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G = Dic119order 476 = 22·7·17

Dicyclic group

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

Aliases: Dic119, C34.D7, C7⋊Dic17, C1193C4, C14.D17, C2.D119, C172Dic7, C238.1C2, SmallGroup(476,3)

Series: Derived Chief Lower central Upper central

C1C119 — Dic119
C1C17C119C238 — Dic119
C119 — Dic119
C1C2

Generators and relations for Dic119
 G = < a,b | a238=1, b2=a119, bab-1=a-1 >

119C4
17Dic7
7Dic17

Smallest permutation representation of Dic119
Regular action on 476 points
Generators in S476
(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)(239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476)
(1 345 120 464)(2 344 121 463)(3 343 122 462)(4 342 123 461)(5 341 124 460)(6 340 125 459)(7 339 126 458)(8 338 127 457)(9 337 128 456)(10 336 129 455)(11 335 130 454)(12 334 131 453)(13 333 132 452)(14 332 133 451)(15 331 134 450)(16 330 135 449)(17 329 136 448)(18 328 137 447)(19 327 138 446)(20 326 139 445)(21 325 140 444)(22 324 141 443)(23 323 142 442)(24 322 143 441)(25 321 144 440)(26 320 145 439)(27 319 146 438)(28 318 147 437)(29 317 148 436)(30 316 149 435)(31 315 150 434)(32 314 151 433)(33 313 152 432)(34 312 153 431)(35 311 154 430)(36 310 155 429)(37 309 156 428)(38 308 157 427)(39 307 158 426)(40 306 159 425)(41 305 160 424)(42 304 161 423)(43 303 162 422)(44 302 163 421)(45 301 164 420)(46 300 165 419)(47 299 166 418)(48 298 167 417)(49 297 168 416)(50 296 169 415)(51 295 170 414)(52 294 171 413)(53 293 172 412)(54 292 173 411)(55 291 174 410)(56 290 175 409)(57 289 176 408)(58 288 177 407)(59 287 178 406)(60 286 179 405)(61 285 180 404)(62 284 181 403)(63 283 182 402)(64 282 183 401)(65 281 184 400)(66 280 185 399)(67 279 186 398)(68 278 187 397)(69 277 188 396)(70 276 189 395)(71 275 190 394)(72 274 191 393)(73 273 192 392)(74 272 193 391)(75 271 194 390)(76 270 195 389)(77 269 196 388)(78 268 197 387)(79 267 198 386)(80 266 199 385)(81 265 200 384)(82 264 201 383)(83 263 202 382)(84 262 203 381)(85 261 204 380)(86 260 205 379)(87 259 206 378)(88 258 207 377)(89 257 208 376)(90 256 209 375)(91 255 210 374)(92 254 211 373)(93 253 212 372)(94 252 213 371)(95 251 214 370)(96 250 215 369)(97 249 216 368)(98 248 217 367)(99 247 218 366)(100 246 219 365)(101 245 220 364)(102 244 221 363)(103 243 222 362)(104 242 223 361)(105 241 224 360)(106 240 225 359)(107 239 226 358)(108 476 227 357)(109 475 228 356)(110 474 229 355)(111 473 230 354)(112 472 231 353)(113 471 232 352)(114 470 233 351)(115 469 234 350)(116 468 235 349)(117 467 236 348)(118 466 237 347)(119 465 238 346)

