Copied to
clipboard

G = Dic94order 376 = 23·47

Dicyclic group

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

C1C94 — Dic94
C1C47C94Dic47 — Dic94
C47C94 — Dic94
C1C2C4

Generators and relations for Dic94
 G = < a,b | a188=1, b2=a94, bab-1=a-1 >

47C4
47C4
47Q8

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

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

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

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

97 conjugacy classes

class 1  2 4A4B4C47A···47W94A···94W188A···188AT
order1244447···4794···94188···188
size11294942···22···22···2

97 irreducible representations

dim1112222
type+++-++-
imageC1C2C2Q8D47D94Dic94
kernelDic94Dic47C188C47C4C2C1
# reps1211232346

Matrix representation of Dic94 in GL2(𝔽941) generated by

769163
778242
,
580216
904361
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

Export

Subgroup lattice of Dic94 in TeX

׿
×
𝔽