direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C3×C17⋊3C8, C51⋊6C8, C17⋊3C24, C68.2C6, C34.2C12, C204.4C2, C102.4C4, C12.4D17, C6.2Dic17, C4.2(C3×D17), C2.(C3×Dic17), SmallGroup(408,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C17 — C3×C17⋊3C8 |
Generators and relations for C3×C17⋊3C8
G = < a,b,c | a3=b17=c8=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C3×C17⋊3C8
►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)(35 171 103)(36 172 104)(37 173 105)(38 174 106)(39 175 107)(40 176 108)(41 177 109)(42 178 110)(43 179 111)(44 180 112)(45 181 113)(46 182 114)(47 183 115)(48 184 116)(49 185 117)(50 186 118)(51 187 119)(52 188 120)(53 189 121)(54 190 122)(55 191 123)(56 192 124)(57 193 125)(58 194 126)(59 195 127)(60 196 128)(61 197 129)(62 198 130)(63 199 131)(64 200 132)(65 201 133)(66 202 134)(67 203 135)(68 204 136)(205 342 284)(206 343 285)(207 344 286)(208 345 287)(209 346 288)(210 347 289)(211 348 273)(212 349 274)(213 350 275)(214 351 276)(215 352 277)(216 353 278)(217 354 279)(218 355 280)(219 356 281)(220 357 282)(221 341 283)(222 367 298)(223 368 299)(224 369 300)(225 370 301)(226 371 302)(227 372 303)(228 373 304)(229 374 305)(230 358 306)(231 359 290)(232 360 291)(233 361 292)(234 362 293)(235 363 294)(236 364 295)(237 365 296)(238 366 297)(239 377 308)(240 378 309)(241 379 310)(242 380 311)(243 381 312)(244 382 313)(245 383 314)(246 384 315)(247 385 316)(248 386 317)(249 387 318)(250 388 319)(251 389 320)(252 390 321)(253 391 322)(254 375 323)(255 376 307)(256 394 326)(257 395 327)(258 396 328)(259 397 329)(260 398 330)(261 399 331)(262 400 332)(263 401 333)(264 402 334)(265 403 335)(266 404 336)(267 405 337)(268 406 338)(269 407 339)(270 408 340)(271 392 324)(272 393 325)
(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)
(1 266 52 232 18 244 35 208)(2 265 53 231 19 243 36 207)(3 264 54 230 20 242 37 206)(4 263 55 229 21 241 38 205)(5 262 56 228 22 240 39 221)(6 261 57 227 23 239 40 220)(7 260 58 226 24 255 41 219)(8 259 59 225 25 254 42 218)(9 258 60 224 26 253 43 217)(10 257 61 223 27 252 44 216)(11 256 62 222 28 251 45 215)(12 272 63 238 29 250 46 214)(13 271 64 237 30 249 47 213)(14 270 65 236 31 248 48 212)(15 269 66 235 32 247 49 211)(16 268 67 234 33 246 50 210)(17 267 68 233 34 245 51 209)(69 336 120 291 86 313 103 287)(70 335 121 290 87 312 104 286)(71 334 122 306 88 311 105 285)(72 333 123 305 89 310 106 284)(73 332 124 304 90 309 107 283)(74 331 125 303 91 308 108 282)(75 330 126 302 92 307 109 281)(76 329 127 301 93 323 110 280)(77 328 128 300 94 322 111 279)(78 327 129 299 95 321 112 278)(79 326 130 298 96 320 113 277)(80 325 131 297 97 319 114 276)(81 324 132 296 98 318 115 275)(82 340 133 295 99 317 116 274)(83 339 134 294 100 316 117 273)(84 338 135 293 101 315 118 289)(85 337 136 292 102 314 119 288)(137 404 188 360 154 382 171 345)(138 403 189 359 155 381 172 344)(139 402 190 358 156 380 173 343)(140 401 191 374 157 379 174 342)(141 400 192 373 158 378 175 341)(142 399 193 372 159 377 176 357)(143 398 194 371 160 376 177 356)(144 397 195 370 161 375 178 355)(145 396 196 369 162 391 179 354)(146 395 197 368 163 390 180 353)(147 394 198 367 164 389 181 352)(148 393 199 366 165 388 182 351)(149 392 200 365 166 387 183 350)(150 408 201 364 167 386 184 349)(151 407 202 363 168 385 185 348)(152 406 203 362 169 384 186 347)(153 405 204 361 170 383 187 346)
