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G = C5×Dic19order 380 = 22·5·19

Direct product of C5 and Dic19

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

Aliases: C5×Dic19, C19⋊C20, C954C4, C38.C10, C190.2C2, C10.2D19, C2.(C5×D19), SmallGroup(380,2)

Series: Derived Chief Lower central Upper central

C1C19 — C5×Dic19
C1C19C38C190 — C5×Dic19
C19 — C5×Dic19
C1C10

Generators and relations for C5×Dic19
 G = < a,b,c | a5=b38=1, c2=b19, ab=ba, ac=ca, cbc-1=b-1 >

19C4
19C20

Smallest permutation representation of C5×Dic19
Regular action on 380 points
Generators in S380
(1 181 118 113 71)(2 182 119 114 72)(3 183 120 77 73)(4 184 121 78 74)(5 185 122 79 75)(6 186 123 80 76)(7 187 124 81 39)(8 188 125 82 40)(9 189 126 83 41)(10 190 127 84 42)(11 153 128 85 43)(12 154 129 86 44)(13 155 130 87 45)(14 156 131 88 46)(15 157 132 89 47)(16 158 133 90 48)(17 159 134 91 49)(18 160 135 92 50)(19 161 136 93 51)(20 162 137 94 52)(21 163 138 95 53)(22 164 139 96 54)(23 165 140 97 55)(24 166 141 98 56)(25 167 142 99 57)(26 168 143 100 58)(27 169 144 101 59)(28 170 145 102 60)(29 171 146 103 61)(30 172 147 104 62)(31 173 148 105 63)(32 174 149 106 64)(33 175 150 107 65)(34 176 151 108 66)(35 177 152 109 67)(36 178 115 110 68)(37 179 116 111 69)(38 180 117 112 70)(191 343 305 286 229)(192 344 306 287 230)(193 345 307 288 231)(194 346 308 289 232)(195 347 309 290 233)(196 348 310 291 234)(197 349 311 292 235)(198 350 312 293 236)(199 351 313 294 237)(200 352 314 295 238)(201 353 315 296 239)(202 354 316 297 240)(203 355 317 298 241)(204 356 318 299 242)(205 357 319 300 243)(206 358 320 301 244)(207 359 321 302 245)(208 360 322 303 246)(209 361 323 304 247)(210 362 324 267 248)(211 363 325 268 249)(212 364 326 269 250)(213 365 327 270 251)(214 366 328 271 252)(215 367 329 272 253)(216 368 330 273 254)(217 369 331 274 255)(218 370 332 275 256)(219 371 333 276 257)(220 372 334 277 258)(221 373 335 278 259)(222 374 336 279 260)(223 375 337 280 261)(224 376 338 281 262)(225 377 339 282 263)(226 378 340 283 264)(227 379 341 284 265)(228 380 342 285 266)
(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)
(1 210 20 191)(2 209 21 228)(3 208 22 227)(4 207 23 226)(5 206 24 225)(6 205 25 224)(7 204 26 223)(8 203 27 222)(9 202 28 221)(10 201 29 220)(11 200 30 219)(12 199 31 218)(13 198 32 217)(14 197 33 216)(15 196 34 215)(16 195 35 214)(17 194 36 213)(18 193 37 212)(19 192 38 211)(39 242 58 261)(40 241 59 260)(41 240 60 259)(42 239 61 258)(43 238 62 257)(44 237 63 256)(45 236 64 255)(46 235 65 254)(47 234 66 253)(48 233 67 252)(49 232 68 251)(50 231 69 250)(51 230 70 249)(52 229 71 248)(53 266 72 247)(54 265 73 246)(55 264 74 245)(56 263 75 244)(57 262 76 243)(77 303 96 284)(78 302 97 283)(79 301 98 282)(80 300 99 281)(81 299 100 280)(82 298 101 279)(83 297 102 278)(84 296 103 277)(85 295 104 276)(86 294 105 275)(87 293 106 274)(88 292 107 273)(89 291 108 272)(90 290 109 271)(91 289 110 270)(92 288 111 269)(93 287 112 268)(94 286 113 267)(95 285 114 304)(115 327 134 308)(116 326 135 307)(117 325 136 306)(118 324 137 305)(119 323 138 342)(120 322 139 341)(121 321 140 340)(122 320 141 339)(123 319 142 338)(124 318 143 337)(125 317 144 336)(126 316 145 335)(127 315 146 334)(128 314 147 333)(129 313 148 332)(130 312 149 331)(131 311 150 330)(132 310 151 329)(133 309 152 328)(153 352 172 371)(154 351 173 370)(155 350 174 369)(156 349 175 368)(157 348 176 367)(158 347 177 366)(159 346 178 365)(160 345 179 364)(161 344 180 363)(162 343 181 362)(163 380 182 361)(164 379 183 360)(165 378 184 359)(166 377 185 358)(167 376 186 357)(168 375 187 356)(169 374 188 355)(170 373 189 354)(171 372 190 353)

