direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C17×C3⋊C8, C3⋊C136, C51⋊7C8, 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
| C3 — C17×C3⋊C8 |
Generators and relations for C17×C3⋊C8
G = < a,b,c | a17=b3=c8=1, ab=ba, ac=ca, cbc-1=b-1 >
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 37 67)(2 38 68)(3 39 52)(4 40 53)(5 41 54)(6 42 55)(7 43 56)(8 44 57)(9 45 58)(10 46 59)(11 47 60)(12 48 61)(13 49 62)(14 50 63)(15 51 64)(16 35 65)(17 36 66)(18 199 118)(19 200 119)(20 201 103)(21 202 104)(22 203 105)(23 204 106)(24 188 107)(25 189 108)(26 190 109)(27 191 110)(28 192 111)(29 193 112)(30 194 113)(31 195 114)(32 196 115)(33 197 116)(34 198 117)(69 328 362)(70 329 363)(71 330 364)(72 331 365)(73 332 366)(74 333 367)(75 334 368)(76 335 369)(77 336 370)(78 337 371)(79 338 372)(80 339 373)(81 340 374)(82 324 358)(83 325 359)(84 326 360)(85 327 361)(86 131 379)(87 132 380)(88 133 381)(89 134 382)(90 135 383)(91 136 384)(92 120 385)(93 121 386)(94 122 387)(95 123 388)(96 124 389)(97 125 390)(98 126 391)(99 127 375)(100 128 376)(101 129 377)(102 130 378)(137 292 401)(138 293 402)(139 294 403)(140 295 404)(141 296 405)(142 297 406)(143 298 407)(144 299 408)(145 300 392)(146 301 393)(147 302 394)(148 303 395)(149 304 396)(150 305 397)(151 306 398)(152 290 399)(153 291 400)(154 257 310)(155 258 311)(156 259 312)(157 260 313)(158 261 314)(159 262 315)(160 263 316)(161 264 317)(162 265 318)(163 266 319)(164 267 320)(165 268 321)(166 269 322)(167 270 323)(168 271 307)(169 272 308)(170 256 309)(171 351 228)(172 352 229)(173 353 230)(174 354 231)(175 355 232)(176 356 233)(177 357 234)(178 341 235)(179 342 236)(180 343 237)(181 344 238)(182 345 222)(183 346 223)(184 347 224)(185 348 225)(186 349 226)(187 350 227)(205 275 251)(206 276 252)(207 277 253)(208 278 254)(209 279 255)(210 280 239)(211 281 240)(212 282 241)(213 283 242)(214 284 243)(215 285 244)(216 286 245)(217 287 246)(218 288 247)(219 289 248)(220 273 249)(221 274 250)
(1 294 289 78 353 380 272 201)(2 295 273 79 354 381 256 202)(3 296 274 80 355 382 257 203)(4 297 275 81 356 383 258 204)(5 298 276 82 357 384 259 188)(6 299 277 83 341 385 260 189)(7 300 278 84 342 386 261 190)(8 301 279 85 343 387 262 191)(9 302 280 69 344 388 263 192)(10 303 281 70 345 389 264 193)(11 304 282 71 346 390 265 194)(12 305 283 72 347 391 266 195)(13 306 284 73 348 375 267 196)(14 290 285 74 349 376 268 197)(15 291 286 75 350 377 269 198)(16 292 287 76 351 378 270 199)(17 293 288 77 352 379 271 200)(18 35 137 246 369 228 130 323)(19 36 138 247 370 229 131 307)(20 37 139 248 371 230 132 308)(21 38 140 249 372 231 133 309)(22 39 141 250 373 232 134 310)(23 40 142 251 374 233 135 311)(24 41 143 252 358 234 136 312)(25 42 144 253 359 235 120 313)(26 43 145 254 360 236 121 314)(27 44 146 255 361 237 122 315)(28 45 147 239 362 238 123 316)(29 46 148 240 363 222 124 317)(30 47 149 241 364 223 125 318)(31 48 150 242 365 224 126 319)(32 49 151 243 366 225 