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)(35,171,103)(36,172,104)(37,173,105)(38,174,106)(39,175,107)(40,176,108)(41,177,109)(42,178,110)(43,179,111)(44,180,112)(45,181,113)(46,182,114)(47,183,115)(48,184,116)(49,185,117)(50,186,118)(51,187,119)(52,188,120)(53,189,121)(54,190,122)(55,191,123)(56,192,124)(57,193,125)(58,194,126)(59,195,127)(60,196,128)(61,197,129)(62,198,130)(63,199,131)(64,200,132)(65,201,133)(66,202,134)(67,203,135)(68,204,136)(205,342,284)(206,343,285)(207,344,286)(208,345,287)(209,346,288)(210,347,289)(211,348,273)(212,349,274)(213,350,275)(214,351,276)(215,352,277)(216,353,278)(217,354,279)(218,355,280)(219,356,281)(220,357,282)(221,341,283)(222,367,298)(223,368,299)(224,369,300)(225,370,301)(226,371,302)(227,372,303)(228,373,304)(229,374,305)(230,358,306)(231,359,290)(232,360,291)(233,361,292)(234,362,293)(235,363,294)(236,364,295)(237,365,296)(238,366,297)(239,377,308)(240,378,309)(241,379,310)(242,380,311)(243,381,312)(244,382,313)(245,383,314)(246,384,315)(247,385,316)(248,386,317)(249,387,318)(250,388,319)(251,389,320)(252,390,321)(253,391,322)(254,375,323)(255,376,307)(256,394,326)(257,395,327)(258,396,328)(259,397,329)(260,398,330)(261,399,331)(262,400,332)(263,401,333)(264,402,334)(265,403,335)(266,404,336)(267,405,337)(268,406,338)(269,407,339)(270,408,340)(271,392,324)(272,393,325), (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), (1,266,52,232,18,244,35,208)(2,265,53,231,19,243,36,207)(3,264,54,230,20,242,37,206)(4,263,55,229,21,241,38,205)(5,262,56,228,22,240,39,221)(6,261,57,227,23,239,40,220)(7,260,58,226,24,255,41,219)(8,259,59,225,25,254,42,218)(9,258,60,224,26,253,43,217)(10,257,61,223,27,252,44,216)(11,256,62,222,28,251,45,215)(12,272,63,238,29,250,46,214)(13,271,64,237,30,249,47,213)(14,270,65,236,31,248,48,212)(15,269,66,235,32,247,49,211)(16,268,67,234,33,246,50,210)(17,267,68,233,34,245,51,209)(69,336,120,291,86,313,103,287)(70,335,121,290,87,312,104,286)(71,334,122,306,88,311,105,285)(72,333,123,305,89,310,106,284)(73,332,124,304,90,309,107,283)(74,331,125,303,91,308,108,282)(75,330,126,302,92,307,109,281)(76,329,127,301,93,323,110,280)(77,328,128,300,94,322,111,279)(78,327,129,299,95,321,112,278)(79,326,130,298,96,320,113,277)(80,325,131,297,97,319,114,276)(81,324,132,296,98,318,115,275)(82,340,133,295,99,317,116,274)(83,339,134,294,100,316,117,273)(84,338,135,293,101,315,118,289)(85,337,136,292,102,314,119,288)(137,404,188,360,154,382,171,345)(138,403,189,359,155,381,172,344)(139,402,190,358,156,380,173,343)(140,401,191,374,157,379,174,342)(141,400,192,373,158,378,175,341)(142,399,193,372,159,377,176,357)(143,398,194,371,160,376,177,356)(144,397,195,370,161,375,178,355)(145,396,196,369,162,391,179,354)(146,395,197,368,163,390,180,353)(147,394,198,367,164,389,181,352)(148,393,199,366,165,388,182,351)(149,392,200,365,166,387,183,350)(150,408,201,364,167,386,184,349)(151,407,202,363,168,385,185,348)(152,406,203,362,169,384,186,347)(153,405,204,361,170,383,187,346)>;
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)(35,171,103)(36,172,104)(37,173,105)(38,174,106)(39,175,107)(40,176,108)(41,177,109)(42,178,110)(43,179,111)(44,180,112)(45,181,113)(46,182,114)(47,183,115)(48,184,116)(49,185,117)(50,186,118)(51,187,119)(52,188,120)(53,189,121)(54,190,122)(55,191,123)(56,192,124)(57,193,125)(58,194,126)(59,195,127)(60,196,128)(61,197,129)(62,198,130)(63,199,131)(64,200,132)(65,201,133)(66,202,134)(67,203,135)(68,204,136)(205,342,284)(206,343,285)(207,344,286)(208,345,287)(209,346,288)(210,347,289)(211,348,273)(212,349,274)(213,350,275)(214,351,276)(215,352,277)(216,353,278)(217,354,279)(218,355,280)(219,356,281)(220,357,282)(221,341,283)(222