313 275 237)(219 371 314 276 238)(220 372 315 277 239)(221 373 316 278 240)(222 374 317 279 241)(223 375 318 280 242)(224 376 319 281 243)(225 377 320 282 244)(226 378 321 283 245)(227 379 322 284 246)(228 380 323 285 247)
(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)(343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380)
(1 191 20 210)(2 228 21 209)(3 227 22 208)(4 226 23 207)(5 225 24 206)(6 224 25 205)(7 223 26 204)(8 222 27 203)(9 221 28 202)(10 220 29 201)(11 219 30 200)(12 218 31 199)(13 217 32 198)(14 216 33 197)(15 215 34 196)(16 214 35 195)(17 213 36 194)(18 212 37 193)(19 211 38 192)(39 259 58 240)(40 258 59 239)(41 257 60 238)(42 256 61 237)(43 255 62 236)(44 254 63 235)(45 253 64 234)(46 252 65 233)(47 251 66 232)(48 250 67 231)(49 249 68 230)(50 248 69 229)(51 247 70 266)(52 246 71 265)(53 245 72 264)(54 244 73 263)(55 243 74 262)(56 242 75 261)(57 241 76 260)(77 293 96 274)(78 292 97 273)(79 291 98 272)(80 290 99 271)(81 289 100 270)(82 288 101 269)(83 287 102 268)(84 286 103 267)(85 285 104 304)(86 284 105 303)(87 283 106 302)(88 282 107 301)(89 281 108 300)(90 280 109 299)(91 279 110 298)(92 278 111 297)(93 277 112 296)(94 276 113 295)(95 275 114 294)(115 340 134 321)(116 339 135 320)(117 338 136 319)(118 337 137 318)(119 336 138 317)(120 335 139 316)(121 334 140 315)(122 333 141 314)(123 332 142 313)(124 331 143 312)(125 330 144 311)(126 329 145 310)(127 328 146 309)(128 327 147 308)(129 326 148 307)(130 325 149 306)(131 324 150 305)(132 323 151 342)(133 322 152 341)(153 380 172 361)(154 379 173 360)(155 378 174 359)(156 377 175 358)(157 376 176 357)(158 375 177 356)(159 374 178 355)(160 373 179 354)(161 372 180 353)(162 371 181 352)(163 370 182 351)(164 369 183 350)(165 368 184 349)(166 367 185 348)(167 366 186 347)(168 365 187 346)(169 364 188 345)(170 363 189 344)(171 362 190 343)
G:=sub<Sym(380)| (1,190,131,84,50)(2,153,132,85,51)(3,154,133,86,52)(4,155,134,87,53)(5,156,135,88,54)(6,157,136,89,55)(7,158,137,90,56)(8,159,138,91,57)(9,160,139,92,58)(10,161,140,93,59)(11,162,141,94,60)(12,163,142,95,61)(13,164,143,96,62)(14,165,144,97,63)(15,166,145,98,64)(16,167,146,99,65)(17,168,147,100,66)(18,169,148,101,67)(19,170,149,102,68)(20,171,150,103,69)(21,172,151,104,70)(22,173,152,105,71)(23,174,115,106,72)(24,175,116,107,73)(25,176,117,108,74)(26,177,118,109,75)(27,178,119,110,76)(28,179,120,111,39)(29,180,121,112,40)(30,181,122,113,41)(31,182,123,114,42)(32,183,124,77,43)(33,184,125,78,44)(34,185,126,79,45)(35,186,127,80,46)(36,187,128,81,47)(37,188,129,82,48)(38,189,130,83,49)(191,343,324,286,248)(192,344,325,287,249)(193,345,326,288,250)(194,346,327,289,251)(195,347,328,290,252)(196,348,329,291,253)(197,349,330,292,254)(198,350,331,293,255)(199,351,332,294,256)(200,352,333,295,257)(201,353,334,296,258)(202,354,335,297,259)(203,355,336,298,260)(204,356,337,299,261)(205,357,338,300,262)(206,358,339,301,263)(207,359,340,302,264)(208,360,341,303,265)(209,361,342,304,266)(210,362,305,267,229)(211,363,306,268,230)(212,364,307,269,231)(213,365,308,270,232)(214,366,309,271,233)(215,367,310,272,234)(216,368,311,273,235)(217,369,312,274,236)(218,370,313,275,237)(219,371,314,276,238)(220,372,315