G:=sub<Sym(380)| (1,181,118,113,71)(2,182,119,114,72)(3,183,120,77,73)(4,184,121,78,74)(5,185,122,79,75)(6,186,123,80,76)(7,187,124,81,39)(8,188,125,82,40)(9,189,126,83,41)(10,190,127,84,42)(11,153,128,85,43)(12,154,129,86,44)(13,155,130,87,45)(14,156,131,88,46)(15,157,132,89,47)(16,158,133,90,48)(17,159,134,91,49)(18,160,135,92,50)(19,161,136,93,51)(20,162,137,94,52)(21,163,138,95,53)(22,164,139,96,54)(23,165,140,97,55)(24,166,141,98,56)(25,167,142,99,57)(26,168,143,100,58)(27,169,144,101,59)(28,170,145,102,60)(29,171,146,103,61)(30,172,147,104,62)(31,173,148,105,63)(32,174,149,106,64)(33,175,150,107,65)(34,176,151,108,66)(35,177,152,109,67)(36,178,115,110,68)(37,179,116,111,69)(38,180,117,112,70)(191,343,305,286,229)(192,344,306,287,230)(193,345,307,288,231)(194,346,308,289,232)(195,347,309,290,233)(196,348,310,291,234)(197,349,311,292,235)(198,350,312,293,236)(199,351,313,294,237)(200,352,314,295,238)(201,353,315,296,239)(202,354,316,297,240)(203,355,317,298,241)(204,356,318,299,242)(205,357,319,300,243)(206,358,320,301,244)(207,359,321,302,245)(208,360,322,303,246)(209,361,323,304,247)(210,362,324,267,248)(211,363,325,268,249)(212,364,326,269,250)(213,365,327,270,251)(214,366,328,271,252)(215,367,329,272,253)(216,368,330,273,254)(217,369,331,274,255)(218,370,332,275,256)(219,371,333,276,257)(220,372,334,277,258)(221,373,335,278,259)(222,374,336,279,260)(223,375,337,280,261)(224,376,338,281,262)(225,377,339,282,263)(226,378,340,283,264)(227,379,341,284,265)(228,380,342,285,266), (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), (1,210,20,191)(2,209,21,228)(3,208,22,227)(4,207,23,226)(5,206,24,225)(6,205,25,224)(7,204,26,223)(8,203,27,222)(9,202,28,221)(10,201,29,220)(11,200,30,219)(12,199,31,218)(13,198,32,217)(14,197,33,216)(15,196,34,215)(16,195,35,214)(17,194,36,213)(18,193,37,212)(19,192,38,211)(39,242,58,261)(40,241,59,260)(41,240,60,259)(42,239,61,258)(43,238,62,257)(44,237,63,256)(45,236,64,255)(46,235,65,254)(47,234,66,253)(48,233,67,252)(49,232,68,251)(50,231,69,250)(51,230,70,249)(52,229,71,248)(53,266,72,247)(54,265,73,246)(55,264,74,245)(56,263,75,244)(57,262,76,243)(77,303,96,284)(78,302,97,283)(79,301,98,282)(80,300,99,281)(81,299,100,280)(82,298,101,279)(83,297,102,278)(84,296,103,277)(85,295,104,276)(86,294,105,275)(87,293,106,274)(88,292,107,273)(89,291,108,272)(90,290,109,271)(91,289,110,270)(92,288,111,269)(93,287,112,268)(94,286,113,267)(95,285,114,304)(115,327,134,308)(116,326,135,307)(117,325,136,306)(118,324,137,305)(119,323,138,342)(120,322,139,341)(121,321,140,340)(122,320,141,339)(123,319,142,338)(124,318,143,337)(125,317,144,336)(126,316,145,335)(127,315,146,334)(128,314,147,333)(129,313,148,332)(130,312,149,331)(131,311,150,330)(132,310,151,329)(133,309,152,328)(153,352,172,371)(154,351,173,370)(155,350,174,369)(156,349,175,368)(157,348,176,367)(158,347,177,366)(159,346,178,365)(160,345,179,364)(161,344,180,363)(162,343,181,362)(163,380,182,361)(164,379,183,360)(165,378,184,359)(166,377,185,358)(167,376,186,357)(168,375,187,356)(169,374,188,355)(170,373,189,354)(171,372,190,353)>;

