direct product, metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: C17×Dic6, C51⋊4Q8, C68.3S3, C12.1C34, C204.5C2, C34.13D6, Dic3.C34, C102.18C22, C3⋊(Q8×C17), C4.(S3×C17), C2.3(S3×C34), C6.1(C2×C34), (Dic3×C17).2C2, SmallGroup(408,20)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C17×Dic6
G = < a,b,c | a17=b12=1, c2=b6, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C17×Dic6
►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)
(1 131 47 345 73 307 186 276 332 195 378 21)(2 132 48 346 74 308 187 277 333 196 379 22)(3 133 49 347 75 309 171 278 334 197 380 23)(4 134 50 348 76 310 172 279 335 198 381 24)(5 135 51 349 77 311 173 280 336 199 382 25)(6 136 35 350 78 312 174 281 337 200 383 26)(7 120 36 351 79 313 175 282 338 201 384 27)(8 121 37 352 80 314 176 283 339 202 385 28)(9 122 38 353 81 315 177 284 340 203 386 29)(10 123 39 354 82 316 178 285 324 204 387 30)(11 124 40 355 83 317 179 286 325 188 388 31)(12 125 41 356 84 318 180 287 326 189 389 32)(13 126 42 357 85 319 181 288 327 190 390 33)(14 127 43 341 69 320 182 289 328 191 391 34)(15 128 44 342 70 321 183 273 329 192 375 18)(16 129 45 343 71 322 184 274 330 193 376 19)(17 130 46 344 72 323 185 275 331 194 377 20)(52 299 256 91 358 160 228 406 111 143 242 215)(53 300 257 92 359 161 229 407 112 144 243 216)(54 301 258 93 360 162 230 408 113 145 244 217)(55 302 259 94 361 163 231 392 114 146 245 218)(56 303 260 95 362 164 232 393 115 147 246 219)(57 304 261 96 363 165 233 394 116 148 247 220)(58 305 262 97 364 166 234 395 117 149 248 221)(59 306 263 98 365 167 235 396 118 150 249 205)(60 290 264 99 366 168 236 397 119 151 250 206)(61 291 265 100 367 169 237 398 103 152 251 207)(62 292 266 101 368 170 238 399 104 153 252 208)(63 293 267 102 369 154 222 400 105 137 253 209)(64 294 268 86 370 155 223 401 106 138 254 210)(65 295 269 87 371 156 224 402 107 139 255 211)(66 296 270 88 372 157 225 403 108 140 239 212)(67 297 271 89 373 158 226 404 109 141 240 213)(68 298 272 90 374 159 227 405 110 142 241 214)
(1 156 186 211)(2 157 187 212)(3 158 171 213)(4 159 172 214)(5 160 173 215)(6 161 174 216)(7 162 175 217)(8 163 176 218)(9 164 177 219)(10 165 178 220)(11 166 179 221)(12 167 180 205)(13 168 181 206)(14 169 182 207)(15 170 183 208)(16 154 184 209)(17 155 185 210)(18 238 321 62)(19 222 322 63)(20 223 323 64)(21 224 307 65)(22 225 308 66)(23 226 309 67)(24 227 310 68)(25 228 311 52)(26 229 312 53)(27 230 313 54)(28 231 314 55)(29 232 315 56)(30 233 316 57)(31 234 317 58)(32 235 318 59)(33 236 319 60)(34 237 320 61)(35 92 337 144)(36 93 338 145)(37 94 339 146)(38 95 340 147)(39 96 324 148)(40 97 325 149)(41 98 326 150)(42 99 327 151)(43 100 328 152)(44 101 329 153)(45 102 330 137)(46 86 331 138)(47 87 332 139)(48 88 333 140)(49 89 334 141)(50 90 335 142)(51 91 336 143)(69 291 391 398)(70 292 375 399)(71 293 376 400)(72 294 377 401)(73 295 378 402)(74 296 379 403)(75 297 380 404)(76 298 381 405)(77 299 382 406)(78 300 383 407)(79 301 384 408)(80 302 385 392)(81 303 386 393)(82 304 387 394)(83 305 388 395)(84 306 389 