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G = C5×C95order 475 = 52·19

Abelian group of type [5,95]

direct product, abelian, monomial, 5-elementary

Aliases: C5×C95, SmallGroup(475,2)

Series: Derived Chief Lower central Upper central

C1 — C5×C95
C1C19C95 — C5×C95
C1 — C5×C95
C1 — C5×C95

Generators and relations for C5×C95
 G = < a,b | a5=b95=1, ab=ba >


Smallest permutation representation of C5×C95
Regular action on 475 points
Generators in S475
(1 381 313 226 183)(2 382 314 227 184)(3 383 315 228 185)(4 384 316 229 186)(5 385 317 230 187)(6 386 318 231 188)(7 387 319 232 189)(8 388 320 233 190)(9 389 321 234 96)(10 390 322 235 97)(11 391 323 236 98)(12 392 324 237 99)(13 393 325 238 100)(14 394 326 239 101)(15 395 327 240 102)(16 396 328 241 103)(17 397 329 242 104)(18 398 330 243 105)(19 399 331 244 106)(20 400 332 245 107)(21 401 333 246 108)(22 402 334 247 109)(23 403 335 248 110)(24 404 336 249 111)(25 405 337 250 112)(26 406 338 251 113)(27 407 339 252 114)(28 408 340 253 115)(29 409 341 254 116)(30 410 342 255 117)(31 411 343 256 118)(32 412 344 257 119)(33 413 345 258 120)(34 414 346 259 121)(35 415 347 260 122)(36 416 348 261 123)(37 417 349 262 124)(38 418 350 263 125)(39 419 351 264 126)(40 420 352 265 127)(41 421 353 266 128)(42 422 354 267 129)(43 423 355 268 130)(44 424 356 269 131)(45 425 357 270 132)(46 426 358 271 133)(47 427 359 272 134)(48 428 360 273 135)(49 429 361 274 136)(50 430 362 275 137)(51 431 363 276 138)(52 432 364 277 139)(53 433 365 278 140)(54 434 366 279 141)(55 435 367 280 142)(56 436 368 281 143)(57 437 369 282 144)(58 438 370 283 145)(59 439 371 284 146)(60 440 372 285 147)(61 441 373 191 148)(62 442 374 192 149)(63 443 375 193 150)(64 444 376 194 151)(65 445 377 195 152)(66 446 378 196 153)(67 447 379 197 154)(68 448 380 198 155)(69 449 286 199 156)(70 450 287 200 157)(71 451 288 201 158)(72 452 289 202 159)(73 453 290 203 160)(74 454 291 204 161)(75 455 292 205 162)(76 456 293 206 163)(77 457 294 207 164)(78 458 295 208 165)(79 459 296 209 166)(80 460 297 210 167)(81 461 298 211 168)(82 462 299 212 169)(83 463 300 213 170)(84 464 301 214 171)(85 465 302 215 172)(86 466 303 216 173)(87 467 304 217 174)(88 468 305 218 175)(89 469 306 219 176)(90 470 307 220 177)(91 471 308 221 178)(92 472 309 222 179)(93 473 310 223 180)(94 474 311 224 181)(95 475 312 225 182)
(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)

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

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

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

475 conjugacy classes

class 1 5A···5X19A···19R95A···95PP
order15···519···1995···95
size11···11···11···1

475 irreducible representations

dim1111
type+
imageC1C5C19C95
kernelC5×C95C95C52C5
# reps12418432

Matrix representation of C5×C95 in GL2(𝔽191) generated by

390
039
,
1300
065
G:=sub<GL(2,GF(191))| [39,0,0,39],[130,0,0,65] >;

C5×C95 in GAP, Magma, Sage, TeX

C_5\times C_{95}
% in TeX

G:=Group("C5xC95");
// GroupNames label

G:=SmallGroup(475,2);
// by ID

G=gap.SmallGroup(475,2);
# by ID

G:=PCGroup([3,-5,-5,-19]);
// Polycyclic

G:=Group<a,b|a^5=b^95=1,a*b=b*a>;
// generators/relations

Export

Subgroup lattice of C5×C95 in TeX

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×
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