metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: Dic95, C95⋊3C4, C2.D95, C38.D5, C19⋊Dic5, C10.D19, C5⋊2Dic19, C190.1C2, SmallGroup(380,3)
Series: Derived ►Chief ►Lower central ►Upper central
| C95 — Dic95 |
Generators and relations for Dic95
G = < a,b | a190=1, b2=a95, bab-1=a-1 >
Smallest permutation representation of Dic95
►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)
(1 242 96 337)(2 241 97 336)(3 240 98 335)(4 239 99 334)(5 238 100 333)(6 237 101 332)(7 236 102 331)(8 235 103 330)(9 234 104 329)(10 233 105 328)(11 232 106 327)(12 231 107 326)(13 230 108 325)(14 229 109 324)(15 228 110 323)(16 227 111 322)(17 226 112 321)(18 225 113 320)(19 224 114 319)(20 223 115 318)(21 222 116 317)(22 221 117 316)(23 220 118 315)(24 219 119 314)(25 218 120 313)(26 217 121 312)(27 216 122 311)(28 215 123 310)(29 214 124 309)(30 213 125 308)(31 212 126 307)(32 211 127 306)(33 210 128 305)(34 209 129 304)(35 208 130 303)(36 207 131 302)(37 206 132 301)(38 205 133 300)(39 204 134 299)(40 203 135 298)(41 202 136 297)(42 201 137 296)(43 200 138 295)(44 199 139 294)(45 198 140 293)(46 197 141 292)(47 196 142 291)(48 195 143 290)(49 194 144 289)(50 193 145 288)(51 192 146 287)(52 191 147 286)(53 380 148 285)(54 379 149 284)(55 378 150 283)(56 377 151 282)(57 376 152 281)(58 375 153 280)(59 374 154 279)(60 373 155 278)(61 372 156 277)(62 371 157 276)(63 370 158 275)(64 369 159 274)(65 368 160 273)(66 367 161 272)(67 366 162 271)(68 365 163 270)(69 364 164 269)(70 363 165 268)(71 362 166 267)(72 361 167 266)(73 360 168 265)(74 359 169 264)(75 358 170 263)(76 357 171 262)(77 356 172 261)(78 355 173 260)(79 354 174 259)(80 353 175 258)(81 352 176 257)(82 351 177 256)(83 350 178 255)(84 349 179 254)(85 348 180 253)(86 347 181 252)(87 346 182 251)(88 345 183 250)(89 344 184 249)(90 343 185 248)(91 342 186 247)(92 341 187 246)(93 340 188 245)(94 339 189 244)(95 338 190 243)
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), (1,242,96,337)(2,241,97,336)(3,240,98,335)(4,239,99,334)(5,238,100,333)(6,237,101,332)(7,236,102,331)(8,235,103,330)(9,234,104,329)(10,233,105,328)(11,232,106,327)(12,231,107,326)(13,230,108,325)(14,229,109,324)(15,228,110,323)(16,227,111,322)(17,226,112,321)(18,225,113,320)(19,224,114,319)(20,223,115,318)(21,222,116,317)(22,221,117,316)(23,220,118,315)(24,219,119,314)(25,218,120,313)(26,217,121,312)(27,216,122,311)(28,215,123,310)(29,214,124,309)(30,213,125,308)(31,212,126,307)(32,211,127,306)(33,210,128,305)(34,209,129,304)(35,208,130,303)(36,207,131,302)(37,206,132,301)(38,205,133,300)(39,204,134,299)(40,203,135,298)(41,202,136,297)(42,201,137,296)(43,200,138,295)(44,199,139,294)(45,198,140,293)(46,197,141,292)(47,196,142,291)(48,195,143,290)(49,194,144,289)(50,193,145,288)(51,192,146,287)(52,191,147,286)(53,380,148,285)(54,379,149,284)(55,378,150,283)(56,377,151,282)(57,376,152,281)(58,375,153,280)(59,374,154,279)(60,373,155,278)(61,372,156,277)(62,371,157,276)(63,370,158,275)(64,369,159,274)(65,368,160,273)(66,367,161,272)(67,366,162,271)(68,365,163,270)(69,364,164,269)(70,363,165,268)(71,362,166,267)(72,361,167,266)(73,360,168,265)(74,359,169,264)(75,358,170,263)(76,357,171,262)(77,356,172,261)(78,355,173,260)(79,354,174,259)(80,353,175,258)(81,352,176,257)(82,351,177,256)(83,350,178,255)(84,349,179,254)(85,348,180,253)(86,347,181,252)(87,346,182,251)(88,345,183,250)(89,344,184,249)(90,343,185,248)(91,342,186,247)(92,341,187,246)(93,340,188,245)(94,339,189,244)(95,338,190,243)>;