396)(85 290 390 397)(103 341 265 191)(104 342 266 192)(105 343 267 193)(106 344 268 194)(107 345 269 195)(108 346 270 196)(109 347 271 197)(110 348 272 198)(111 349 256 199)(112 350 257 200)(113 351 258 201)(114 352 259 202)(115 353 260 203)(116 354 261 204)(117 355 262 188)(118 356 263 189)(119 357 264 190)(120 360 282 244)(121 361 283 245)(122 362 284 246)(123 363 285 247)(124 364 286 248)(125 365 287 249)(126 366 288 250)(127 367 289 251)(128 368 273 252)(129 369 274 253)(130 370 275 254)(131 371 276 255)(132 372 277 239)(133 373 278 240)(134 374 279 241)(135 358 280 242)(136 359 281 243)
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), (1,131,47,345,73,307,186,276,332,195,378,21)(2,132,48,346,74,308,187,277,333,196,379,22)(3,133,49,347,75,309,171,278,334,197,380,23)(4,134,50,348,76,310,172,279,335,198,381,24)(5,135,51,349,77,311,173,280,336,199,382,25)(6,136,35,350,78,312,174,281,337,200,383,26)(7,120,36,351,79,313,175,282,338,201,384,27)(8,121,37,352,80,314,176,283,339,202,385,28)(9,122,38,353,81,315,177,284,340,203,386,29)(10,123,39,354,82,316,178,285,324,204,387,30)(11,124,40,355,83,317,179,286,325,188,388,31)(12,125,41,356,84,318,180,287,326,189,389,32)(13,126,42,357,85,319,181,288,327,190,390,33)(14,127,43,341,69,320,182,289,328,191,391,34)(15,128,44,342,70,321,183,273,329,192,375,18)(16,129,45,343,71,322,184,274,330,193,376,19)(17,130,46,344,72,323,185,275,331,194,377,20)(52,299,256,91,358,160,228,406,111,143,242,215)(53,300,257,92,359,161,229,407,112,144,243,216)(54,301,258,93,360,162,230,408,113,145,244,217)(55,302,259,94,361,163,231,392,114,146,245,218)(56,303,260,95,362,164,232,393,115,147,246,219)(57,304,261,96,363,165,233,394,116,148,247,220)(58,305,262,97,364,166,234,395,117,149,248,221)(59,306,263,98,365,167,235,396,118,150,249,205)(60,290,264,99,366,168,236,397,119,151,250,206)(61,291,265,100,367,169,237,398,103,152,251,207)(62,292,266,101,368,170,238,399,104,153,252,208)(63,293,267,102,369,154,222,400,105,137,253,209)(64,294,268,86,370,155,223,401,106,138,254,210)(65,295,269,87,371,156,224,402,107,139,255,211)(66,296,270,88,372,157,225,403,108,140,239,212)(67,297,271,89,373,158,226,404,109,141,240,213)(68,298,272,90,374,159,227,405,110,142,241,214), (1,156,186,211)(2,157,187,212)(3,158,171,213)(4,159,172,214)(5,160,173,215)(6,161,174,216)(7,162,175,217)(8,163,176,218)(9,164,177,219)(10,165,178,220)(11,166,179,221)(12,167,180,205)(13,168,181,206)(14,169,182,207)(15,170,183,208)(16,154,184,209)(17,155,185,210)(18,238,321,62)(19,222,322,63)(20,223,323,64)(21,224,307,65)(22,225,308,66)(23,226,309,67)(24,227,310,68)(25,228,311,52)(26,229,312,53)(27,230,313,54)(28,231,314,55)(29,232,315,56)(30,233,316,57)(31,234,317,58)(32,235,318,59)(33,236,319,60)(34,237,320,61)(35,92,337,144)(36,93,338,145)(37,94,339,146)(38,95,340,147)(39,96,324,148)(40,97,325,149)(41,98,326,150)(42,99,327,151)(43,100,328,152)(44,101,329,153)(45,102,330,137)(46,86,331,138)(47,87,332,139)(48,88,333,140)(49,89,334,141)(50,90,335,142)(51,91,336,143)(69,291,391,398)(70,292,375,399)(71,293,376,400)(