direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C6×C7⋊C8, C42⋊2C8, C14⋊3C24, C84.6C4, C28.9C12, C12.58D14, C12.6Dic7, C84.66C22, C21⋊8(C2×C8), C7⋊5(C2×C24), (C2×C42).4C4, C4.14(C6×D7), (C2×C28).17C6, C42.33(C2×C4), C28.38(C2×C6), (C2×C14).6C12, (C2×C84).13C2, (C2×C12).11D7, (C2×C6).4Dic7, C2.1(C6×Dic7), C4.3(C3×Dic7), C14.19(C2×C12), C6.11(C2×Dic7), C22.2(C3×Dic7), (C2×C4).5(C3×D7), SmallGroup(336,63)
Series: Derived ►Chief ►Lower central ►Upper central
| C7 — C6×C7⋊C8 |
Generators and relations for C6×C7⋊C8
G = < a,b,c | a6=b7=c8=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C6×C7⋊C8
►Regular action on 336 points
Generators in S336
(1 139 196 28 333 309)(2 140 197 29 334 310)(3 141 198 30 335 311)(4 142 199 31 336 312)(5 143 200 32 329 305)(6 144 193 25 330 306)(7 137 194 26 331 307)(8 138 195 27 332 308)(9 317 102 158 204 47)(10 318 103 159 205 48)(11 319 104 160 206 41)(12 320 97 153 207 42)(13 313 98 154 208 43)(14 314 99 155 201 44)(15 315 100 156 202 45)(16 316 101 157 203 46)(17 212 110 166 325 55)(18 213 111 167 326 56)(19 214 112 168 327 49)(20 215 105 161 328 50)(21 216 106 162 321 51)(22 209 107 163 322 52)(23 210 108 164 323 53)(24 211 109 165 324 54)(33 270 135 96 152 80)(34 271 136 89 145 73)(35 272 129 90 146 74)(36 265 130 91 147 75)(37 266 131 92 148 76)(38 267 132 93 149 77)(39 268 133 94 150 78)(40 269 134 95 151 79)(57 172 228 120 285 255)(58 173 229 113 286 256)(59 174 230 114 287 249)(60 175 231 115 288 250)(61 176 232 116 281 251)(62 169 225 117 282 252)(63 170 226 118 283 253)(64 171 227 119 284 254)(65 293 263 128 180 236)(66 294 264 121 181 237)(67 295 257 122 182 238)(68 296 258 123 183 239)(69 289 259 124 184 240)(70 290 260 125 177 233)(71 291 261 126 178 234)(72 292 262 127 179 235)(81 301 279 220 188 244)(82 302 280 221 189 245)(83 303 273 222 190 246)(84 304 274 223 191 247)(85 297 275 224 192 248)(86 298 276 217 185 241)(87 299 277 218 186 242)(88 300 278 219 187 243)
(1 173 99 78 67 325 83)(2 84 326 68 79 100 174)(3 175 101 80 69 327 85)(4 86 328 70 73 102 176)(5 169 103 74 71 321 87)(6 88 322 72 75 104 170)(7 171 97 76 65 323 81)(8 82 324 66 77 98 172)(9 251 336 185 105 177 89)(10 90 178 106 186 329 252)(11 253 330 187 107 179 91)(12 92 180 108 188 331 254)(13 255 332 189 109 181 93)(14 94 182 110 190 333 256)(15 249 334 191 111 183 95)(16 96 184 112 192 335 250)(17 273 196 113 201 268 257)(18 258 269 202 114 197 274)(19 275 198 115 203 270 259)(20 260 271 204 116 199 276)(21 277 200 117 205 272 261)(22 262 265 206 118 193 278)(23 279 194 119 207 266 263)(24 264 267 208 120 195 280)(25 219 209 127 130 41 283)(26 284 42 131 128 210 220)(27 221 211 121 132 43 285)(28 286 44 133 122 212 222)(29 223 213 123 134 45 287)(30 288 46 135 124 214 224)(31 217 215 125 136 47 281)(32 282 48 129 126 216 218)(33 289 49 297 141 231 157)(34 158 232 142 298 50 290)(35 291 51 299 143 225 159)(36 160 226 144 300 52 292)(37 293 53 301 137 227 153)(38 154 228 138 302 54 294)(39 295 55 303 139 229 155)(40 156 230 140 304 56 296)(57 308 245 165 237 149 313)(58 314 150 238 166 246 309)(59 310 247 167 239 151 315)(60 316 152 240 168 248 311)(61 312 241 161 233 145 317)(62 318 146 234 162 242 305)(63 306 243 163 235 147 319)(64 320 148 236 164 244 307)
(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)
G:=sub<Sym(336)| (1,139,196,28,333,309)(2,140,197,29,334,310)(3,141,198,30,335,311)(4,142,199,31,336,312)(5,143,200,32,329,305)(6,144,193,25,330,306)(7,137,194,26,331,307)(8,138,195,27,332,308)(9,317,102,158,204,47)(10,318,103,159,205,48)(11,319,104,160,206,41)(12,320,97,153,207,42)(13,313,98,154,208,43)(14,314,99,155,201,44)(15,315,100,156,202,45)(16,316,101,157,203,46)(17,212,110,166,325,55)(18,213,111,167,326,56)(19,214,112,168,327,49)(20,215,105,161,328,50)(21,216,106,162,321,51)(22,209,107,163,322,52)(23,210,108,164,323,53)(24,211,109,165,324,54)(33,270,135,96,152,80)(34,271,136,89,145,73)(35,272,129,90,146,74)(36,265,130,91,147,75)(37,266,131,92,148,76)(38,267,132,93,149,77)(39,268,133,94,150,78)(40,269,134,95,151,79)