,367,298)(223,368,299)(224,369,300)(225,370,301)(226,371,302)(227,372,303)(228,373,304)(229,374,305)(230,358,306)(231,359,290)(232,360,291)(233,361,292)(234,362,293)(235,363,294)(236,364,295)(237,365,296)(238,366,297)(239,377,308)(240,378,309)(241,379,310)(242,380,311)(243,381,312)(244,382,313)(245,383,314)(246,384,315)(247,385,316)(248,386,317)(249,387,318)(250,388,319)(251,389,320)(252,390,321)(253,391,322)(254,375,323)(255,376,307)(256,394,326)(257,395,327)(258,396,328)(259,397,329)(260,398,330)(261,399,331)(262,400,332)(263,401,333)(264,402,334)(265,403,335)(266,404,336)(267,405,337)(268,406,338)(269,407,339)(270,408,340)(271,392,324)(272,393,325), (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), (1,266,52,232,18,244,35,208)(2,265,53,231,19,243,36,207)(3,264,54,230,20,242,37,206)(4,263,55,229,21,241,38,205)(5,262,56,228,22,240,39,221)(6,261,57,227,23,239,40,220)(7,260,58,226,24,255,41,219)(8,259,59,225,25,254,42,218)(9,258,60,224,26,253,43,217)(10,257,61,223,27,252,44,216)(11,256,62,222,28,251,45,215)(12,272,63,238,29,250,46,214)(13,271,64,237,30,249,47,213)(14,270,65,236,31,248,48,212)(15,269,66,235,32,247,49,211)(16,268,67,234,33,246,50,210)(17,267,68,233,34,245,51,209)(69,336,120,291,86,313,103,287)(70,335,121,290,87,312,104,286)(71,334,122,306,88,311,105,285)(72,333,123,305,89,310,106,284)(73,332,124,304,90,309,107,283)(74,331,125,303,91,308,108,282)(75,330,126,302,92,307,109,281)(76,329,127,301,93,323,110,280)(77,328,128,300,94,322,111,279)(78,327,129,299,95,321,112,278)(79,326,130,298,96,320,113,277)(80,325,131,297,97,319,114,276)(81,324,132,296,98,318,115,275)(82,340,133,295,99,317,116,274)(83,339,134,294,100,316,117,273)(84,338,135,293,101,315,118,289)(85,337,136,292,102,314,119,288)(137,404,188,360,154,382,171,345)(138,403,189,359,155,381,172,344)(139,402,190,358,156,380,173,343)(140,401,191,374,157,379,174,342)(141,400,192,373,158,378,175,341)(142,399,193,372,159,377,176,357)(143,398,194,371,160,376,177,356)(144,397,195,370,161,375,178,355)(145,396,196,369,162,391,179,354)(146,395,197,368,163,390,180,353)(147,394,198,367,164,389,181,352)(148,393,199,366,165,388,182,351)(149,392,200,365,166,387,183,350)(150,408,201,364,167,386,184,349)(151,407,202,363,168,385,185,348)(152,406,203,362,169,384,186,347)(153,405,204,361,170,383,187,346) );
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),(35,171,103),(36,172,104),(37,173,105),(38,174,106),(39,175,107),(40,176,108),(41,177,109),(42,178,110),(43,179,111),(44,180,112),(45,181,113),(46,182,114),(47,183,115),(48,184,116),(49,185,117),(50,186,118),(51,187,119),(52,188,120),(53,189,121),(54,190,122),(55,191,123),(56,192,124),(57,193,125),(58,194,126),(59,195,127),(60,196,128),(61,197,129),(62,198,130),(63,199,131),(64,200,132),(65,201,133),(66,202,134),(67,203,135),(68,204,136),(205,342,284),(206,343,285),(207,344,286),(208,345,287),(209,346,288),(210,347,289),(211,348,273),(212,349,274),(213,350,275),(214,351,276),(215,352,277),(216,353,278),(217,354,279),(218,355,280),(219,356,281),(220,357,282),(221,341,283),(222,367,298),(223,368,299),(224,369,300),(225,370,301),(226,371,302),(227,372,303),(228,373,304),(229,374,305),(230,358,306),(231,359,290),(232,360,291),(233,361,292),(234,362,293),(235,363,294),(236,364,295),(237,365,296),(238,366,297),(239,377,308),(240,378,309),(241,379,310),(242,380,311),(243,381,312),(244,382,313),(245,383,314),(246,384,315),(247,385,316),(248,386,317),(249,387,318),(250,388,319),(251,389,320),(252,390,321),(253,391,322),(254,375,323),(255,376,307),(256,394,326),