G:=Group( (1,181,118,113,71)(2,182,119,114,72)(3,183,120,77,73)(4,184,121,78,74)(5,185,122,79,75)(6,186,123,80,76)(7,187,124,81,39)(8,188,125,82,40)(9,189,126,83,41)(10,190,127,84,42)(11,153,128,85,43)(12,154,129,86,44)(13,155,130,87,45)(14,156,131,88,46)(15,157,132,89,47)(16,158,133,90,48)(17,159,134,91,49)(18,160,135,92,50)(19,161,136,93,51)(20,162,137,94,52)(21,163,138,95,53)(22,164,139,96,54)(23,165,140,97,55)(24,166,141,98,56)(25,167,142,99,57)(26,168,143,100,58)(27,169,144,101,59)(28,170,145,102,60)(29,171,146,103,61)(30,172,147,104,62)(31,173,148,105,63)(32,174,149,106,64)(33,175,150,107,65)(34,176,151,108,66)(35,177,152,109,67)(36,178,115,110,68)(37,179,116,111,69)(38,180,117,112,70)(191,343,305,286,229)(192,344,306,287,230)(193,345,307,288,231)(194,346,308,289,232)(195,347,309,290,233)(196,348,310,291,234)(197,349,311,292,235)(198,350,312,293,236)(199,351,313,294,237)(200,352,314,295,238)(201,353,315,296,239)(202,354,316,297,240)(203,355,317,298,241)(204,356,318,299,242)(205,357,319,300,243)(206,358,320,301,244)(207,359,321,302,245)(208,360,322,303,246)(209,361,323,304,247)(210,362,324,267,248)(211,363,325,268,249)(212,364,326,269,250)(213,365,327,270,251)(214,366,328,271,252)(215,367,329,272,253)(216,368,330,273,254)(217,369,331,274,255)(218,370,332,275,256)(219,371,333,276,257)(220,372,334,277,258)(221,373,335,278,259)(222,374,336,279,260)(223,375,337,280,261)(224,376,338,281,262)(225,377,339,282,263)(226,378,340,283,264)(227,379,341,284,265)(228,380,342,285,266), (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), (1,210,20,191)(2,209,21,228)(3,208,22,227)(4,207,23,226)(5,206,24,225)(6,205,25,224)(7,204,26,223)(8,203,27,222)(9,202,28,221)(10,201,29,220)(11,200,30,219)(12,199,31,218)(13,198,32,217)(14,197,33,216)(15,196,34,215)(16,195,35,214)(17,194,36,213)(18,193,37,212)(19,192,38,211)(39,242,58,261)(40,241,59,260)(41,240,60,259)(42,239,61,258)(43,238,62,257)(44,237,63,256)(45,236,64,255)(46,235,65,254)(47,234,66,253)(48,233,67,252)(49,232,68,251)(50,231,69,250)(51,230,70,249)(52,229,71,248)(53,266,72,247)(54,265,73,246)(55,264,74,245)(56,263,75,244)(57,262,76,243)(77,303,96,284)(78,302,97,283)(79,301,98,282)(80,300,99,281)(81,299,100,280)(82,298,101,279)(83,297,102,278)(84,296,103,277)(85,295,104,276)(86,294,105,275)(87,293,106,274)(88,292,107,273)(89,291,108,272)(90,290,109,271)(91,289,110,270)(92,288,111,269)(93,287,112,268)(94,286,113,267)(95,285,114,304)(115,327,134,308)(116,326,135,307)(117,325,136,306)(118,324,137,305)(119,323,138,342)(120,322,139,341)(121,321,140,340)(122,320,141,339)(123,319,142,338)(124,318,143,337)(125,317,144,336)(126,316,145,335)(127,315,146,334)(128,314,147,333)(129,313,148,332)(130,312,149,331)(131,311,150,330)(132,310,151,329)(133,309,152,328)(153,352,172,371)(154,351,173,370)(155,350,174,369)(156,349,175,368)(157,348,176,367)(158,347,177,366)(159,346,178,365)(160,345,179,364)(161,344,180,363)(162,343,181,362)(163,380,182,361)(164,379,183,360)(165,378,184,359)(166,377,185,358)(167,376,186,357)(168,375,187,356)(169,374,188,355)(170,373,189,354)(171,372,190,353) );