72,294,377,401)(73,295,378,402)(74,296,379,403)(75,297,380,404)(76,298,381,405)(77,299,382,406)(78,300,383,407)(79,301,384,408)(80,302,385,392)(81,303,386,393)(82,304,387,394)(83,305,388,395)(84,306,389,396)(85,290,390,397)(103,341,265,191)(104,342,266,192)(105,343,267,193)(106,344,268,194)(107,345,269,195)(108,346,270,196)(109,347,271,197)(110,348,272,198)(111,349,256,199)(112,350,257,200)(113,351,258,201)(114,352,259,202)(115,353,260,203)(116,354,261,204)(117,355,262,188)(118,356,263,189)(119,357,264,190)(120,360,282,244)(121,361,283,245)(122,362,284,246)(123,363,285,247)(124,364,286,248)(125,365,287,249)(126,366,288,250)(127,367,289,251)(128,368,273,252)(129,369,274,253)(130,370,275,254)(131,371,276,255)(132,372,277,239)(133,373,278,240)(134,374,279,241)(135,358,280,242)(136,359,281,243)>;
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), (1,131,47,345,73,307,186,276,332,195,378,21)(2,132,48,346,74,308,187,277,333,196,379,22)(3,133,49,347,75,309,171,278,334,197,380,23)(4,134,50,348,76,310,172,279,335,198,381,24)(5,135,51,349,77,311,173,280,336,199,382,25)(6,136,35,350,78,312,174,281,337,200,383,26)(7,120,36,351,79,313,175,282,338,201,384,27)(8,121,37,352,80,314,176,283,339,202,385,28)(9,122,38,353,81,315,177,284,340,203,386,29)(10,123,39,354,82,316,178,285,324,204,387,30)(11,124,40,355,83,317,179,286,325,188,388,31)(12,125,41,356,84,318,180,287,326,189,389,32)(13,126,42,357,85,319,181,288,327,190,390,33)(14,127,43,341,69,320,182,289,328,191,391,34)(15,128,44,342,70,321,183,273,329,192,375,18)(16,129,45,343,71,322,184,274,330,193,376,19)(17,130,46,344,72,323,185,275,331,194,377,20)(52,299,256,91,358,160,228,406,111,143,242,215)(53,300,257,92,359,161,229,407,112,144,243,216)(54,301,258,93,360,162,230,408,113,145,244,217)(55,302,259,94,361,163,231,392,114,146,245,218)(56,303,260,95,362,164,232,393,115,147,246,219)(57,304,261,96,363,165,233,394,116,148,247,220)(58,305,262,97,364,166,234,395,117,149,248,221)(59,306,263,98,365,167,235,396,118,150,249,205)(60,290,264,99,366,168,236,397,119,151,250,206)(61,291,265,100,367,169,237,398,103,152,251,207)(62,292,266,101,368,170,238,399,104,153,252,208)(63,293,267,102,369,154,222,400,105,137,253,209)(64,294,268,86,370,155,223,401,106,138,254,210)(65,295,269,87,371,156,224,402,107,139,255,211)(66,296,270,88,372,157,225,403,108,140,239,212)(67,297,271,89,373,158,226,404,109,141,240,213)(68,298,272,90,374,159,227,405,110,142,241,214), (1,156,186,211)(2,157,187,212)(3,158,171,213)(4,159,172,214)(5,160,173,215)(6,161,174,216)(7,162,175,217)(8,163,176,218)(9,164,177,219)(10,165,178,220)(11,166,179,221)(12,167,180,205)(13,168,181,206)(14,169,182,207)(15,170,183,208)(16,154,184,209)(17,155,185,210)(18,238,321,62)(19,222,322,63)(20,223,323,64)(21,224,307,65)(22,225,308,66)(23,226,309,67)(24,227,310,68)(25,228,311,52)(26,229,312,53)(27,230,313,54)(28,231,314,55)(29,232,315,56)(30,233,316,57)(31,234,317,58)(32,235,318,59)(33,236,319,60)(34,237,320,61)(35,92,337,144)(36,93,338,145)(37,94,339,146)(38,95,340,147)(39,96,324,148)(40,97,325,149)(41,98,326,150