direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C3×C17⋊2C8, C51⋊4C8, C17⋊2C24, C34.C12, C102.2C4, Dic17.2C6, C6.2(C17⋊C4), (C3×Dic17).4C2, C2.(C3×C17⋊C4), SmallGroup(408,5)
Series: Derived ►Chief ►Lower central ►Upper central
| C17 — C3×C17⋊2C8 |
Generators and relations for C3×C17⋊2C8
G = < a,b,c | a3=b17=c8=1, ab=ba, ac=ca, cbc-1=b4 >
Smallest permutation representation of C3×C17⋊2C8
►Regular action on 408 points
Generators in S408
(1 137 69)(2 138 70)(3 139 71)(4 140 72)(5 141 73)(6 142 74)(7 143 75)(8 144 76)(9 145 77)(10 146 78)(11 147 79)(12 148 80)(13 149 81)(14 150 82)(15 151 83)(16 152 84)(17 153 85)(18 154 86)(19 155 87)(20 156 88)(21 157 89)(22 158 90)(23 159 91)(24 160 92)(25 161 93)(26 162 94)(27 163 95)(28 164 96)(29 165 97)(30 166 98)(31 167 99)(32 168 100)(33 169 101)(34 170 102)(35 185 103)(36 186 104)(37 187 105)(38 171 106)(39 172 107)(40 173 108)(41 174 109)(42 175 110)(43 176 111)(44 177 112)(45 178 113)(46 179 114)(47 180 115)(48 181 116)(49 182 117)(50 183 118)(51 184 119)(52 195 123)(53 196 124)(54 197 125)(55 198 126)(56 199 127)(57 200 128)(58 201 129)(59 202 130)(60 203 131)(61 204 132)(62 188 133)(63 189 134)(64 190 135)(65 191 136)(66 192 120)(67 193 121)(68 194 122)(205 345 282)(206 346 283)(207 347 284)(208 348 285)(209 349 286)(210 350 287)(211 351 288)(212 352 289)(213 353 273)(214 354 274)(215 355 275)(216 356 276)(217 357 277)(218 341 278)(219 342 279)(220 343 280)(221 344 281)(222 369 306)(223 370 290)(224 371 291)(225 372 292)(226 373 293)(227 374 294)(228 358 295)(229 359 296)(230 360 297)(231 361 298)(232 362 299)(233 363 300)(234 364 301)(235 365 302)(236 366 303)(237 367 304)(238 368 305)(239 376 315)(240 377 316)(241 378 317)(242 379 318)(243 380 319)(244 381 320)(245 382 321)(246 383 322)(247 384 323)(248 385 307)(249 386 308)(250 387 309)(251 388 310)(252 389 311)(253 390 312)(254 391 313)(255 375 314)(256 394 329)(257 395 330)(258 396 331)(259 397 332)(260 398 333)(261 399 334)(262 400 335)(263 401 336)(264 402 337)(265 403 338)(266 404 339)(267 405 340)(268 406 324)(269 407 325)(270 408 326)(271 392 327)(272 393 328)
(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)
(1 268 62 229 18 248 43 214)(2 264 61 233 19 244 42 218)(3 260 60 237 20 240 41 205)(4 256 59 224 21 253 40 209)(5 269 58 228 22 249 39 213)(6 265 57 232 23 245 38 217)(7 261 56 236 24 241 37 221)(8 257 55 223 25 254 36 208)(9 270 54 227 26 250 35 212)(10 266 53 231 27 246 51 216)(11 262 52 235 28 242 50 220)(12 258 68 222 29 255 49 207)(13 271 67 226 30 251 48 211)(14 267 66 230 31 247 47 215)(15 263 65 234 32 243 46 219)(16 259 64 238 33 239 45 206)(17 272 63 225 34 252 44 210)(69 324 133 296 86 307 111 274)(70 337 132 300 87 320 110 278)(71 333 131 304 88 316 109 282)(72 329 130 291 89 312 108 286)(73 325 129 295 90 308 107 273)(74 338 128 299 91 321 106 277)(75 334 127 303 92 317 105 281)(76 330 126 290 93 313 104 285)(77 326 125 294 94 309 103 289)(78 339 124 298 95 322 119 276)(79 335 123 302 96 318 118 280)(80 331 122 306 97 314 117 284)(81 327 121 293 98 310 116 288)(82 340 120 297 99 323 115 275)(83 336 136 301 100 319 114 279)(84 332 135 305 101 315 113 283)(85 