G:=sub<Sym(476)| (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)(239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476), (1,345,120,464)(2,344,121,463)(3,343,122,462)(4,342,123,461)(5,341,124,460)(6,340,125,459)(7,339,126,458)(8,338,127,457)(9,337,128,456)(10,336,129,455)(11,335,130,454)(12,334,131,453)(13,333,132,452)(14,332,133,451)(15,331,134,450)(16,330,135,449)(17,329,136,448)(18,328,137,447)(19,327,138,446)(20,326,139,445)(21,325,140,444)(22,324,141,443)(23,323,142,442)(24,322,143,441)(25,321,144,440)(26,320,145,439)(27,319,146,438)(28,318,147,437)(29,317,148,436)(30,316,149,435)(31,315,150,434)(32,314,151,433)(33,313,152,432)(34,312,153,431)(35,311,154,430)(36,310,155,429)(37,309,156,428)(38,308,157,427)(39,307,158,426)(40,306,159,425)(41,305,160,424)(42,304,161,423)(43,303,162,422)(44,302,163,421)(45,301,164,420)(46,300,165,419)(47,299,166,418)(48,298,167,417)(49,297,168,416)(50,296,169,415)(51,295,170,414)(52,294,171,413)(53,293,172,412)(54,292,173,411)(55,291,174,410)(56,290,175,409)(57,289,176,408)(58,288,177,407)(59,287,178,406)(60,286,179,405)(61,285,180,404)(62,284,181,403)(63,283,182,402)(64,282,183,401)(65,281,184,400)(66,280,185,399)(67,279,186,398)(68,278,187,397)(69,277,188,396)(70,276,189,395)(71,275,190,394)(72,274,191,393)(73,273,192,392)(74,272,193,391)(75,271,194,390)(76,270,195,389)(77,269,196,388)(78,268,197,387)(79,267,198,386)(80,266,199,385)(81,265,200,384)(82,264,201,383)(83,263,202,382)(84,262,203,381)(85,261,204,380)(86,260,205,379)(87,259,206,378)(88,258,207,377)(89,257,208,376)(90,256,209,375)(91,255,210,374)(92,254,211,373)(93,253,212,372)(94,252,213,371)(95,251,214,370)(96,250,215,369)(97,249,216,368)(98,248,217,367)(99,247,218,366)(100,246,219,365)(101,245,220,364)(102,244,221,363)(103,243,222,362)(104,242,223,361)(105,241,224,360)(106,240,225,359)(107,239,226,358)(108,476,227,357)(109,475,228,356)(110,474,229,355)(111,473,230,354)(112,472,231,353)(113,471,232,352)(114,470,233,351)(115,469,234,350)(116,468,235,349)(117,467,236,348)(118,466,237,347)(119,465,238,346)>;

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)(239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476), (1,345,120,464)(2,344,121,463)(3,343,122,462)(4,342,123,461)(5,341,124,460)(6,340,125,459)(7,339,126,458)(8,338,127,457)(9,337,128,456)(10,336,129,455)(11,335,130,454)(12,334,131,453)(13,333,132,452)(14,332,133,451)(15,331,134,450)(16,330,135,449)(17,329,136,448)(18,328,137,447)(19,327,138,446)(20,326,139,445)(21,325,140,444)(22,324,141,443)(23,323,142,442)(24,322,143,441)(25,321,144,440)(26,320,145,439)(27,319,146,438)(28,318,147,437)(29,317,148,436)(30,316,149,435)(31,315,150,434)(32,314,151,433)(33,313,152,432)(34,312,153,431)(35,311,154,430)(36,310,155,429)(37,309,156,428)(38,308,157,427)(39,307,158,426)(40,306,159,425)(41,305,160,424)(42,304,161,423)(43,303,162,422)(44,302,163,421)(45,301,164,420)(46,300,165,419)(47,299,166,418)(48,298,167,417)(49,297,168,416)(50,296,169,415)(51,295,170,414)(52,294,171,413)(53,293,172,412)(54,292,173,411)(55,291,174,410)(56,290,175,409)(57,289,176,408)(58,288,177,407)(59,287,178,406)(60,286,179,405)(61,285,180,404)(62,284,181,403)(63,283,182,402)(64,282,183,401)(65,281,184,400)(66,280,185,399)(67,279,186,398)(68,278,187,397)(69,277,188,396)(70,276,189,395)(71,275,190,394)(72,274,191,393)(73,273,192,392)(74,272,193,391)(75,271,194,390)(76,270,195,389)(77,269,196,388)(78,268,197,387)(79,267,198,386)(80,266,199,385)(81,265,200,384)(82,264,201,383)(83,263,202,382)(84,262,203,381)(85,261,204,380)(86,260,205,379)(87,259,206,378)(88,258,207,377)(89,257,208,376)(90,256,209,375)(91,255,210,374)(92,254,211,373)(93,253,212,372)(94,252,213,371)(95,251,214,370)(96,250,215,369)(97,249,216,368)(98,248,217,367)(99,247,218,366)(100,246,219,365)(101,245,220,364)(102,244,221,363)(103,243,222,362)(104,242,223,361)(105,241,224,360)(106,240,225,359)(107,239,226,358)(108,476,227,357)(109,475,228,356)(110,474,229,355)(111,473,230,354)(112,472,231,353)(113,471,232,352)(114,470,233,351)(115,469,234,350)(116,468,235,349)(117,467,236,348)(118,466,237,347)(119,465,238,346) );