(257,395,327),(258,396,328),(259,397,329),(260,398,330),(261,399,331),(262,400,332),(263,401,333),(264,402,334),(265,403,335),(266,404,336),(267,405,337),(268,406,338),(269,407,339),(270,408,340),(271,392,324),(272,393,325)], [(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)], [(1,266,52,232,18,244,35,208),(2,265,53,231,19,243,36,207),(3,264,54,230,20,242,37,206),(4,263,55,229,21,241,38,205),(5,262,56,228,22,240,39,221),(6,261,57,227,23,239,40,220),(7,260,58,226,24,255,41,219),(8,259,59,225,25,254,42,218),(9,258,60,224,26,253,43,217),(10,257,61,223,27,252,44,216),(11,256,62,222,28,251,45,215),(12,272,63,238,29,250,46,214),(13,271,64,237,30,249,47,213),(14,270,65,236,31,248,48,212),(15,269,66,235,32,247,49,211),(16,268,67,234,33,246,50,210),(17,267,68,233,34,245,51,209),(69,336,120,291,86,313,103,287),(70,335,121,290,87,312,104,286),(71,334,122,306,88,311,105,285),(72,333,123,305,89,310,106,284),(73,332,124,304,90,309,107,283),(74,331,125,303,91,308,108,282),(75,330,126,302,92,307,109,281),(76,329,127,301,93,323,110,280),(77,328,128,300,94,322,111,279),(78,327,129,299,95,321,112,278),(79,326,130,298,96,320,113,277),(80,325,131,297,97,319,114,276),(81,324,132,296,98,318,115,275),(82,340,133,295,99,317,116,274),(83,339,134,294,100,316,117,273),(84,338,135,293,101,315,118,289),(85,337,136,292,102,314,119,288),(137,404,188,360,154,382,171,345),(138,403,189,359,155,381,172,344),(139,402,190,358,156,380,173,343),(140,401,191,374,157,379,174,342),(141,400,192,373,158,378,175,341),(142,399,193,372,159,377,176,357),(143,398,194,371,160,376,177,356),(144,397,195,370,161,375,178,355),(145,396,196,369,162,391,179,354),(146,395,197,368,163,390,180,353),(147,394,198,367,164,389,181,352),(148,393,199,366,165,388,182,351),(149,392,200,365,166,387,183,350),(150,408,201,364,167,386,184,349),(151,407,202,363,168,385,185,348),(152,406,203,362,169,384,186,347),(153,405,204,361,170,383,187,346)]])
120 conjugacy classes
| class | 1 | 2 | 3A | 3B | 4A | 4B | 6A | 6B | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 17A | ··· | 17H | 24A | ··· | 24H | 34A | ··· | 34H | 51A | ··· | 51P | 68A | ··· | 68P | 102A | ··· | 102P | 204A | ··· | 204AF |
| order | 1 | 2 | 3 | 3 | 4 | 4 | 6 | 6 | 8 | 8 | 8 | 8 | 12 | 12 | 12 | 12 | 17 | ··· | 17 | 24 | ··· | 24 | 34 | ··· | 34 | 51 | ··· | 51 | 68 | ··· | 68 | 102 | ··· | 102 | 204 | ··· | 204 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 17 | 17 | 17 | 17 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 17 | ··· | 17 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
120 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||||||
| image | C1 | C2 | C3 | C4 | C6 | C8 | C12 | C24 | D17 | Dic17 | C3×D17 | C17⋊3C8 | C3×Dic17 | C3×C17⋊3C8 |
| kernel | C3×C17⋊3C8 | C204 | C17⋊3C8 | C102 | C68 | C51 | C34 | C17 | C12 | C6 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 8 | 8 | 8 | 16 | 16 | 16 | 32 |
Matrix representation of C3×C17⋊3C8 ►in GL3(𝔽409) generated by
| 1 | 0 | 0 |
| 0 | 355 | 0 |
| 0 | 0 | 355 |
| 1 | 0 | 0 |
| 0 | 180 | 408 |
| 0 | 1 | 0 |
| 31 | 0 | 0 |
| 0 | 119 | 177 |
| 0 | 329 | 290 |
G:=sub<GL(3,GF(409))| [1,0,0,0,355,0,0,0,355],[1,0,0,0,180,1,0,408,0],[31,0,0,0,119,329,0,177,290] >;
C3×C17⋊3C8 in GAP, Magma, Sage, TeX
C_3\times C_{17}\rtimes_3C_8 % in TeX
G:=Group("C3xC17:3C8"); // GroupNames label
G:=SmallGroup(408,2);
// by ID
G=gap.SmallGroup(408,2);
# by ID
G:=PCGroup([5,-2,-3,-2,-2,-17,30,42,9604]);
// 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^-1>;
// generators/relations
Export