127 320)(33 50 152 244 367 226 128 321)(34 51 153 245 368 227 129 322)(52 405 221 339 175 89 154 105)(53 406 205 340 176 90 155 106)(54 407 206 324 177 91 156 107)(55 408 207 325 178 92 157 108)(56 392 208 326 179 93 158 109)(57 393 209 327 180 94 159 110)(58 394 210 328 181 95 160 111)(59 395 211 329 182 96 161 112)(60 396 212 330 183 97 162 113)(61 397 213 331 184 98 163 114)(62 398 214 332 185 99 164 115)(63 399 215 333 186 100 165 116)(64 400 216 334 187 101 166 117)(65 401 217 335 171 102 167 118)(66 402 218 336 172 86 168 119)(67 403 219 337 173 87 169 103)(68 404 220 338 174 88 170 104)
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), (1,37,67)(2,38,68)(3,39,52)(4,40,53)(5,41,54)(6,42,55)(7,43,56)(8,44,57)(9,45,58)(10,46,59)(11,47,60)(12,48,61)(13,49,62)(14,50,63)(15,51,64)(16,35,65)(17,36,66)(18,199,118)(19,200,119)(20,201,103)(21,202,104)(22,203,105)(23,204,106)(24,188,107)(25,189,108)(26,190,109)(27,191,110)(28,192,111)(29,193,112)(30,194,113)(31,195,114)(32,196,115)(33,197,116)(34,198,117)(69,328,362)(70,329,363)(71,330,364)(72,331,365)(73,332,366)(74,333,367)(75,334,368)(76,335,369)(77,336,370)(78,337,371)(79,338,372)(80,339,373)(81,340,374)(82,324,358)(83,325,359)(84,326,360)(85,327,361)(86,131,379)(87,132,380)(88,133,381)(89,134,382)(90,135,383)(91,136,384)(92,120,385)(93,121,386)(94,122,387)(95,123,388)(96,124,389)(97,125,390)(98,126,391)(99,127,375)(100,128,376)(101,129,377)(102,130,378)(137,292,401)(138,293,402)(139,294,403)(140,295,404)(141,296,405)(142,297,406)(143,298,407)(144,299,408)(145,300,392)(146,301,393)(147,302,394)(148,303,395)(149,304,396)(150,305,397)(151,306,398)(152,290,399)(153,291,400)(154,257,310)(155,258,311)(156,259,312)(157,260,313)(158,261,314)(159,262,315)(160,263,316)(161,264,317)(162,265,318)(163,266,319)(164,267,320)(165,268,321)(166,269,322)(167,270,323)(168,271,307)(169,272,308)(170,256,309)(171,351,228)(172,352,229)(173,353,230)(174,354,231)(175,355,232)(176,356,233)(177,357,234)(178,341,235)(179,342,236)(180,343,237)(181,344,238)(182,345,222)(183,346,223)(184,347,224)(185,348,225)(186,349,226)(187,350,227)(205,275,251)(206,276,252)(207,277,253)(208,278,254)(209,279,255)(210,280,239)(211,281,240)(212,282,241)(213,283,242)(214,284,243)(215,285,244)(216,286,245)(217,287,246)(218,288,247)(219,289,248)(220,273,249)(221,274,250), (1,294,289,78,353,380,272,201)(2,295,273,79,354,381,256,202)(3,296,274,80,355,382,257,203)(4,297,275,81,356,383,258,204)(5,298,276,82,357,384,259,188)(6,299,277,83,341,385,260,189)(7,300,278,84,342,386,261,190)(8,301,279,85,343,387,262,191)(9,302,280,69,344,388,263,192)(10,303,281,70,345,389,264,193)(11,304,282,71,346,390,265,194)(12,305,283,72,347,391,266,195)(13,306,284,73,348,375,267,196)(14,290,285,74,349,376,268,197)(15,291,286,75,350,377,269,198)(16,292,287,76,351,378,270,199)(17,293,288,77,352,379,271,200)(18,35,137,246,369,228,130,323)(19,36,138,247,370,229,131,307)(20,37,139,248,371,230,132,308)(21,38