Copied to
clipboard

G = C17×C3⋊C8order 408 = 23·3·17

Direct product of C17 and C3⋊C8

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

Aliases: C17×C3⋊C8, C3⋊C136, C517C8, C6.C68, C68.4S3, C12.2C34, C204.6C2, C102.5C4, C34.3Dic3, C4.2(S3×C17), C2.(Dic3×C17), SmallGroup(408,1)

Series: Derived Chief Lower central Upper central

C1C3 — C17×C3⋊C8
C1C3C6C12C204 — C17×C3⋊C8
C3 — C17×C3⋊C8
C1C68

Generators and relations for C17×C3⋊C8
 G = < a,b,c | a17=b3=c8=1, ab=ba, ac=ca, cbc-1=b-1 >

3C8
3C136

Smallest permutation representation of C17×C3⋊C8
Regular action on 408 points
Generators in S408
(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)
(1 276 335)(2 277 336)(3 278 337)(4 279 338)(5 280 339)(6 281 340)(7 282 324)(8 283 325)(9 284 326)(10 285 327)(11 286 328)(12 287 329)(13 288 330)(14 289 331)(15 273 332)(16 274 333)(17 275 334)(18 36 197)(19 37 198)(20 38 199)(21 39 200)(22 40 201)(23 41 202)(24 42 203)(25 43 204)(26 44 188)(27 45 189)(28 46 190)(29 47 191)(30 48 192)(31 49 193)(32 50 194)(33 51 195)(34 35 196)(52 304 183)(53 305 184)(54 306 185)(55 290 186)(56 291 187)(57 292 171)(58 293 172)(59 294 173)(60 295 174)(61 296 175)(62 297 176)(63 298 177)(64 299 178)(65 300 179)(66 301 180)(67 302 181)(68 303 182)(69 109 265)(70 110 266)(71 111 267)(72 112 268)(73 113 269)(74 114 270)(75 115 271)(76 116 272)(77 117 256)(78 118 257)(79 119 258)(80 103 259)(81 104 260)(82 105 261)(83 106 262)(84 107 263)(85 108 264)(86 376 358)(87 377 359)(88 378 360)(89 379 361)(90 380 362)(91 381 363)(92 382 364)(93 383 365)(94 384 366)(95 385 367)(96 386 368)(97 387 369)(98 388 370)(99 389 371)(100 390 372)(101 391 373)(102 375 374)(120 307 255)(121 308 239)(122 309 240)(123 310 241)(124 311 242)(125 312 243)(126 313 244)(127 314 245)(128 315 246)(129 316 247)(130 317 248)(131 318 249)(132 319 250)(133 320 251)(134 321 252)(135 322 253)(136 323 254)(137 236 344)(138 237 345)(139 238 346)(140 222 347)(141 223 348)(142 224 349)(143 225 350)(144 226 351)(145 227 352)(146 228 353)(147 229 354)(148 230 355)(149 231 356)(150 232 357)(151 233 341)(152 234 342)(153 235 343)(154 406 220)(155 407 221)(156 408 205)(157 392 206)(158 393 207)(159 394 208)(160 395 209)(161 396 210)(162 397 211)(163 398 212)(164 399 213)(165 400 214)(166 401 215)(167 402 216)(168 403 217)(169 404 218)(170 405 219)
(1 81 390 189 121 177 228 211)(2 82 391 190 122 178 229 212)(3 83 375 191 123 179 230 213)(4 84 376 192 124 180 231 214)(5 85 377 193 125 181 232 215)(6 69 378 194 126 182 233 216)(7 70 379 195 127 183 234 217)(8 71 380 196 128 184 235 218)(9 72 381 197 129 185 236 219)(10 73 382 198 130 186 237 220)(11 74 383 199 131 187 238 221)(12 75 384 200 132 171 222 205)(13 76 385 201 133 172 223 206)(14 77 386 202 134 173 224 207)(15 78 387 203 135 174 225 208)(16 79 388 204 136 175 226 209)(17 80 389 188 120 176 227 210)(18 247 54 137 170 326 112 91)(19 248 55 138 154 327 113 92)(20 249 56 139 155 328 114 93)(21 250 57 140 156 329 115 94)(22 251 58 141 157 330 116 95)(23 252 59 142 158 331 117 96)(24 253 60 143 159 332 118 97)(25 254 61 144 160 333 119 98)(26 255 62 145 161 334 103 99)(27 239 63 146 162 335 104 100)(28 240 64 147 163 336 105 101)(29 241 65 148 164 337 106 102)(30 242 66 149 165 338 107 86)(31 243 67 150 166 339 108 87)(32 244 68 151 167 340 109 88)(33 245 52 152 168 324 110 89)(34 246 53 153 169 325 111 90)(35 315 305 343 404 283 267 362)(36 316 306 344 405 284 268 363)(37 317 290 345 406 285 269 364)(38 318 291 346 407 286 270 365)(39 319 292 347 408 287 271 366)(40 320 293 348 392 288 272 367)(41 321 294 349 393 289 256 368)(42 322 295 350 394 273 257 369)(43 323 296 351 395 274 258 370)(44 307 297 352 396 275 259 371)(45 308 298 353 397 276 260 372)(46 309 299 354 398 277 261 373)(47 310 300 355 399 278 262 374)(48 311 301 356 400 279 263 358)(49 312 302 357 401 280 264 359)(50 313 303 341 402 281 265 360)(51 314 304 342 403 282 266 361)

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

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

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

204 conjugacy classes

class 1  2  3 4A4B 6 8A8B8C8D12A12B17A···17P34A···34P51A···51P68A···68AF102A···102P136A···136BL204A···204AF
order1234468888121217···1734···3451···5168···68102···102136···136204···204
size1121123333221···11···12···21···12···23···32···2

204 irreducible representations

dim11111111222222
type+++-
imageC1C2C4C8C17C34C68C136S3Dic3C3⋊C8S3×C17Dic3×C17C17×C3⋊C8
kernelC17×C3⋊C8C204C102C51C3⋊C8C12C6C3C68C34C17C4C2C1
# reps112416163264112161632

Matrix representation of C17×C3⋊C8 in GL2(𝔽409) generated by

830
083
,
0408
1408
,
24517
262164
G:=sub<GL(2,GF(409))| [83,0,0,83],[0,1,408,408],[245,262,17,164] >;

C17×C3⋊C8 in GAP, Magma, Sage, TeX

C_{17}\times C_3\rtimes C_8
% in TeX

G:=Group("C17xC3:C8");
// GroupNames label

G:=SmallGroup(408,1);
// by ID

G=gap.SmallGroup(408,1);
# by ID

G:=PCGroup([5,-2,-17,-2,-2,-3,170,42,6804]);
// Polycyclic

G:=Group<a,b,c|a^17=b^3=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C17×C3⋊C8 in TeX

׿
×
𝔽