G=PermutationGroup([(1,181,118,113,71),(2,182,119,114,72),(3,183,120,77,73),(4,184,121,78,74),(5,185,122,79,75),(6,186,123,80,76),(7,187,124,81,39),(8,188,125,82,40),(9,189,126,83,41),(10,190,127,84,42),(11,153,128,85,43),(12,154,129,86,44),(13,155,130,87,45),(14,156,131,88,46),(15,157,132,89,47),(16,158,133,90,48),(17,159,134,91,49),(18,160,135,92,50),(19,161,136,93,51),(20,162,137,94,52),(21,163,138,95,53),(22,164,139,96,54),(23,165,140,97,55),(24,166,141,98,56),(25,167,142,99,57),(26,168,143,100,58),(27,169,144,101,59),(28,170,145,102,60),(29,171,146,103,61),(30,172,147,104,62),(31,173,148,105,63),(32,174,149,106,64),(33,175,150,107,65),(34,176,151,108,66),(35,177,152,109,67),(36,178,115,110,68),(37,179,116,111,69),(38,180,117,112,70),(191,343,305,286,229),(192,344,306,287,230),(193,345,307,288,231),(194,346,308,289,232),(195,347,309,290,233),(196,348,310,291,234),(197,349,311,292,235),(198,350,312,293,236),(199,351,313,294,237),(200,352,314,295,238),(201,353,315,296,239),(202,354,316,297,240),(203,355,317,298,241),(204,356,318,299,242),(205,357,319,300,243),(206,358,320,301,244),(207,359,321,302,245),(208,360,322,303,246),(209,361,323,304,247),(210,362,324,267,248),(211,363,325,268,249),(212,364,326,269,250),(213,365,327,270,251),(214,366,328,271,252),(215,367,329,272,253),(216,368,330,273,254),(217,369,331,274,255),(218,370,332,275,256),(219,371,333,276,257),(220,372,334,277,258),(221,373,335,278,259),(222,374,336,279,260),(223,375,337,280,261),(224,376,338,281,262),(225,377,339,282,263),(226,378,340,283,264),(227,379,341,284,265),(228,380,342,285,266)], [(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)], [(1,210,20,191),(2,209,21,228),(3,208,22,227),(4,207,23,226),(5,206,24,225),(6,205,25,224),(7,204,26,223),(8,203,27,222),(9,202,28,221),(10,201,29,220),(11,200,30,219),(12,199,31,218),(13,198,32,217),(14,197,33,216),(15,196,34,215),(16,195,35,214),(17,194,36,213),(18,193,37,212),(19,192,38,211),(39,242,58,261),(40,241,59,260),(41,240,60,259),(42,239,61,258),(43,238,62,257),(44,237,63,256),(45,236,64,255),(46,235,65,254),(47,234,66,253),(48,233,67,252),(49,232,68,251),(50,231,69,250),(51,230,70,249),(52,229,71,248),(53,266,72,247),(54,265,73,246),(55,264,74,245),(56,263,75,244),(57,262,76,243),(77,303,96,284),(78,302,97,283),(79,301,98,282),(80,300,99,281),(81,299,100,280),(82,298,101,279),(83,297,102,278),(84,296,103,277),(85,295,104,276),(86,294,105,275),(87,293,106,274),(88,292,107,273),(89,291,108,272),(90,290,109,271),(91,289,110,270),(92,288,111,269),(93,287,112,268),(94,286,113,267),(95,285,114,304),(115,327,134,308),(116,326,135,307),(117,325,136,306),(118,324,137,305),(119,323,138,342),(120,322,139,341),(121,321,140,340),(122,320,141,339),(123,319,142,338),(124,318,143,337),(125,317,144,336),(126,316,145,335),(127,315,146,334),(128,314,147,333),(129,313,148,332),(130,312,149,331),(131,311,150,330),(132,310,151,329),(133,309,152,328),(153,352,172,371),(154,351,173,370),(155,350,174,369),(156,349,175,368),(157,348,176,367),(158,347,177,366),(159,346,178,365),(160,345,179,364),(161,344,180,363),(162,343,181,362),(163,380,182,361),(164,379,183,360),(165,378,184,359),(166,377,185,358),(167,376,186,357),(168,375,187,356),(169,374,188,355),(170,373,189,354),(171,372,190,353)])

110 conjugacy classes

class 1  2 4A4B5A5B5C5D10A10B10C10D19A···19I20A···20H38A···38I95A···95AJ190A···190AJ
order124455551010101019···1920···2038···3895···95190···190
size111919111111112···219···192···22···22···2

110 irreducible representations

dim1111112222
type+++-
imageC1C2C4C5C10C20D19Dic19C5×D19C5×Dic19
kernelC5×Dic19C190C95Dic19C38C19C10C5C2C1
# reps112448993636

Matrix representation of C5×Dic19 in GL2(𝔽761) generated by

1680
0168
,
0760
1611
,
690742
74671
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

Subgroup lattice of C5×Dic19 in TeX

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