328 134 292 102 311 112 287)(137 406 188 359 154 385 176 354)(138 402 204 363 155 381 175 341)(139 398 203 367 156 377 174 345)(140 394 202 371 157 390 173 349)(141 407 201 358 158 386 172 353)(142 403 200 362 159 382 171 357)(143 399 199 366 160 378 187 344)(144 395 198 370 161 391 186 348)(145 408 197 374 162 387 185 352)(146 404 196 361 163 383 184 356)(147 400 195 365 164 379 183 343)(148 396 194 369 165 375 182 347)(149 392 193 373 166 388 181 351)(150 405 192 360 167 384 180 355)(151 401 191 364 168 380 179 342)(152 397 190 368 169 376 178 346)(153 393 189 372 170 389 177 350)
G:=sub<Sym(408)| (1,137,69)(2,138,70)(3,139,71)(4,140,72)(5,141,73)(6,142,74)(7,143,75)(8,144,76)(9,145,77)(10,146,78)(11,147,79)(12,148,80)(13,149,81)(14,150,82)(15,151,83)(16,152,84)(17,153,85)(18,154,86)(19,155,87)(20,156,88)(21,157,89)(22,158,90)(23,159,91)(24,160,92)(25,161,93)(26,162,94)(27,163,95)(28,164,96)(29,165,97)(30,166,98)(31,167,99)(32,168,100)(33,169,101)(34,170,102)(35,185,103)(36,186,104)(37,187,105)(38,171,106)(39,172,107)(40,173,108)(41,174,109)(42,175,110)(43,176,111)(44,177,112)(45,178,113)(46,179,114)(47,180,115)(48,181,116)(49,182,117)(50,183,118)(51,184,119)(52,195,123)(53,196,124)(54,197,125)(55,198,126)(56,199,127)(57,200,128)(58,201,129)(59,202,130)(60,203,131)(61,204,132)(62,188,133)(63,189,134)(64,190,135)(65,191,136)(66,192,120)(67,193,121)(68,194,122)(205,345,282)(206,346,283)(207,347,284)(208,348,285)(209,349,286)(210,350,287)(211,351,288)(212,352,289)(213,353,273)(214,354,274)(215,355,275)(216,356,276)(217,357,277)(218,341,278)(219,342,279)(220,343,280)(221,344,281)(222,369,306)(223,370,290)(224,371,291)(225,372,292)(226,373,293)(227,374,294)(228,358,295)(229,359,296)(230,360,297)(231,361,298)(232,362,299)(233,363,300)(234,364,301)(235,365,302)(236,366,303)(237,367,304)(238,368,305)(239,376,315)(240,377,316)(241,378,317)(242,379,318)(243,380,319)(244,381,320)(245,382,321)(246,383,322)(247,384,323)(248,385,307)(249,386,308)(250,387,309)(251,388,310)(252,389,311)(253,390,312)(254,391,313)(255,375,314)(256,394,329)(257,395,330)(258,396,331)(259,397,332)(260,398,333)(261,399,334)(262,400,335)(263,401,336)(264,402,337)(265,403,338)(266,404,339)(267,405,340)(268,406,324)(269,407,325)(270,408,326)(271,392,327)(272,393,328), (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), (1,268,62,229,18,248,43,214)(2,264,61,233,19,244,42,218)(3,260,60,237,20,240,41,205)(4,256,59,224,21,253,40,209)(5,269,58,228,22,249,39,213)(6,265,57,232,23,245,38,217)(7,261,56,236,24,241,37,221)(8,257,55,223,25,254,36,208)(9,270,54,227,26,250,35,212)(10,266,53,231,27,246,51,216)(11,262,52,235,28,242,50,220)(12,258,68,222,29,255,49,207)(13,271,67,226,30,251,48,211)(14,267,66,230,31,247,47,215)(15,263,65,234,32,243,46,219)(16,259,64,238,33,239,45,206)(17,272,63,225,34,252,44,210)(69,324,133,296,86,307,111,274)(70,337,132,300,87,320,110,278)(71,333,131,304,88,316,109,282)(72,329,130,291,89,312,108,286)(73,325,129,295,90,308,107,273)(74,338,128,299,91,321,106,277)(75,334,127,303,92,317,105,281)(76,330,126,290,93,313,104,285)(77,326,125,294,94,309,103,289)(78,339,124,298,95,322,119,276)(79,335,123,302,96,318,