,140,249,372,231,133,309)(22,39,141,250,373,232,134,310)(23,40,142,251,374,233,135,311)(24,41,143,252,358,234,136,312)(25,42,144,253,359,235,120,313)(26,43,145,254,360,236,121,314)(27,44,146,255,361,237,122,315)(28,45,147,239,362,238,123,316)(29,46,148,240,363,222,124,317)(30,47,149,241,364,223,125,318)(31,48,150,242,365,224,126,319)(32,49,151,243,366,225,127,320)(33,50,152,244,367,226,128,321)(34,51,153,245,368,227,129,322)(52,405,221,339,175,89,154,105)(53,406,205,340,176,90,155,106)(54,407,206,324,177,91,156,107)(55,408,207,325,178,92,157,108)(56,392,208,326,179,93,158,109)(57,393,209,327,180,94,159,110)(58,394,210,328,181,95,160,111)(59,395,211,329,182,96,161,112)(60,396,212,330,183,97,162,113)(61,397,213,331,184,98,163,114)(62,398,214,332,185,99,164,115)(63,399,215,333,186,100,165,116)(64,400,216,334,187,101,166,117)(65,401,217,335,171,102,167,118)(66,402,218,336,172,86,168,119)(67,403,219,337,173,87,169,103)(68,404,220,338,174,88,170,104)>;
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), (1,37,67)(2,38,68)(3,39,52)(4,40,53)(5,41,54)(6,42,55)(7,43,56)(8,44,57)(9,45,58)(10,46,59)(11,47,60)(12,48,61)(13,49,62)(14,50,63)(15,51,64)(16,35,65)(17,36,66)(18,199,118)(19,200,119)(20,201,103)(21,202,104)(22,203,105)(23,204,106)(24,188,107)(25,189,108)(26,190,109)(27,191,110)(28,192,111)(29,193,112)(30,194,113)(31,195,114)(32,196,115)(33,197,116)(34,198,117)(69,328,362)(70,329,363)(71,330,364)(72,331,365)(73,332,366)(74,333,367)(75,334,368)(76,335,369)(77,336,370)(78,337,371)(79,338,372)(80,339,373)(81,340,374)(82,324,358)(83,325,359)(84,326,360)(85,327,361)(86,131,379)(87,132,380)(88,133,381)(89,134,382)(90,135,383)(91,136,384)(92,120,385)(93,121,386)(94,122,387)(95,123,388)(96,124,389)(97,125,390)(98,126,391)(99,127,375)(100,128,376)(101,129,377)(102,130,378)(137,292,401)(138,293,402)(139,294,403)(140,295,404)(141,296,405)(142,297,406)(143,298,407)(144,299,408)(145,300,392)(146,301,393)(147,302,394)(148,303,395)(149,304,396)(150,305,397)(151,306,398)(152,290,399)(153,291,400)(154,257,310)(155,258,311)(156,259,312)(157,260,313)(158,261,314)(159,262,315)(160,263,316)(161,264,317)(162,265,318)(163,266,319)(164,267,320)(165,268,321)(166,269,322)(167,270,323)(168,271,307)(169,272,308)(170,256,309)(171,351,228)(172,352,229)(173,353,230)(174,354,231)(175,355,232)(176,356,233)(177,357,234)(178,341,235)(179,342,236)(180,343,237)(181,344,238)(182,345,222)(183,346,223)(184,347,224)(185,348,225)(186,349,226)(187,350,227)(205,275,251)(206,276,252)(207,277,253)(208,278,254)(209,279,255)(210,280,239)(211,281,240)(212,282,241)(213,283,242)(214,284,243)(215,285,244)(216,286,245)(217,287,246)(218,288,247)(219,289,248)(220,273,249)(221,274,250), (1,294,289,78,353,380,272,201)(2,295,273,79,354,381,256,202)(3,296,274,80,355,382,257,203)(4,297,275,81,356,383,258,204)(5,298,276,82,357,384,259,188)(6,299,277,83,341,385,260,189)(7,300,278,84,342,386,261,190)(8,301,279,85,343,387,262,191)(9,302,280,69,344