,277,239)(221,373,316,278,240)(222,374,317,279,241)(223,375,318,280,242)(224,376,319,281,243)(225,377,320,282,244)(226,378,321,283,245)(227,379,322,284,246)(228,380,323,285,247), (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)(343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380), (1,191,20,210)(2,228,21,209)(3,227,22,208)(4,226,23,207)(5,225,24,206)(6,224,25,205)(7,223,26,204)(8,222,27,203)(9,221,28,202)(10,220,29,201)(11,219,30,200)(12,218,31,199)(13,217,32,198)(14,216,33,197)(15,215,34,196)(16,214,35,195)(17,213,36,194)(18,212,37,193)(19,211,38,192)(39,259,58,240)(40,258,59,239)(41,257,60,238)(42,256,61,237)(43,255,62,236)(44,254,63,235)(45,253,64,234)(46,252,65,233)(47,251,66,232)(48,250,67,231)(49,249,68,230)(50,248,69,229)(51,247,70,266)(52,246,71,265)(53,245,72,264)(54,244,73,263)(55,243,74,262)(56,242,75,261)(57,241,76,260)(77,293,96,274)(78,292,97,273)(79,291,98,272)(80,290,99,271)(81,289,100,270)(82,288,101,269)(83,287,102,268)(84,286,103,267)(85,285,104,304)(86,284,105,303)(87,283,106,302)(88,282,107,301)(89,281,108,300)(90,280,109,299)(91,279,110,298)(92,278,111,297)(93,277,112,296)(94,276,113,295)(95,275,114,294)(115,340,134,321)(116,339,135,320)(117,338,136,319)(118,337,137,318)(119,336,138,317)(120,335,139,316)(121,334,140,315)(122,333,141,314)(123,332,142,313)(124,331,143,312)(125,330,144,311)(126,329,145,310)(127,328,146,309)(128,327,147,308)(129,326,148,307)(130,325,149,306)(131,324,150,305)(132,323,151,342)(133,322,152,341)(153,380,172,361)(154,379,173,360)(155,378,174,359)(156,377,175,358)(157,376,176,357)(158,375,177,356)(159,374,178,355)(160,373,179,354)(161,372,180,353)(162,371,181,352)(163,370,182,351)(164,369,183,350)(165,368,184,349)(166,367,185,348)(167,366,186,347)(168,365,187,346)(169,364,188,345)(170,363,189,344)(171,362,190,343)>;
G:=Group( (1,190,131,84,50)(2,153,132,85,51)(3,154,133,86,52)(4,155,134,87,53)(5,156,135,88,54)(6,157,136,89,55)(7,158,137,90,56)(8,159,138,91,57)(9,160,139,92,58)(10,161,140,93,59)(11,162,141,94,60)(12,163,142,95,61)(13,164,143,96,62)(14,165,144,97,63)(15,166,145,98,64)(16,167,146,99,65)(17,168,147,100,66)(18,169,148,101,67)(19,170,149,102,68)(20,171,150,103,69)(21,172,151,104,70)(22,173,152,105,71)(23,174,115,106,72)(24,175,116,107,73)(25,176,117,108,74)(26,177,118,109,75)(27,178,119,110,76)(28,179,120,111,39)(29,180,121,112,40)(30,181,122,113,41)(31,182,123,114,42)(32,183,124,77,43)(33,184,125,78,44)(34,185,126,79,45)(35,186,127,80,46)(36,187,128,81,47)(37,188,129,82,48)(38,189,130,83,49)(191,343,324,286,248)(192,344,325,287,249)(193,345,326,288,250)(194,346,327,289,251)(195,347,328,290,252)(196,348,329,291,253)(197,349,330,292,254)(198,350,331,293,255)(199,351,332,294,256)(200,352,333,295,257)(201,353,334,296,258)(202,354,335,297,259)(203,355,336,298,260)(204,356,337,299,261)(205,357,338,300,262)(206,358,339,301,263)(207,359,340,302,264)(208,360,341,303,265)(209,361,342,304,266)(210,362,305,267,229)(211,363,306,268,230)(212,364,307,269,231)(213,365,308,270,232)(214,366,309,271,233)(215,367,310,272,234)(216,368,311,273,235)(217,369,312,274,236)(218,370,313,275,237)(219,371,314,276,238)(220,372,315,277,239)(221,373,316,278,240)(222,374,317,279