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),(239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476)], [(1,345,120,464),(2,344,121,463),(3,343,122,462),(4,342,123,461),(5,341,124,460),(6,340,125,459),(7,339,126,458),(8,338,127,457),(9,337,128,456),(10,336,129,455),(11,335,130,454),(12,334,131,453),(13,333,132,452),(14,332,133,451),(15,331,134,450),(16,330,135,449),(17,329,136,448),(18,328,137,447),(19,327,138,446),(20,326,139,445),(21,325,140,444),(22,324,141,443),(23,323,142,442),(24,322,143,441),(25,321,144,440),(26,320,145,439),(27,319,146,438),(28,318,147,437),(29,317,148,436),(30,316,149,435),(31,315,150,434),(32,314,151,433),(33,313,152,432),(34,312,153,431),(35,311,154,430),(36,310,155,429),(37,309,156,428),(38,308,157,427),(39,307,158,426),(40,306,159,425),(41,305,160,424),(42,304,161,423),(43,303,162,422),(44,302,163,421),(45,301,164,420),(46,300,165,419),(47,299,166,418),(48,298,167,417),(49,297,168,416),(50,296,169,415),(51,295,170,414),(52,294,171,413),(53,293,172,412),(54,292,173,411),(55,291,174,410),(56,290,175,409),(57,289,176,408),(58,288,177,407),(59,287,178,406),(60,286,179,405),(61,285,180,404),(62,284,181,403),(63,283,182,402),(64,282,183,401),(65,281,184,400),(66,280,185,399),(67,279,186,398),(68,278,187,397),(69,277,188,396),(70,276,189,395),(71,275,190,394),(72,274,191,393),(73,273,192,392),(74,272,193,391),(75,271,194,390),(76,270,195,389),(77,269,196,388),(78,268,197,387),(79,267,198,386),(80,266,199,385),(81,265,200,384),(82,264,201,383),(83,263,202,382),(84,262,203,381),(85,261,204,380),(86,260,205,379),(87,259,206,378),(88,258,207,377),(89,257,208,376),(90,256,209,375),(91,255,210,374),(92,254,211,373),(93,253,212,372),(94,252,213,371),(95,251,214,370),(96,250,215,369),(97,249,216,368),(98,248,217,367),(99,247,218,366),(100,246,219,365),(101,245,220,364),(102,244,221,363),(103,243,222,362),(104,242,223,361),(105,241,224,360),(106,240,225,359),(107,239,226,358),(108,476,227,357),(109,475,228,356),(110,474,229,355),(111,473,230,354),(112,472,231,353),(113,471,232,352),(114,470,233,351),(115,469,234,350),(116,468,235,349),(117,467,236,348),(118,466,237,347),(119,465,238,346)])

122 conjugacy classes

class 1  2 4A4B7A7B7C14A14B14C17A···17H34A···34H119A···119AV238A···238AV
order124477714141417···1734···34119···119238···238
size111191192222222···22···22···22···2

122 irreducible representations

dim111222222
type+++-+-+-
imageC1C2C4D7Dic7D17Dic17D119Dic119
kernelDic119C238C119C34C17C14C7C2C1
# reps11233884848

Matrix representation of Dic119 in GL2(𝔽953) generated by

300123
830191
,
118648
280835
G:=sub<GL(2,GF(953))| [300,830,123,191],[118,280,648,835] >;

Dic119 in GAP, Magma, Sage, TeX

{\rm Dic}_{119}
% in TeX

G:=Group("Dic119");
// GroupNames label

G:=SmallGroup(476,3);
// by ID

G=gap.SmallGroup(476,3);
# by ID

G:=PCGroup([4,-2,-2,-7,-17,8,290,7171]);
// Polycyclic

G:=Group<a,b|a^238=1,b^2=a^119,b*a*b^-1=a^-1>;
// generators/relations

Export

Subgroup lattice of Dic119 in TeX

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