,388,263,192)(10,303,281,70,345,389,264,193)(11,304,282,71,346,390,265,194)(12,305,283,72,347,391,266,195)(13,306,284,73,348,375,267,196)(14,290,285,74,349,376,268,197)(15,291,286,75,350,377,269,198)(16,292,287,76,351,378,270,199)(17,293,288,77,352,379,271,200)(18,35,137,246,369,228,130,323)(19,36,138,247,370,229,131,307)(20,37,139,248,371,230,132,308)(21,38,140,249,372,231,133,309)(22,39,141,250,373,232,134,310)(23,40,142,251,374,233,135,311)(24,41,143,252,358,234,136,312)(25,42,144,253,359,235,120,313)(26,43,145,254,360,236,121,314)(27,44,146,255,361,237,122,315)(28,45,147,239,362,238,123,316)(29,46,148,240,363,222,124,317)(30,47,149,241,364,223,125,318)(31,48,150,242,365,224,126,319)(32,49,151,243,366,225,127,320)(33,50,152,244,367,226,128,321)(34,51,153,245,368,227,129,322)(52,405,221,339,175,89,154,105)(53,406,205,340,176,90,155,106)(54,407,206,324,177,91,156,107)(55,408,207,325,178,92,157,108)(56,392,208,326,179,93,158,109)(57,393,209,327,180,94,159,110)(58,394,210,328,181,95,160,111)(59,395,211,329,182,96,161,112)(60,396,212,330,183,97,162,113)(61,397,213,331,184,98,163,114)(62,398,214,332,185,99,164,115)(63,399,215,333,186,100,165,116)(64,400,216,334,187,101,166,117)(65,401,217,335,171,102,167,118)(66,402,218,336,172,86,168,119)(67,403,219,337,173,87,169,103)(68,404,220,338,174,88,170,104) );
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)], [(1,37,67),(2,38,68),(3,39,52),(4,40,53),(5,41,54),(6,42,55),(7,43,56),(8,44,57),(9,45,58),(10,46,59),(11,47,60),(12,48,61),(13,49,62),(14,50,63),(15,51,64),(16,35,65),(17,36,66),(18,199,118),(19,200,119),(20,201,103),(21,202,104),(22,203,105),(23,204,106),(24,188,107),(25,189,108),(26,190,109),(27,191,110),(28,192,111),(29,193,112),(30,194,113),(31,195,114),(32,196,115),(33,197,116),(34,198,117),(69,328,362),(70,329,363),(71,330,364),(72,331,365),(73,332,366),(74,333,367),(75,334,368),(76,335,369),(77,336,370),(78,337,371),(79,338,372),(80,339,373),(81,340,374),(82,324,358),(83,325,359),(84,326,360),(85,327,361),(86,131,379),(87,132,380),(88,133,381),(89,134,382),(90,135,383),(91,136,384),(92,120,385),(93,121,386),(94,122,387),(95,123,388),(96,124,389),(97,125,390),(98,126,391),(99,127,375),(100,128,376),(101,129,377),(102,130,378),(137,292,401),(138,293,402),(139,294,403),(140,295,404),(141,296,405),(142,297,406),(143,298,407),(144,299,408),(145,300,392),(146,301,393),(147,302,394),(148,303,395),(149,304,396),(150,305,397),(151,306,398),(152,290,399),(153,291,400),(154,257,310),(155,258,311),(156,259,312),(157,260,313),(158,261,314),(159,262,315),(160,263,316),(161,264,317),(162,265,318),(163,266,319),(164,267,320),(165,268,321),(166,269,322),(167,270,323),(168,271,307),(169,272,308),(170,256,309),(171,351,228),(172,352,229),(173,353,230),(174,354,231),(175,355,232),(176,356,233),(177,357,234),(178,341,235),(179,342,236),(180,343,237),(181,344,238),(182,345,222),(183,346,223),(184,347,224),(185,348,225),(186,349,226),(187,350,227