,241)(223,375,318,280,242)(224,376,319,281,243)(225,377,320,282,244)(226,378,321,283,245)(227,379,322,284,246)(228,380,323,285,247), (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)(343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380), (1,191,20,210)(2,228,21,209)(3,227,22,208)(4,226,23,207)(5,225,24,206)(6,224,25,205)(7,223,26,204)(8,222,27,203)(9,221,28,202)(10,220,29,201)(11,219,30,200)(12,218,31,199)(13,217,32,198)(14,216,33,197)(15,215,34,196)(16,214,35,195)(17,213,36,194)(18,212,37,193)(19,211,38,192)(39,259,58,240)(40,258,59,239)(41,257,60,238)(42,256,61,237)(43,255,62,236)(44,254,63,235)(45,253,64,234)(46,252,65,233)(47,251,66,232)(48,250,67,231)(49,249,68,230)(50,248,69,229)(51,247,70,266)(52,246,71,265)(53,245,72,264)(54,244,73,263)(55,243,74,262)(56,242,75,261)(57,241,76,260)(77,293,96,274)(78,292,97,273)(79,291,98,272)(80,290,99,271)(81,289,100,270)(82,288,101,269)(83,287,102,268)(84,286,103,267)(85,285,104,304)(86,284,105,303)(87,283,106,302)(88,282,107,301)(89,281,108,300)(90,280,109,299)(91,279,110,298)(92,278,111,297)(93,277,112,296)(94,276,113,295)(95,275,114,294)(115,340,134,321)(116,339,135,320)(117,338,136,319)(118,337,137,318)(119,336,138,317)(120,335,139,316)(121,334,140,315)(122,333,141,314)(123,332,142,313)(124,331,143,312)(125,330,144,311)(126,329,145,310)(127,328,146,309)(128,327,147,308)(129,326,148,307)(130,325,149,306)(131,324,150,305)(132,323,151,342)(133,322,152,341)(153,380,172,361)(154,379,173,360)(155,378,174,359)(156,377,175,358)(157,376,176,357)(158,375,177,356)(159,374,178,355)(160,373,179,354)(161,372,180,353)(162,371,181,352)(163,370,182,351)(164,369,183,350)(165,368,184,349)(166,367,185,348)(167,366,186,347)(168,365,187,346)(169,364,188,345)(170,363,189,344)(171,362,190,343) );
G=PermutationGroup([[(1,190,131,84,50),(2,153,132,85,51),(3,154,133,86,52),(4,155,134,87,53),(5,156,135,88,54),(6,157,136,89,55),(7,158,137,90,56),(8,159,138,91,57),(9,160,139,92,58),(10,161,140,93,59),(11,162,141,94,60),(12,163,142,95,61),(13,164,143,96,62),(14,165,144,97,63),(15,166,145,98,64),(16,167,146,99,65),(17,168,147,100,66),(18,169,148,101,67),(19,170,149,102,68),(20,171,150,103,69),(21,172,151,104,70),(22,173,152,105,71),(23,174,115,106,72),(24,175,116,107,73),(25,176,117,108,74),(26,177,118,109,75),(27,178,119,110,76),(28,179,120,111,39),(29,180,121,112,40),(30,181,122,113,41),(31,182,123,114,42),(32,183,124,77,43),(33,184,125,78,44),(34,185,126,79,45),(35,186,127,80,46),(36,187,128,81,47),(37,188,129,82,48),(38,189,130,83,49),(191,343,324,286,248),(192,344,325,287,249),(193,345,326,288,250),(194,346,327,289,251),(195,347,328,290,252),(196,348,329,291,253),(197,349,330,292,254),(198,350,331,293,255),(199,351,332,294,256),(200,352,333,295,257),(201,353,334,296,258),(202,354,335,297,259),(203,355,336,298,260),(204,356,337,299,261),(205,357,338,300,262),(206,358,339,301,263),(207,359,340,302,264),(208,360,341,303,265),(209,361,342,304,266),(210,362,305,267,229),(211,363,306,268,230),(212,364,307,269,231),(213,365,308,270,232),(214,366,309,271,233),(215,367,310,272,234),(216,368,311,273,235),(217,369,312,274,236),(218,370,313,275,237),(219,371,314,276,238),(220,372,315,277,239),(