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G = C3×C173C8order 408 = 23·3·17

Direct product of C3 and C173C8

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

Aliases: C3×C173C8, C516C8, C173C24, 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

C1C17 — C3×C173C8
C1C17C34C68C204 — C3×C173C8
C17 — C3×C173C8
C1C12

Generators and relations for C3×C173C8
 G = < a,b,c | a3=b17=c8=1, ab=ba, ac=ca, cbc-1=b-1 >

17C8
17C24

Smallest permutation representation of C3×C173C8
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)(205 343 280)(206 344 281)(207 345 282)(208 346 283)(209 347 284)(210 348 285)(211 349 286)(212 350 287)(213 351 288)(214 352 289)(215 353 273)(216 354 274)(217 355 275)(218 356 276)(219 357 277)(220 341 278)(221 342 279)(222 365 298)(223 366 299)(224 367 300)(225 368 301)(226 369 302)(227 370 303)(228 371 304)(229 372 305)(230 373 306)(231 374 290)(232 358 291)(233 359 292)(234 360 293)(235 361 294)(236 362 295)(237 363 296)(238 364 297)(239 379 319)(240 380 320)(241 381 321)(242 382 322)(243 383 323)(244 384 307)(245 385 308)(246 386 309)(247 387 310)(248 388 311)(249 389 312)(250 390 313)(251 391 314)(252 375 315)(253 376 316)(254 377 317)(255 378 318)(256 395 330)(257 396 331)(258 397 332)(259 398 333)(260 399 334)(261 400 335)(262 401 336)(263 402 337)(264 403 338)(265 404 339)(266 405 340)(267 406 324)(268 407 325)(269 408 326)(270 392 327)(271 393 328)(272 394 329)
(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)
(1 263 52 234 18 246 35 214)(2 262 53 233 19 245 36 213)(3 261 54 232 20 244 37 212)(4 260 55 231 21 243 38 211)(5 259 56 230 22 242 39 210)(6 258 57 229 23 241 40 209)(7 257 58 228 24 240 41 208)(8 256 59 227 25 239 42 207)(9 272 60 226 26 255 43 206)(10 271 61 225 27 254 44 205)(11 270 62 224 28 253 45 221)(12 269 63 223 29 252 46 220)(13 268 64 222 30 251 47 219)(14 267 65 238 31 250 48 218)(15 266 66 237 32 249 49 217)(16 265 67 236 33 248 50 216)(17 264 68 235 34 247 51 215)(69 337 120 293 86 309 103 289)(70 336 121 292 87 308 104 288)(71 335 122 291 88 307 105 287)(72 334 123 290 89 323 106 286)(73 333 124 306 90 322 107 285)(74 332 125 305 91 321 108 284)(75 331 126 304 92 320 109 283)(76 330 127 303 93 319 110 282)(77 329 128 302 94 318 111 281)(78 328 129 301 95 317 112 280)(79 327 130 300 96 316 113 279)(80 326 131 299 97 315 114 278)(81 325 132 298 98 314 115 277)(82 324 133 297 99 313 116 276)(83 340 134 296 100 312 117 275)(84 339 135 295 101 311 118 274)(85 338 136 294 102 310 119 273)(137 402 188 360 154 386 171 352)(138 401 189 359 155 385 172 351)(139 400 190 358 156 384 173 350)(140 399 191 374 157 383 174 349)(141 398 192 373 158 382 175 348)(142 397 193 372 159 381 176 347)(143 396 194 371 160 380 177 346)(144 395 195 370 161 379 178 345)(145 394 196 369 162 378 179 344)(146 393 197 368 163 377 180 343)(147 392 198 367 164 376 181 342)(148 408 199 366 165 375 182 341)(149 407 200 365 166 391 183 357)(150 406 201 364 167 390 184 356)(151 405 202 363 168 389 185 355)(152 404 203 362 169 388 186 354)(153 403 204 361 170 387 187 353)

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

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

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

120 conjugacy classes

class 1  2 3A3B4A4B6A6B8A8B8C8D12A12B12C12D17A···17H24A···24H34A···34H51A···51P68A···68P102A···102P204A···204AF
order1233446688881212121217···1724···2434···3451···5168···68102···102204···204
size111111111717171711112···217···172···22···22···22···22···2

120 irreducible representations

dim11111111222222
type+++-
imageC1C2C3C4C6C8C12C24D17Dic17C3×D17C173C8C3×Dic17C3×C173C8
kernelC3×C173C8C204C173C8C102C68C51C34C17C12C6C4C3C2C1
# reps112224488816161632

Matrix representation of C3×C173C8 in GL3(𝔽409) generated by

100
03550
00355
,
100
0180408
010
,
3100
0119177
0329290
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×C173C8 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

Subgroup lattice of C3×C173C8 in TeX

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