118,280)(80,331,122,306,97,314,117,284)(81,327,121,293,98,310,116,288)(82,340,120,297,99,323,115,275)(83,336,136,301,100,319,114,279)(84,332,135,305,101,315,113,283)(85,328,134,292,102,311,112,287)(137,406,188,359,154,385,176,354)(138,402,204,363,155,381,175,341)(139,398,203,367,156,377,174,345)(140,394,202,371,157,390,173,349)(141,407,201,358,158,386,172,353)(142,403,200,362,159,382,171,357)(143,399,199,366,160,378,187,344)(144,395,198,370,161,391,186,348)(145,408,197,374,162,387,185,352)(146,404,196,361,163,383,184,356)(147,400,195,365,164,379,183,343)(148,396,194,369,165,375,182,347)(149,392,193,373,166,388,181,351)(150,405,192,360,167,384,180,355)(151,401,191,364,168,380,179,342)(152,397,190,368,169,376,178,346)(153,393,189,372,170,389,177,350)>;
G:=Group( (1,137,69)(2,138,70)(3,139,71)(4,140,72)(5,141,73)(6,142,74)(7,143,75)(8,144,76)(9,145,77)(10,146,78)(11,147,79)(12,148,80)(13,149,81)(14,150,82)(15,151,83)(16,152,84)(17,153,85)(18,154,86)(19,155,87)(20,156,88)(21,157,89)(22,158,90)(23,159,91)(24,160,92)(25,161,93)(26,162,94)(27,163,95)(28,164,96)(29,165,97)(30,166,98)(31,167,99)(32,168,100)(33,169,101)(34,170,102)(35,185,103)(36,186,104)(37,187,105)(38,171,106)(39,172,107)(40,173,108)(41,174,109)(42,175,110)(43,176,111)(44,177,112)(45,178,113)(46,179,114)(47,180,115)(48,181,116)(49,182,117)(50,183,118)(51,184,119)(52,195,123)(53,196,124)(54,197,125)(55,198,126)(56,199,127)(57,200,128)(58,201,129)(59,202,130)(60,203,131)(61,204,132)(62,188,133)(63,189,134)(64,190,135)(65,191,136)(66,192,120)(67,193,121)(68,194,122)(205,345,282)(206,346,283)(207,347,284)(208,348,285)(209,349,286)(210,350,287)(211,351,288)(212,352,289)(213,353,273)(214,354,274)(215,355,275)(216,356,276)(217,357,277)(218,341,278)(219,342,279)(220,343,280)(221,344,281)(222,369,306)(223,370,290)(224,371,291)(225,372,292)(226,373,293)(227,374,294)(228,358,295)(229,359,296)(230,360,297)(231,361,298)(232,362,299)(233,363,300)(234,364,301)(235,365,302)(236,366,303)(237,367,304)(238,368,305)(239,376,315)(240,377,316)(241,378,317)(242,379,318)(243,380,319)(244,381,320)(245,382,321)(246,383,322)(247,384,323)(248,385,307)(249,386,308)(250,387,309)(251,388,310)(252,389,311)(253,390,312)(254,391,313)(255,375,314)(256,394,329)(257,395,330)(258,396,331)(259,397,332)(260,398,333)(261,399,334)(262,400,335)(263,401,336)(264,402,337)(265,403,338)(266,404,339)(267,405,340)(268,406,324)(269,407,325)(270,408,326)(271,392,327)(272,393,328), (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), (1,268,62,229,18,248,43,214)(2,264,61,233,19,244,42,218)(3,260,60,237,20,240,41,205)(4,256,59,224,21,253,40,209)(5,269,58,228,22,249,39,213)(6,265,57,232,23,245,38,217)(7,261,56,236,24,241,37,221)(8,257,55,223,25,254,36,208)(9,270,54,227,26,250,35,212)(10,266,53,231,27,246,51,216)(11,262,52,235,28,242,50,220)(12,258,68,222,29,255,49,207)(13,271,67,226,30,251,48,211)(14,267,66,230,31,247,47,215)(15,263,65,234,32,243,46,219)(16,259,64,238,33,239,45,206)(17,272,63,225,34,252,44,210)(69,324,133,296,86,307,111,274)(70,337,132,300,87,320,110,278)(71,333,131,304,88,316,109,282)(72,329,130,291,89,312,108,286)(73,325,129,295,90,308,107,273)(74,338,128,299,91