221,373,316,278,240),(222,374,317,279,241),(223,375,318,280,242),(224,376,319,281,243),(225,377,320,282,244),(226,378,321,283,245),(227,379,322,284,246),(228,380,323,285,247)], [(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),(343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380)], [(1,191,20,210),(2,228,21,209),(3,227,22,208),(4,226,23,207),(5,225,24,206),(6,224,25,205),(7,223,26,204),(8,222,27,203),(9,221,28,202),(10,220,29,201),(11,219,30,200),(12,218,31,199),(13,217,32,198),(14,216,33,197),(15,215,34,196),(16,214,35,195),(17,213,36,194),(18,212,37,193),(19,211,38,192),(39,259,58,240),(40,258,59,239),(41,257,60,238),(42,256,61,237),(43,255,62,236),(44,254,63,235),(45,253,64,234),(46,252,65,233),(47,251,66,232),(48,250,67,231),(49,249,68,230),(50,248,69,229),(51,247,70,266),(52,246,71,265),(53,245,72,264),(54,244,73,263),(55,243,74,262),(56,242,75,261),(57,241,76,260),(77,293,96,274),(78,292,97,273),(79,291,98,272),(80,290,99,271),(81,289,100,270),(82,288,101,269),(83,287,102,268),(84,286,103,267),(85,285,104,304),(86,284,105,303),(87,283,106,302),(88,282,107,301),(89,281,108,300),(90,280,109,299),(91,279,110,298),(92,278,111,297),(93,277,112,296),(94,276,113,295),(95,275,114,294),(115,340,134,321),(116,339,135,320),(117,338,136,319),(118,337,137,318),(119,336,138,317),(120,335,139,316),(121,334,140,315),(122,333,141,314),(123,332,142,313),(124,331,143,312),(125,330,144,311),(126,329,145,310),(127,328,146,309),(128,327,147,308),(129,326,148,307),(130,325,149,306),(131,324,150,305),(132,323,151,342),(133,322,152,341),(153,380,172,361),(154,379,173,360),(155,378,174,359),(156,377,175,358),(157,376,176,357),(158,375,177,356),(159,374,178,355),(160,373,179,354),(161,372,180,353),(162,371,181,352),(163,370,182,351),(164,369,183,350),(165,368,184,349),(166,367,185,348),(167,366,186,347),(168,365,187,346),(169,364,188,345),(170,363,189,344),(171,362,190,343)]])
110 conjugacy classes
| class | 1 | 2 | 4A | 4B | 5A | 5B | 5C | 5D | 10A | 10B | 10C | 10D | 19A | ··· | 19I | 20A | ··· | 20H | 38A | ··· | 38I | 95A | ··· | 95AJ | 190A | ··· | 190AJ |
| order | 1 | 2 | 4 | 4 | 5 | 5 | 5 | 5 | 10 | 10 | 10 | 10 | 19 | ··· | 19 | 20 | ··· | 20 | 38 | ··· | 38 | 95 | ··· | 95 | 190 | ··· | 190 |
| size | 1 | 1 | 19 | 19 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 19 | ··· | 19 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
110 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||
| image | C1 | C2 | C4 | C5 | C10 | C20 | D19 | Dic19 | C5×D19 | C5×Dic19 |
| kernel | C5×Dic19 | C190 | C95 | Dic19 | C38 | C19 | C10 | C5 | C2 | C1 |
| # reps | 1 | 1 | 2 | 4 | 4 | 8 | 9 | 9 | 36 | 36 |
Matrix representation of C5×Dic19 ►in GL2(𝔽761) generated by
| 168 | 0 |
| 0 | 168 |
| 0 | 760 |
| 1 | 611 |
| 690 | 742 |
| 746 | 71 |
G:=sub<GL(2,GF(761))| [168,0,0,168],[0,1,760,611],[690,746,742,71] >;
C5×Dic19 in GAP, Magma, Sage, TeX
C_5\times {\rm Dic}_{19} % in TeX
G:=Group("C5xDic19"); // GroupNames label
G:=SmallGroup(380,2);
// by ID
G=gap.SmallGroup(380,2);
# by ID
G:=PCGroup([4,-2,-5,-2,-19,40,5763]);
// Polycyclic
G:=Group<a,b,c|a^5=b^38=1,c^2=b^19,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export