)(42,99,327,151)(43,100,328,152)(44,101,329,153)(45,102,330,137)(46,86,331,138)(47,87,332,139)(48,88,333,140)(49,89,334,141)(50,90,335,142)(51,91,336,143)(69,291,391,398)(70,292,375,399)(71,293,376,400)(72,294,377,401)(73,295,378,402)(74,296,379,403)(75,297,380,404)(76,298,381,405)(77,299,382,406)(78,300,383,407)(79,301,384,408)(80,302,385,392)(81,303,386,393)(82,304,387,394)(83,305,388,395)(84,306,389,396)(85,290,390,397)(103,341,265,191)(104,342,266,192)(105,343,267,193)(106,344,268,194)(107,345,269,195)(108,346,270,196)(109,347,271,197)(110,348,272,198)(111,349,256,199)(112,350,257,200)(113,351,258,201)(114,352,259,202)(115,353,260,203)(116,354,261,204)(117,355,262,188)(118,356,263,189)(119,357,264,190)(120,360,282,244)(121,361,283,245)(122,362,284,246)(123,363,285,247)(124,364,286,248)(125,365,287,249)(126,366,288,250)(127,367,289,251)(128,368,273,252)(129,369,274,253)(130,370,275,254)(131,371,276,255)(132,372,277,239)(133,373,278,240)(134,374,279,241)(135,358,280,242)(136,359,281,243) );
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)], [(1,131,47,345,73,307,186,276,332,195,378,21),(2,132,48,346,74,308,187,277,333,196,379,22),(3,133,49,347,75,309,171,278,334,197,380,23),(4,134,50,348,76,310,172,279,335,198,381,24),(5,135,51,349,77,311,173,280,336,199,382,25),(6,136,35,350,78,312,174,281,337,200,383,26),(7,120,36,351,79,313,175,282,338,201,384,27),(8,121,37,352,80,314,176,283,339,202,385,28),(9,122,38,353,81,315,177,284,340,203,386,29),(10,123,39,354,82,316,178,285,324,204,387,30),(11,124,40,355,83,317,179,286,325,188,388,31),(12,125,41,356,84,318,180,287,326,189,389,32),(13,126,42,357,85,319,181,288,327,190,390,33),(14,127,43,341,69,320,182,289,328,191,391,34),(15,128,44,342,70,321,183,273,329,192,375,18),(16,129,45,343,71,322,184,274,330,193,376,19),(17,130,46,344,72,323,185,275,331,194,377,20),(52,299,256,91,358,160,228,406,111,143,242,215),(53,300,257,92,359,161,229,407,112,144,243,216),(54,301,258,93,360,162,230,408,113,145,244,217),(55,302,259,94,361,163,231,392,114,146,245,218),(56,303,260,95,362,164,232,393,115,147,246,219),(57,304,261,96,363,165,233,394,116,148,247,220),(58,305,262,97,364,166,234,395,117,149,248,221),(59,306,263,98,365,167,235,396,118,150,249,205),(60,290,264,99,366,168,236,397,119,151,250,206),(61,291,265,100,367,169,237,398,103,152,251,207),(62,292,266,101,368,170,238,399,104,153,252,208),(63,293,267,102,369,154,222,400,105,137,253,209),(64,294,268,86,370,155,223,401,106,138,254,210),(65,295,269,87,371,156,224,402,107,139,255,211),(66,296,270,88,372,157,225,403,108,140,239,212),(67,297,271,89,373,158,226,404,109,141,240,213),(68,298,272,90,374,159,227,405,110,142,241,214)], [(1,156,186,211),(2,157,187,212),(3,158,171,213),(4,159,172,214),(5,160,173,215),(6,161,174,216),(7,162,175,217),(8,163,176,218),(9,164,177,219),(10,165,178,220),(11,166,179,221),(12,167,180,205),(13,168,181,206),(14,169,182,207),(15,170,183,208),(16,154,184,209),(17,155,185,210),(18,238,321,62),(19,222,322,63),(20,223,323,64),(21,224,307,65),(22,225,308,66),(23,226,309,67),(24