,321,106,277)(75,334,127,303,92,317,105,281)(76,330,126,290,93,313,104,285)(77,326,125,294,94,309,103,289)(78,339,124,298,95,322,119,276)(79,335,123,302,96,318,118,280)(80,331,122,306,97,314,117,284)(81,327,121,293,98,310,116,288)(82,340,120,297,99,323,115,275)(83,336,136,301,100,319,114,279)(84,332,135,305,101,315,113,283)(85,328,134,292,102,311,112,287)(137,406,188,359,154,385,176,354)(138,402,204,363,155,381,175,341)(139,398,203,367,156,377,174,345)(140,394,202,371,157,390,173,349)(141,407,201,358,158,386,172,353)(142,403,200,362,159,382,171,357)(143,399,199,366,160,378,187,344)(144,395,198,370,161,391,186,348)(145,408,197,374,162,387,185,352)(146,404,196,361,163,383,184,356)(147,400,195,365,164,379,183,343)(148,396,194,369,165,375,182,347)(149,392,193,373,166,388,181,351)(150,405,192,360,167,384,180,355)(151,401,191,364,168,380,179,342)(152,397,190,368,169,376,178,346)(153,393,189,372,170,389,177,350) );
G=PermutationGroup([[(1,137,69),(2,138,70),(3,139,71),(4,140,72),(5,141,73),(6,142,74),(7,143,75),(8,144,76),(9,145,77),(10,146,78),(11,147,79),(12,148,80),(13,149,81),(14,150,82),(15,151,83),(16,152,84),(17,153,85),(18,154,86),(19,155,87),(20,156,88),(21,157,89),(22,158,90),(23,159,91),(24,160,92),(25,161,93),(26,162,94),(27,163,95),(28,164,96),(29,165,97),(30,166,98),(31,167,99),(32,168,100),(33,169,101),(34,170,102),(35,185,103),(36,186,104),(37,187,105),(38,171,106),(39,172,107),(40,173,108),(41,174,109),(42,175,110),(43,176,111),(44,177,112),(45,178,113),(46,179,114),(47,180,115),(48,181,116),(49,182,117),(50,183,118),(51,184,119),(52,195,123),(53,196,124),(54,197,125),(55,198,126),(56,199,127),(57,200,128),(58,201,129),(59,202,130),(60,203,131),(61,204,132),(62,188,133),(63,189,134),(64,190,135),(65,191,136),(66,192,120),(67,193,121),(68,194,122),(205,345,282),(206,346,283),(207,347,284),(208,348,285),(209,349,286),(210,350,287),(211,351,288),(212,352,289),(213,353,273),(214,354,274),(215,355,275),(216,356,276),(217,357,277),(218,341,278),(219,342,279),(220,343,280),(221,344,281),(222,369,306),(223,370,290),(224,371,291),(225,372,292),(226,373,293),(227,374,294),(228,358,295),(229,359,296),(230,360,297),(231,361,298),(232,362,299),(233,363,300),(234,364,301),(235,365,302),(236,366,303),(237,367,304),(238,368,305),(239,376,315),(240,377,316),(241,378,317),(242,379,318),(243,380,319),(244,381,320),(245,382,321),(246,383,322),(247,384,323),(248,385,307),(249,386,308),(250,387,309),(251,388,310),(252,389,311),(253,390,312),(254,391,313),(255,375,314),(256,394,329),(257,395,330),(258,396,331),(259,397,332),(260,398,333),(261,399,334),(262,400,335),(263,401,336),(264,402,337),(265,403,338),(266,404,339),(267,405,340),(268,406,324),(269,407,325),(270,408,326),(271,392,327),(272,393,328)], [(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)], [(1,268,62,229,18,248,43,214),(2,264,61,233,19,244,42,218),(3,260,60,237,20,240,41,205),(4,256,59,224,21,253,40,209),(5,269,58,228,22,249,39,213),(6,265,57,232,23,245,38,217),(7,261,56,236,24,241,37,221),(8,257,55,223,25,254,36,208),(9,270,54,227,26,250,35,212),(10,266,53,231,27,246,51,216),(11,262,52,235,28,242,50,220),(12,258,68,222,29,255,49