),(205,275,251),(206,276,252),(207,277,253),(208,278,254),(209,279,255),(210,280,239),(211,281,240),(212,282,241),(213,283,242),(214,284,243),(215,285,244),(216,286,245),(217,287,246),(218,288,247),(219,289,248),(220,273,249),(221,274,250)], [(1,294,289,78,353,380,272,201),(2,295,273,79,354,381,256,202),(3,296,274,80,355,382,257,203),(4,297,275,81,356,383,258,204),(5,298,276,82,357,384,259,188),(6,299,277,83,341,385,260,189),(7,300,278,84,342,386,261,190),(8,301,279,85,343,387,262,191),(9,302,280,69,344,388,263,192),(10,303,281,70,345,389,264,193),(11,304,282,71,346,390,265,194),(12,305,283,72,347,391,266,195),(13,306,284,73,348,375,267,196),(14,290,285,74,349,376,268,197),(15,291,286,75,350,377,269,198),(16,292,287,76,351,378,270,199),(17,293,288,77,352,379,271,200),(18,35,137,246,369,228,130,323),(19,36,138,247,370,229,131,307),(20,37,139,248,371,230,132,308),(21,38,140,249,372,231,133,309),(22,39,141,250,373,232,134,310),(23,40,142,251,374,233,135,311),(24,41,143,252,358,234,136,312),(25,42,144,253,359,235,120,313),(26,43,145,254,360,236,121,314),(27,44,146,255,361,237,122,315),(28,45,147,239,362,238,123,316),(29,46,148,240,363,222,124,317),(30,47,149,241,364,223,125,318),(31,48,150,242,365,224,126,319),(32,49,151,243,366,225,127,320),(33,50,152,244,367,226,128,321),(34,51,153,245,368,227,129,322),(52,405,221,339,175,89,154,105),(53,406,205,340,176,90,155,106),(54,407,206,324,177,91,156,107),(55,408,207,325,178,92,157,108),(56,392,208,326,179,93,158,109),(57,393,209,327,180,94,159,110),(58,394,210,328,181,95,160,111),(59,395,211,329,182,96,161,112),(60,396,212,330,183,97,162,113),(61,397,213,331,184,98,163,114),(62,398,214,332,185,99,164,115),(63,399,215,333,186,100,165,116),(64,400,216,334,187,101,166,117),(65,401,217,335,171,102,167,118),(66,402,218,336,172,86,168,119),(67,403,219,337,173,87,169,103),(68,404,220,338,174,88,170,104)]])
204 conjugacy classes
| class | 1 | 2 | 3 | 4A | 4B | 6 | 8A | 8B | 8C | 8D | 12A | 12B | 17A | ··· | 17P | 34A | ··· | 34P | 51A | ··· | 51P | 68A | ··· | 68AF | 102A | ··· | 102P | 136A | ··· | 136BL | 204A | ··· | 204AF |
| order | 1 | 2 | 3 | 4 | 4 | 6 | 8 | 8 | 8 | 8 | 12 | 12 | 17 | ··· | 17 | 34 | ··· | 34 | 51 | ··· | 51 | 68 | ··· | 68 | 102 | ··· | 102 | 136 | ··· | 136 | 204 | ··· | 204 |
| size | 1 | 1 | 2 | 1 | 1 | 2 | 3 | 3 | 3 | 3 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 3 | ··· | 3 | 2 | ··· | 2 |
204 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||||||
| image | C1 | C2 | C4 | C8 | C17 | C34 | C68 | C136 | S3 | Dic3 | C3⋊C8 | S3×C17 | Dic3×C17 | C17×C3⋊C8 |
| kernel | C17×C3⋊C8 | C204 | C102 | C51 | C3⋊C8 | C12 | C6 | C3 | C68 | C34 | C17 | C4 | C2 | C1 |
| # reps | 1 | 1 | 2 | 4 | 16 | 16 | 32 | 64 | 1 | 1 | 2 | 16 | 16 | 32 |
Matrix representation of C17×C3⋊C8 ►in GL2(𝔽409) generated by
| 83 | 0 |
| 0 | 83 |
| 0 | 408 |
| 1 | 408 |
| 245 | 17 |
| 262 | 164 |
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