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), (1,242,96,337)(2,241,97,336)(3,240,98,335)(4,239,99,334)(5,238,100,333)(6,237,101,332)(7,236,102,331)(8,235,103,330)(9,234,104,329)(10,233,105,328)(11,232,106,327)(12,231,107,326)(13,230,108,325)(14,229,109,324)(15,228,110,323)(16,227,111,322)(17,226,112,321)(18,225,113,320)(19,224,114,319)(20,223,115,318)(21,222,116,317)(22,221,117,316)(23,220,118,315)(24,219,119,314)(25,218,120,313)(26,217,121,312)(27,216,122,311)(28,215,123,310)(29,214,124,309)(30,213,125,308)(31,212,126,307)(32,211,127,306)(33,210,128,305)(34,209,129,304)(35,208,130,303)(36,207,131,302)(37,206,132,301)(38,205,133,300)(39,204,134,299)(40,203,135,298)(41,202,136,297)(42,201,137,296)(43,200,138,295)(44,199,139,294)(45,198,140,293)(46,197,141,292)(47,196,142,291)(48,195,143,290)(49,194,144,289)(50,193,145,288)(51,192,146,287)(52,191,147,286)(53,380,148,285)(54,379,149,284)(55,378,150,283)(56,377,151,282)(57,376,152,281)(58,375,153,280)(59,374,154,279)(60,373,155,278)(61,372,156,277)(62,371,157,276)(63,370,158,275)(64,369,159,274)(65,368,160,273)(66,367,161,272)(67,366,162,271)(68,365,163,270)(69,364,164,269)(70,363,165,268)(71,362,166,267)(72,361,167,266)(73,360,168,265)(74,359,169,264)(75,358,170,263)(76,357,171,262)(77,356,172,261)(78,355,173,260)(79,354,174,259)(80,353,175,258)(81,352,176,257)(82,351,177,256)(83,350,178,255)(84,349,179,254)(85,348,180,253)(86,347,181,252)(87,346,182,251)(88,345,183,250)(89,344,184,249)(90,343,185,248)(91,342,186,247)(92,341,187,246)(93,340,188,245)(94,339,189,244)(95,338,190,243) );
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)], [(1,242,96,337),(2,241,97,336),(3,240,98,335),(4,239,99,334),(5,238,100,333),(6,237,101,332),(7,236,102,331),(8,235,103,330),(9,234,104,329),(10,233,105,328),(11,232,106,327),(12,231,107,326),(13,230,108,325),(14,229,109,324),(15,228,110,323),(16,227,111,322),(17,226,112,321),(18,225,113,320),(19,224,114,319),(20,223,115,318),(21,222,116,317),(22,221,117,316),(23,220,118,315),(24,219,119,314),(25,218,120,313),(26,217,121,312),(27,216,122,311),(28,215,123,310),(29,214,124,309),(30,213,125,308),(31,212,126,307),(32,211,127,306),(33,210,128,305),(34,209,129,304),(35,208,130,303),(36,207,131,302),(37,206,132,301),(38,205,133,300),(39,204,134,299),(40,203,135,298),(41,202,136,297),(42,201,137,296),(43,200,138,295),(44,199,139,294),(45,198,140,293),(46,197,141,292),(47,196,142,291),(48,195,143,290),(49,194,144,289),(50,193,145,288),(51,192,146,287),(52,191,147,286),(53,380,148,285),(54,379,149,284),(55,378,150,283),(56,377,151,282),(57,376,152,281),(58,375,153,280),(59,374,154,279),(60,373,155,278),(61,372,156,277),(62,371,157,276),(63,370,158,275),(64,369,159,274),(65,368,160,273),(66,367,161,272),(67,366,162,271),(68,365,163,270),(69,364,164,269),(70,363,165,268),(71,362,166,267),(72,361,167,266),(73,360,168,265),(74,359,169,264),(75,358,170,263),(76,357,171,262),(77,356,172,261),(78,355,173,260),(79,354,174,259),(80,353,175,258),(81,352,176,257),(82,351,177,256),(83,350,178,255),(84,349,179,254),(85,348,180,253),(86,347,181,252),(87,346,182,251),(88,345,183,250),(89,344,184,249),(90,343,185,248),(91,342,186,247),(92,341,187,246),(93,340,188,245),(94,339,189,244),(95,338,190,243)]])
98 conjugacy classes
| class | 1 | 2 | 4A | 4B | 5A | 5B | 10A | 10B | 19A | ··· | 19I | 38A | ··· | 38I | 95A | ··· | 95AJ | 190A | ··· | 190AJ |
| order | 1 | 2 | 4 | 4 | 5 | 5 | 10 | 10 | 19 | ··· | 19 | 38 | ··· | 38 | 95 | ··· | 95 | 190 | ··· | 190 |
| size | 1 | 1 | 95 | 95 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
98 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | + | - | + | - | |
| image | C1 | C2 | C4 | D5 | Dic5 | D19 | Dic19 | D95 | Dic95 |
| kernel | Dic95 | C190 | C95 | C38 | C19 | C10 | C5 | C2 | C1 |
| # reps | 1 | 1 | 2 | 2 | 2 | 9 | 9 | 36 | 36 |
Matrix representation of Dic95 ►in GL3(𝔽761) generated by
| 760 | 0 | 0 |
| 0 | 488 | 136 |
| 0 | 625 | 235 |
| 722 | 0 | 0 |
| 0 | 274 | 523 |
| 0 | 114 | 487 |
G:=sub<GL(3,GF(761))| [760,0,0,0,488,625,0,136,235],[722,0,0,0,274,114,0,523,487] >;
Dic95 in GAP, Magma, Sage, TeX
{\rm Dic}_{95} % in TeX
G:=Group("Dic95"); // GroupNames label
G:=SmallGroup(380,3);
// by ID
G=gap.SmallGroup(380,3);
# by ID
G:=PCGroup([4,-2,-2,-5,-19,8,194,5763]);
// Polycyclic
G:=Group<a,b|a^190=1,b^2=a^95,b*a*b^-1=a^-1>;
// generators/relations
Export