,207),(13,271,67,226,30,251,48,211),(14,267,66,230,31,247,47,215),(15,263,65,234,32,243,46,219),(16,259,64,238,33,239,45,206),(17,272,63,225,34,252,44,210),(69,324,133,296,86,307,111,274),(70,337,132,300,87,320,110,278),(71,333,131,304,88,316,109,282),(72,329,130,291,89,312,108,286),(73,325,129,295,90,308,107,273),(74,338,128,299,91,321,106,277),(75,334,127,303,92,317,105,281),(76,330,126,290,93,313,104,285),(77,326,125,294,94,309,103,289),(78,339,124,298,95,322,119,276),(79,335,123,302,96,318,118,280),(80,331,122,306,97,314,117,284),(81,327,121,293,98,310,116,288),(82,340,120,297,99,323,115,275),(83,336,136,301,100,319,114,279),(84,332,135,305,101,315,113,283),(85,328,134,292,102,311,112,287),(137,406,188,359,154,385,176,354),(138,402,204,363,155,381,175,341),(139,398,203,367,156,377,174,345),(140,394,202,371,157,390,173,349),(141,407,201,358,158,386,172,353),(142,403,200,362,159,382,171,357),(143,399,199,366,160,378,187,344),(144,395,198,370,161,391,186,348),(145,408,197,374,162,387,185,352),(146,404,196,361,163,383,184,356),(147,400,195,365,164,379,183,343),(148,396,194,369,165,375,182,347),(149,392,193,373,166,388,181,351),(150,405,192,360,167,384,180,355),(151,401,191,364,168,380,179,342),(152,397,190,368,169,376,178,346),(153,393,189,372,170,389,177,350)]])
48 conjugacy classes
| class | 1 | 2 | 3A | 3B | 4A | 4B | 6A | 6B | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 17A | 17B | 17C | 17D | 24A | ··· | 24H | 34A | 34B | 34C | 34D | 51A | ··· | 51H | 102A | ··· | 102H |
| order | 1 | 2 | 3 | 3 | 4 | 4 | 6 | 6 | 8 | 8 | 8 | 8 | 12 | 12 | 12 | 12 | 17 | 17 | 17 | 17 | 24 | ··· | 24 | 34 | 34 | 34 | 34 | 51 | ··· | 51 | 102 | ··· | 102 |
| size | 1 | 1 | 1 | 1 | 17 | 17 | 1 | 1 | 17 | 17 | 17 | 17 | 17 | 17 | 17 | 17 | 4 | 4 | 4 | 4 | 17 | ··· | 17 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 |
48 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 |
| type | + | + | + | - | ||||||||
| image | C1 | C2 | C3 | C4 | C6 | C8 | C12 | C24 | C17⋊C4 | C17⋊2C8 | C3×C17⋊C4 | C3×C17⋊2C8 |
| kernel | C3×C17⋊2C8 | C3×Dic17 | C17⋊2C8 | C102 | Dic17 | C51 | C34 | C17 | C6 | C3 | C2 | C1 |
| # reps | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 8 | 4 | 4 | 8 | 8 |
Matrix representation of C3×C17⋊2C8 ►in GL5(𝔽409)
| 53 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 90 | 15 | 90 | 408 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 31 | 0 | 0 | 0 | 0 |
| 0 | 179 | 346 | 48 | 33 |
| 0 | 357 | 114 | 111 | 379 |
| 0 | 86 | 247 | 264 | 213 |
| 0 | 18 | 79 | 393 | 261 |
G:=sub<GL(5,GF(409))| [53,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,90,1,0,0,0,15,0,1,0,0,90,0,0,1,0,408,0,0,0],[31,0,0,0,0,0,179,357,86,18,0,346,114,247,79,0,48,111,264,393,0,33,379,213,261] >;
C3×C17⋊2C8 in GAP, Magma, Sage, TeX
C_3\times C_{17}\rtimes_2C_8 % in TeX
G:=Group("C3xC17:2C8"); // GroupNames label
G:=SmallGroup(408,5);
// by ID
G=gap.SmallGroup(408,5);
# by ID
G:=PCGroup([5,-2,-3,-2,-2,-17,30,42,7804,1614]);
// Polycyclic
G:=Group<a,b,c|a^3=b^17=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^4>;
// generators/relations
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