metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: Dic94, C47⋊Q8, C4.D47, C2.3D94, C188.1C2, Dic47.C2, C94.1C22, SmallGroup(376,3)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic94
G = < a,b | a188=1, b2=a94, bab-1=a-1 >
Smallest permutation representation of Dic94
►Regular action on 376 points
Generators in S376
(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)
(1 324 95 230)(2 323 96 229)(3 322 97 228)(4 321 98 227)(5 320 99 226)(6 319 100 225)(7 318 101 224)(8 317 102 223)(9 316 103 222)(10 315 104 221)(11 314 105 220)(12 313 106 219)(13 312 107 218)(14 311 108 217)(15 310 109 216)(16 309 110 215)(17 308 111 214)(18 307 112 213)(19 306 113 212)(20 305 114 211)(21 304 115 210)(22 303 116 209)(23 302 117 208)(24 301 118 207)(25 300 119 206)(26 299 120 205)(27 298 121 204)(28 297 122 203)(29 296 123 202)(30 295 124 201)(31 294 125 200)(32 293 126 199)(33 292 127 198)(34 291 128 197)(35 290 129 196)(36 289 130 195)(37 288 131 194)(38 287 132 193)(39 286 133 192)(40 285 134 191)(41 284 135 190)(42 283 136 189)(43 282 137 376)(44 281 138 375)(45 280 139 374)(46 279 140 373)(47 278 141 372)(48 277 142 371)(49 276 143 370)(50 275 144 369)(51 274 145 368)(52 273 146 367)(53 272 147 366)(54 271 148 365)(55 270 149 364)(56 269 150 363)(57 268 151 362)(58 267 152 361)(59 266 153 360)(60 265 154 359)(61 264 155 358)(62 263 156 357)(63 262 157 356)(64 261 158 355)(65 260 159 354)(66 259 160 353)(67 258 161 352)(68 257 162 351)(69 256 163 350)(70 255 164 349)(71 254 165 348)(72 253 166 347)(73 252 167 346)(74 251 168 345)(75 250 169 344)(76 249 170 343)(77 248 171 342)(78 247 172 341)(79 246 173 340)(80 245 174 339)(81 244 175 338)(82 243 176 337)(83 242 177 336)(84 241 178 335)(85 240 179 334)(86 239 180 333)(87 238 181 332)(88 237 182 331)(89 236 183 330)(90 235 184 329)(91 234 185 328)(92 233 186 327)(93 232 187 326)(94 231 188 325)
G:=sub<Sym(376)| (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), (1,324,95,230)(2,323,96,229)(3,322,97,228)(4,321,98,227)(5,320,99,226)(6,319,100,225)(7,318,101,224)(8,317,102,223)(9,316,103,222)(10,315,104,221)(11,314,105,220)(12,313,106,219)(13,312,107,218)(14,311,108,217)(15,310,109,216)(16,309,110,215)(17,308,111,214)(18,307,112,213)(19,306,113,212)(20,305,114,211)(21,304,115,210)(22,303,116,209)(23,302,117,208)(24,301,118,207)(25,300,119,206)(26,299,120,205)(27,298,121,204)(28,297,122,203)(29,296,123,202)(30,295,124,201)(31,294,125,200)(32,293,126,199)(33,292,127,198)(34,291,128,197)(35,290,129,196)(36,289,130,195)(37,288,131,194)(38,287,132,193)(39,286,133,192)(40,285,134,191)(41,284,135,190)(42,283,136,189)(43,282,137,376)(44,281,138,375)(45,280,139,374)(46,279,140,373)(47,278,141,372)(48,277,142,371)(49,276,143,370)(50,275,144,369)(51,274,145,368)(52,273,146,367)(53,272,147,366)(54,271,148,365)(55,270,149,364)(56,269,150,363)(57,268,151,362)(58,267,152,361)(59,266,153,360)(60,265,154,359)(61,264,155,358)(62,263,156,357)(63,262,157,356)(64,261,158,355)(65,260,159,354)(66,259,160,353)(67,258,161,352)(68,257,162,351)(69,256,163,350)(70,255,164,349)(71,254,165,348)(72,253,166,347)(73,252,167,346)(74,251,168,345)(75,250,169,344)(76,249,170,343)(77,248,171,342)(78,247,172,341)(79,246,173,340)(80,245,174,339)(81,244,175,338)(82,243,176,337)(83,242,177,336)(84,241,178,335)(85,240,179,334)(86,239,180,333)(87,238,181,332)(88,237,182,331)(89,236,183,330)(90,235,184,329)(91,234,185,328)(92,233,186,327)(93,232,187,326)(94,231,188,325)>;
