Copied to
clipboard

G = C19×Dic5order 380 = 22·5·19

Direct product of C19 and Dic5

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

Aliases: C19×Dic5, C955C4, C52C76, C10.C38, C38.2D5, C190.3C2, C2.(D5×C19), SmallGroup(380,1)

Series: Derived Chief Lower central Upper central

C1C5 — C19×Dic5
C1C5C10C190 — C19×Dic5
C5 — C19×Dic5
C1C38

Generators and relations for C19×Dic5
 G = < a,b,c | a19=b10=1, c2=b5, ab=ba, ac=ca, cbc-1=b-1 >

5C4
5C76

Smallest permutation representation of C19×Dic5
Regular action on 380 points
Generators in S380
(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)
(1 160 136 276 242 220 199 252 133 175)(2 161 137 277 243 221 200 253 115 176)(3 162 138 278 244 222 201 254 116 177)(4 163 139 279 245 223 202 255 117 178)(5 164 140 280 246 224 203 256 118 179)(6 165 141 281 247 225 204 257 119 180)(7 166 142 282 229 226 205 258 120 181)(8 167 143 283 230 227 206 259 121 182)(9 168 144 284 231 228 207 260 122 183)(10 169 145 285 232 210 208 261 123 184)(11 170 146 267 233 211 209 262 124 185)(12 171 147 268 234 212 191 263 125 186)(13 153 148 269 235 213 192 264 126 187)(14 154 149 270 236 214 193 265 127 188)(15 155 150 271 237 215 194 266 128 189)(16 156 151 272 238 216 195 248 129 190)(17 157 152 273 239 217 196 249 130 172)(18 158 134 274 240 218 197 250 131 173)(19 159 135 275 241 219 198 251 132 174)(20 355 335 379 97 65 297 44 81 313)(21 356 336 380 98 66 298 45 82 314)(22 357 337 362 99 67 299 46 83 315)(23 358 338 363 100 68 300 47 84 316)(24 359 339 364 101 69 301 48 85 317)(25 360 340 365 102 70 302 49 86 318)(26 361 341 366 103 71 303 50 87 319)(27 343 342 367 104 72 304 51 88 320)(28 344 324 368 105 73 286 52 89 321)(29 345 325 369 106 74 287 53 90 322)(30 346 326 370 107 75 288 54 91 323)(31 347 327 371 108 76 289 55 92 305)(32 348 328 372 109 58 290 56 93 306)(33 349 329 373 110 59 291 57 94 307)(34 350 330 374 111 60 292 39 95 308)(35 351 331 375 112 61 293 40 77 309)(36 352 332 376 113 62 294 41 78 310)(37 353 333 377 114 63 295 42 79 311)(38 354 334 378 96 64 296 43 80 312)
(1 373 220 94)(2 374 221 95)(3 375 222 77)(4 376 223 78)(5 377 224 79)(6 378 225 80)(7 379 226 81)(8 380 227 82)(9 362 228 83)(10 363 210 84)(11 364 211 85)(12 365 212 86)(13 366 213 87)(14 367 214 88)(15 368 215 89)(16 369 216 90)(17 370 217 91)(18 371 218 92)(19 372 219 93)(20 120 65 282)(21 121 66 283)(22 122 67 284)(23 123 68 285)(24 124 69 267)(25 125 70 268)(26 126 71 269)(27 127 72 270)(28 128 73 271)(29 129 74 272)(30 130 75 273)(31 131 76 274)(32 132 58 275)(33 133 59 276)(34 115 60 277)(35 116 61 278)(36 117 62 279)(37 118 63 280)(38 119 64 281)(39 161 330 200)(40 162 331 201)(41 163 332 202)(42 164 333 203)(43 165 334 204)(44 166 335 205)(45 167 336 206)(46 168 337 207)(47 169 338 208)(48 170 339 209)(49 171 340 191)(50 153 341 192)(51 154 342 193)(52 155 324 194)(53 156 325 195)(54 157 326 196)(55 158 327 197)(56 159 328 198)(57 160 329 199)(96 247 312 180)(97 229 313 181)(98 230 314 182)(99 231 315 183)(100 232 316 184)(101 233 317 185)(102 234 318 186)(103 235 319 187)(104 236 320 188)(105 237 321 189)(106 238 322 190)(107 239 323 172)(108 240 305 173)(109 241 306 174)(110 242 307 175)(111 243 308 176)(112 244 309 177)(113 245 310 178)(114 246 311 179)(134 347 250 289)(135 348 251 290)(136 349 252 291)(137 350 253 292)(138 351 254 293)(139 352 255 294)(140 353 256 295)(141 354 257 296)(142 355 258 297)(143 356 259 298)(144 357 260 299)(145 358 261 300)(146 359 262 301)(147 360 263 302)(148 361 264 303)(149 343 265 304)(150 344 266 286)(151 345 248 287)(152 346 249 288)

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

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

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

152 conjugacy classes

class 1  2 4A4B5A5B10A10B19A···19R38A···38R76A···76AJ95A···95AJ190A···190AJ
order124455101019···1938···3876···7695···95190···190
size115522221···11···15···52···22···2

152 irreducible representations

dim1111112222
type+++-
imageC1C2C4C19C38C76D5Dic5D5×C19C19×Dic5
kernelC19×Dic5C190C95Dic5C10C5C38C19C2C1
# reps112181836223636

Matrix representation of C19×Dic5 in GL3(𝔽761) generated by

100
06800
00680
,
76000
07601
066892
,
3900
0706293
06555
G:=sub<GL(3,GF(761))| [1,0,0,0,680,0,0,0,680],[760,0,0,0,760,668,0,1,92],[39,0,0,0,706,65,0,293,55] >;

C19×Dic5 in GAP, Magma, Sage, TeX

C_{19}\times {\rm Dic}_5
% in TeX

G:=Group("C19xDic5");
// GroupNames label

G:=SmallGroup(380,1);
// by ID

G=gap.SmallGroup(380,1);
# by ID

G:=PCGroup([4,-2,-19,-2,-5,152,4867]);
// Polycyclic

G:=Group<a,b,c|a^19=b^10=1,c^2=b^5,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C19×Dic5 in TeX

׿
×
𝔽