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## G = Dic3×C28order 336 = 24·3·7

### Direct product of C28 and Dic3

Series: Derived Chief Lower central Upper central

 Derived series C1 — C3 — Dic3×C28
 Chief series C1 — C3 — C6 — C2×C6 — C2×C42 — Dic3×C14 — Dic3×C28
 Lower central C3 — Dic3×C28
 Upper central C1 — C2×C28

Generators and relations for Dic3×C28
G = < a,b,c | a28=b6=1, c2=b3, ab=ba, ac=ca, cbc-1=b-1 >

Subgroups: 88 in 60 conjugacy classes, 46 normal (18 characteristic)
C1, C2, C2, C3, C4, C4, C22, C6, C6, C7, C2×C4, C2×C4, Dic3, C12, C2×C6, C14, C14, C42, C21, C2×Dic3, C2×C12, C28, C28, C2×C14, C42, C42, C4×Dic3, C2×C28, C2×C28, C7×Dic3, C84, C2×C42, C4×C28, Dic3×C14, C2×C84, Dic3×C28
Quotients: C1, C2, C4, C22, S3, C7, C2×C4, Dic3, D6, C14, C42, C4×S3, C2×Dic3, C28, C2×C14, S3×C7, C4×Dic3, C2×C28, C7×Dic3, S3×C14, C4×C28, S3×C28, Dic3×C14, Dic3×C28

Smallest permutation representation of Dic3×C28
Regular action on 336 points
Generators in S336
(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)
(1 323 75 251 138 41)(2 324 76 252 139 42)(3 325 77 225 140 43)(4 326 78 226 113 44)(5 327 79 227 114 45)(6 328 80 228 115 46)(7 329 81 229 116 47)(8 330 82 230 117 48)(9 331 83 231 118 49)(10 332 84 232 119 50)(11 333 57 233 120 51)(12 334 58 234 121 52)(13 335 59 235 122 53)(14 336 60 236 123 54)(15 309 61 237 124 55)(16 310 62 238 125 56)(17 311 63 239 126 29)(18 312 64 240 127 30)(19 313 65 241 128 31)(20 314 66 242 129 32)(21 315 67 243 130 33)(22 316 68 244 131 34)(23 317 69 245 132 35)(24 318 70 246 133 36)(25 319 71 247 134 37)(26 320 72 248 135 38)(27 321 73 249 136 39)(28 322 74 250 137 40)(85 278 215 191 305 142)(86 279 216 192 306 143)(87 280 217 193 307 144)(88 253 218 194 308 145)(89 254 219 195 281 146)(90 255 220 196 282 147)(91 256 221 169 283 148)(92 257 222 170 284 149)(93 258 223 171 285 150)(94 259 224 172 286 151)(95 260 197 173 287 152)(96 261 198 174 288 153)(97 262 199 175 289 154)(98 263 200 176 290 155)(99 264 201 177 291 156)(100 265 202 178 292 157)(101 266 203 179 293 158)(102 267 204 180 294 159)(103 268 205 181 295 160)(104 269 206 182 296 161)(105 270 207 183 297 162)(106 271 208 184 298 163)(107 272 209 185 299 164)(108 273 210 186 300 165)(109 274 211 187 301 166)(110 275 212 188 302 167)(111 276 213 189 303 168)(112 277 214 190 304 141)
(1 221 251 148)(2 222 252 149)(3 223 225 150)(4 224 226 151)(5 197 227 152)(6 198 228 153)(7 199 229 154)(8 200 230 155)(9 201 231 156)(10 202 232 157)(11 203 233 158)(12 204 234 159)(13 205 235 160)(14 206 236 161)(15 207 237 162)(16 208 238 163)(17 209 239 164)(18 210 240 165)(19 211 241 166)(20 212 242 167)(21 213 243 168)(22 214 244 141)(23 215 245 142)(24 216 246 143)(25 217 247 144)(26 218 248 145)(27 219 249 146)(28 220 250 147)(29 185 63 107)(30 186 64 108)(31 187 65 109)(32 188 66 110)(33 189 67 111)(34 190 68 112)(35 191 69 85)(36 192 70 86)(37 193 71 87)(38 194 72 88)(39 195 73 89)(40 196 74 90)(41 169 75 91)(42 170 76 92)(43 171 77 93)(44 172 78 94)(45 173 79 95)(46 174 80 96)(47 175 81 97)(48 176 82 98)(49 177 83 99)(50 178 84 100)(51 179 57 101)(52 180 58 102)(53 181 59 103)(54 182 60 104)(55 183 61 105)(56 184 62 106)(113 286 326 259)(114 287 327 260)(115 288 328 261)(116 289 329 262)(117 290 330 263)(118 291 331 264)(119 292 332 265)(120 293 333 266)(121 294 334 267)(122 295 335 268)(123 296 336 269)(124 297 309 270)(125 298 310 271)(126 299 311 272)(127 300 312 273)(128 301 313 274)(129 302 314 275)(130 303 315 276)(131 304 316 277)(132 305 317 278)(133 306 318 279)(134 307 319 280)(135 308 320 253)(136 281 321 254)(137 282 322 255)(138 283 323 256)(139 284 324 257)(140 285 325 258)

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

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

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

168 conjugacy classes

 class 1 2A 2B 2C 3 4A 4B 4C 4D 4E ··· 4L 6A 6B 6C 7A ··· 7F 12A 12B 12C 12D 14A ··· 14R 21A ··· 21F 28A ··· 28X 28Y ··· 28BT 42A ··· 42R 84A ··· 84X order 1 2 2 2 3 4 4 4 4 4 ··· 4 6 6 6 7 ··· 7 12 12 12 12 14 ··· 14 21 ··· 21 28 ··· 28 28 ··· 28 42 ··· 42 84 ··· 84 size 1 1 1 1 2 1 1 1 1 3 ··· 3 2 2 2 1 ··· 1 2 2 2 2 1 ··· 1 2 ··· 2 1 ··· 1 3 ··· 3 2 ··· 2 2 ··· 2

168 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 type + + + + - + image C1 C2 C2 C4 C4 C7 C14 C14 C28 C28 S3 Dic3 D6 C4×S3 S3×C7 C7×Dic3 S3×C14 S3×C28 kernel Dic3×C28 Dic3×C14 C2×C84 C7×Dic3 C84 C4×Dic3 C2×Dic3 C2×C12 Dic3 C12 C2×C28 C28 C2×C14 C14 C2×C4 C4 C22 C2 # reps 1 2 1 8 4 6 12 6 48 24 1 2 1 4 6 12 6 24

Matrix representation of Dic3×C28 in GL3(𝔽337) generated by

 1 0 0 0 187 0 0 0 187
,
 336 0 0 0 336 1 0 336 0
,
 148 0 0 0 214 131 0 8 123
G:=sub<GL(3,GF(337))| [1,0,0,0,187,0,0,0,187],[336,0,0,0,336,336,0,1,0],[148,0,0,0,214,8,0,131,123] >;

Dic3×C28 in GAP, Magma, Sage, TeX

{\rm Dic}_3\times C_{28}
% in TeX

G:=Group("Dic3xC28");
// GroupNames label

G:=SmallGroup(336,81);
// by ID

G=gap.SmallGroup(336,81);
# by ID

G:=PCGroup([6,-2,-2,-7,-2,-2,-3,168,343,8069]);
// Polycyclic

G:=Group<a,b,c|a^28=b^6=1,c^2=b^3,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

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