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), (1,324,95,230)(2,323,96,229)(3,322,97,228)(4,321,98,227)(5,320,99,226)(6,319,100,225)(7,318,101,224)(8,317,102,223)(9,316,103,222)(10,315,104,221)(11,314,105,220)(12,313,106,219)(13,312,107,218)(14,311,108,217)(15,310,109,216)(16,309,110,215)(17,308,111,214)(18,307,112,213)(19,306,113,212)(20,305,114,211)(21,304,115,210)(22,303,116,209)(23,302,117,208)(24,301,118,207)(25,300,119,206)(26,299,120,205)(27,298,121,204)(28,297,122,203)(29,296,123,202)(30,295,124,201)(31,294,125,200)(32,293,126,199)(33,292,127,198)(34,291,128,197)(35,290,129,196)(36,289,130,195)(37,288,131,194)(38,287,132,193)(39,286,133,192)(40,285,134,191)(41,284,135,190)(42,283,136,189)(43,282,137,376)(44,281,138,375)(45,280,139,374)(46,279,140,373)(47,278,141,372)(48,277,142,371)(49,276,143,370)(50,275,144,369)(51,274,145,368)(52,273,146,367)(53,272,147,366)(54,271,148,365)(55,270,149,364)(56,269,150,363)(57,268,151,362)(58,267,152,361)(59,266,153,360)(60,265,154,359)(61,264,155,358)(62,263,156,357)(63,262,157,356)(64,261,158,355)(65,260,159,354)(66,259,160,353)(67,258,161,352)(68,257,162,351)(69,256,163,350)(70,255,164,349)(71,254,165,348)(72,253,166,347)(73,252,167,346)(74,251,168,345)(75,250,169,344)(76,249,170,343)(77,248,171,342)(78,247,172,341)(79,246,173,340)(80,245,174,339)(81,244,175,338)(82,243,176,337)(83,242,177,336)(84,241,178,335)(85,240,179,334)(86,239,180,333)(87,238,181,332)(88,237,182,331)(89,236,183,330)(90,235,184,329)(91,234,185,328)(92,233,186,327)(93,232,187,326)(94,231,188,325) );
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)], [(1,324,95,230),(2,323,96,229),(3,322,97,228),(4,321,98,227),(5,320,99,226),(6,319,100,225),(7,318,101,224),(8,317,102,223),(9,316,103,222),(10,315,104,221),(11,314,105,220),(12,313,106,219),(13,312,107,218),(14,311,108,217),(15,310,109,216),(16,309,110,215),(17,308,111,214),(18,307,112,213),(19,306,113,212),(20,305,114,211),(21,304,115,210),(22,303,116,209),(23,302,117,208),(24,301,118,207),(25,300,119,206),(26,299,120,205),(27,298,121,204),(28,297,122,203),(29,296,123,202),(30,295,124,201),(31,294,125,200),(32,293,126,199),(33,292,127,198),(34,291,128,197),(35,290,129,196),(36,289,130,195),(37,288,131,194),(38,287,132,193),(39,286,133,192),(40,285,134,191),(41,284,135,190),(42,283,136,189),(43,282,137,376),(44,281,138,375),(45,280,139,374),(46,279,140,373),(47,278,141,372),(48,277,142,371),(49,276,143,370),(50,275,144,369),(51,274,145,368),(52,273,146,367),(53,272,147,366),(54,271,148,365),(55,270,149,364),(56,269,150,363),(57,268,151,362),(58,267,152,361),(59,266,153,360),(60,265,154,359),(61,264,155,358),(62,263,156,357),(63,262,157,356),(64,261,158,355),(65,260,159,354),(66,259,160,353),(67,258,161,352),(68,257,162,351),(69,256,163,350),(70,255,164,349),(71,254,165,348),(72,253,166,347),(73,252,167,346),(74,251,168,345),(75,250,169,344),(76,249,170,343),(77,248,171,342),(78,247,172,341),(79,246,173,340),(80,245,174,339),(81,244,175,338),(82,243,176,337),(83,242,177,336),(84,241,178,335),(85,240,179,334),(86,239,180,333),(87,238,181,332),(88,237,182,331),(89,236,183,330),(90,235,184,329),(91,234,185,328),(92,233,186,327),(93,232,187,326),(94,231,188,325)]])
97 conjugacy classes
| class | 1 | 2 | 4A | 4B | 4C | 47A | ··· | 47W | 94A | ··· | 94W | 188A | ··· | 188AT |
| order | 1 | 2 | 4 | 4 | 4 | 47 | ··· | 47 | 94 | ··· | 94 | 188 | ··· | 188 |
| size | 1 | 1 | 2 | 94 | 94 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
97 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | + | + | - |
| image | C1 | C2 | C2 | Q8 | D47 | D94 | Dic94 |
| kernel | Dic94 | Dic47 | C188 | C47 | C4 | C2 | C1 |
| # reps | 1 | 2 | 1 | 1 | 23 | 23 | 46 |
Matrix representation of Dic94 ►in GL2(𝔽941) generated by
| 769 | 163 |
| 778 | 242 |
| 580 | 216 |
| 904 | 361 |
G:=sub<GL(2,GF(941))| [769,778,163,242],[580,904,216,361] >;
Dic94 in GAP, Magma, Sage, TeX
{\rm Dic}_{94} % in TeX
G:=Group("Dic94"); // GroupNames label
G:=SmallGroup(376,3);
// by ID
G=gap.SmallGroup(376,3);
# by ID
G:=PCGroup([4,-2,-2,-2,-47,16,49,21,5891]);
// Polycyclic
G:=Group<a,b|a^188=1,b^2=a^94,b*a*b^-1=a^-1>;
// generators/relations
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