,227,310,68),(25,228,311,52),(26,229,312,53),(27,230,313,54),(28,231,314,55),(29,232,315,56),(30,233,316,57),(31,234,317,58),(32,235,318,59),(33,236,319,60),(34,237,320,61),(35,92,337,144),(36,93,338,145),(37,94,339,146),(38,95,340,147),(39,96,324,148),(40,97,325,149),(41,98,326,150),(42,99,327,151),(43,100,328,152),(44,101,329,153),(45,102,330,137),(46,86,331,138),(47,87,332,139),(48,88,333,140),(49,89,334,141),(50,90,335,142),(51,91,336,143),(69,291,391,398),(70,292,375,399),(71,293,376,400),(72,294,377,401),(73,295,378,402),(74,296,379,403),(75,297,380,404),(76,298,381,405),(77,299,382,406),(78,300,383,407),(79,301,384,408),(80,302,385,392),(81,303,386,393),(82,304,387,394),(83,305,388,395),(84,306,389,396),(85,290,390,397),(103,341,265,191),(104,342,266,192),(105,343,267,193),(106,344,268,194),(107,345,269,195),(108,346,270,196),(109,347,271,197),(110,348,272,198),(111,349,256,199),(112,350,257,200),(113,351,258,201),(114,352,259,202),(115,353,260,203),(116,354,261,204),(117,355,262,188),(118,356,263,189),(119,357,264,190),(120,360,282,244),(121,361,283,245),(122,362,284,246),(123,363,285,247),(124,364,286,248),(125,365,287,249),(126,366,288,250),(127,367,289,251),(128,368,273,252),(129,369,274,253),(130,370,275,254),(131,371,276,255),(132,372,277,239),(133,373,278,240),(134,374,279,241),(135,358,280,242),(136,359,281,243)]])
153 conjugacy classes
| class | 1 | 2 | 3 | 4A | 4B | 4C | 6 | 12A | 12B | 17A | ··· | 17P | 34A | ··· | 34P | 51A | ··· | 51P | 68A | ··· | 68P | 68Q | ··· | 68AV | 102A | ··· | 102P | 204A | ··· | 204AF |
| order | 1 | 2 | 3 | 4 | 4 | 4 | 6 | 12 | 12 | 17 | ··· | 17 | 34 | ··· | 34 | 51 | ··· | 51 | 68 | ··· | 68 | 68 | ··· | 68 | 102 | ··· | 102 | 204 | ··· | 204 |
| size | 1 | 1 | 2 | 2 | 6 | 6 | 2 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 6 | ··· | 6 | 2 | ··· | 2 | 2 | ··· | 2 |
153 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | |||||||
| image | C1 | C2 | C2 | C17 | C34 | C34 | S3 | Q8 | D6 | Dic6 | S3×C17 | Q8×C17 | S3×C34 | C17×Dic6 |
| kernel | C17×Dic6 | Dic3×C17 | C204 | Dic6 | Dic3 | C12 | C68 | C51 | C34 | C17 | C4 | C3 | C2 | C1 |
| # reps | 1 | 2 | 1 | 16 | 32 | 16 | 1 | 1 | 1 | 2 | 16 | 16 | 16 | 32 |
Matrix representation of C17×Dic6 ►in GL4(𝔽409) generated by
| 341 | 0 | 0 | 0 |
| 0 | 341 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 408 | 0 | 0 |
| 1 | 1 | 0 | 0 |
| 0 | 0 | 408 | 3 |
| 0 | 0 | 272 | 1 |
| 189 | 166 | 0 | 0 |
| 386 | 220 | 0 | 0 |
| 0 | 0 | 288 | 168 |
| 0 | 0 | 93 | 121 |
G:=sub<GL(4,GF(409))| [341,0,0,0,0,341,0,0,0,0,1,0,0,0,0,1],[0,1,0,0,408,1,0,0,0,0,408,272,0,0,3,1],[189,386,0,0,166,220,0,0,0,0,288,93,0,0,168,121] >;
C17×Dic6 in GAP, Magma, Sage, TeX
C_{17}\times {\rm Dic}_6 % in TeX
G:=Group("C17xDic6"); // GroupNames label
G:=SmallGroup(408,20);
// by ID
G=gap.SmallGroup(408,20);
# by ID
G:=PCGroup([5,-2,-2,-17,-2,-3,340,701,346,6804]);
// Polycyclic
G:=Group<a,b,c|a^17=b^12=1,c^2=b^6,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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