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G = Dic95order 380 = 22·5·19

Dicyclic group

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

Aliases: Dic95, C953C4, C2.D95, C38.D5, C19⋊Dic5, C10.D19, C52Dic19, C190.1C2, SmallGroup(380,3)

Series: Derived Chief Lower central Upper central

C1C95 — Dic95
C1C19C95C190 — Dic95
C95 — Dic95
C1C2

Generators and relations for Dic95
 G = < a,b | a190=1, b2=a95, bab-1=a-1 >

95C4
19Dic5
5Dic19

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

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

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

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

98 conjugacy classes

class 1  2 4A4B5A5B10A10B19A···19I38A···38I95A···95AJ190A···190AJ
order124455101019···1938···3895···95190···190
size11959522222···22···22···22···2

98 irreducible representations

dim111222222
type+++-+-+-
imageC1C2C4D5Dic5D19Dic19D95Dic95
kernelDic95C190C95C38C19C10C5C2C1
# reps11222993636

Matrix representation of Dic95 in GL3(𝔽761) generated by

76000
0488136
0625235
,
72200
0274523
0114487
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

Subgroup lattice of Dic95 in TeX

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