(57,172,228,120,285,255)(58,173,229,113,286,256)(59,174,230,114,287,249)(60,175,231,115,288,250)(61,176,232,116,281,251)(62,169,225,117,282,252)(63,170,226,118,283,253)(64,171,227,119,284,254)(65,293,263,128,180,236)(66,294,264,121,181,237)(67,295,257,122,182,238)(68,296,258,123,183,239)(69,289,259,124,184,240)(70,290,260,125,177,233)(71,291,261,126,178,234)(72,292,262,127,179,235)(81,301,279,220,188,244)(82,302,280,221,189,245)(83,303,273,222,190,246)(84,304,274,223,191,247)(85,297,275,224,192,248)(86,298,276,217,185,241)(87,299,277,218,186,242)(88,300,278,219,187,243), (1,173,99,78,67,325,83)(2,84,326,68,79,100,174)(3,175,101,80,69,327,85)(4,86,328,70,73,102,176)(5,169,103,74,71,321,87)(6,88,322,72,75,104,170)(7,171,97,76,65,323,81)(8,82,324,66,77,98,172)(9,251,336,185,105,177,89)(10,90,178,106,186,329,252)(11,253,330,187,107,179,91)(12,92,180,108,188,331,254)(13,255,332,189,109,181,93)(14,94,182,110,190,333,256)(15,249,334,191,111,183,95)(16,96,184,112,192,335,250)(17,273,196,113,201,268,257)(18,258,269,202,114,197,274)(19,275,198,115,203,270,259)(20,260,271,204,116,199,276)(21,277,200,117,205,272,261)(22,262,265,206,118,193,278)(23,279,194,119,207,266,263)(24,264,267,208,120,195,280)(25,219,209,127,130,41,283)(26,284,42,131,128,210,220)(27,221,211,121,132,43,285)(28,286,44,133,122,212,222)(29,223,213,123,134,45,287)(30,288,46,135,124,214,224)(31,217,215,125,136,47,281)(32,282,48,129,126,216,218)(33,289,49,297,141,231,157)(34,158,232,142,298,50,290)(35,291,51,299,143,225,159)(36,160,226,144,300,52,292)(37,293,53,301,137,227,153)(38,154,228,138,302,54,294)(39,295,55,303,139,229,155)(40,156,230,140,304,56,296)(57,308,245,165,237,149,313)(58,314,150,238,166,246,309)(59,310,247,167,239,151,315)(60,316,152,240,168,248,311)(61,312,241,161,233,145,317)(62,318,146,234,162,242,305)(63,306,243,163,235,147,319)(64,320,148,236,164,244,307), (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)>;
G:=Group( (1,139,196,28,333,309)(2,140,197,29,334,310)(3,141,198,30,335,311)(4,142,199,31,336,312)(5,143,200,32,329,305)(6,144,193,25,330,306)(7,137,194,26,331,307)(8,138,195,27,332,308)(9,317,102,158,204,47)(10,318,103,159,205,48)(11,319,104,160,206,41)(12,320,97,153,207,42)(13,313,98,154,208,43)(14,314,99,155,201,44)(15,315,100,156,202,45)(16,316,101,157,203,46)(17,212,110,166,325,55)(18,213,111,167,326,56)(19,214,112,168,327,49)(20,215,105,161,328,50)(21,216,106,162,321,51)(22,209,107,163,322,52)(23,210,108,164,323,53)(24,211,109,165,324,54)(33,270,135,96,152,80)(34,271,136,89,145,73)(35,272,129,90,146,74)(36,265,130,91,147,75)(37,266,131,92,148,76)(38,267,132,93,149,77)(39,268,133,94,150,78)(40,269,134,95,151,79)(57,172,228,120,285,255)(58,173,229,113,286,256)(59,174,230,114,287,249)(60,175,231,115,288,250)(61,176,232,116,281,251)(62,169,225,117,282,252)(63,170,226,118,283,253)(64,171,227,119,284,254)(65,293,263,128,180,236)(66,294,264,121,181,237)(67,295,257,122,182,238)(68,296,258,123,183,239)(69,289,259,124,184,240)(70,290,260,125,177,233)(71,291,261,126,178,234)(72,292,262,127,179,235)(81,301,279,220,188,244)(82,302,280,221,189,245)(83,303,273,222,190,246)(84,304,274,223,191,247)(85,297,275,224,192,248)(86,298,276,217,185,241)(87,299,277,218,186,242)(88,300,278,219,187,243), (1,173,99,78,67,325,83)(2,84,326,68,79,100,174)(3,175,101,80,69,327,85)(4,86,328,70,73,102,176)(5,169,103,74,71,321,87)(6,88,322,72,75,104,170)(7,171,97,76,65,323,81)(8,82,324,66,77,98,172)(9,251,336,185,105,177,89)(10,90,178,106,186,329,252)(11,253,330,187,107,179,91)(12,92,180,108,188,331,254)(13,255,332,189,109,181,93)(14,94,182,110,190,333,256)(15,249,334,191,111,183,95)(16,96,184,112,192,335,250)(17,273,196,113,201,268,257)(18,258,269,202,114,197,274)(19,275,198,115,203,270,259)(20,260,271,204,116,199,276)(21,277,200,117,205,272,261)(22,262,265,206,118,193,278)(23,279,194,119,207,266,263)(24,264,267,208,120,195,280)(25,219,209,127,130,41,283)(26,284,42,131,128,210,220)(27,221,211,121,132,43,285)(28,286,44,133,122,212,222)(29,223,213,123,134,45,287)(30,288,46,135,124,214,224)(31,217,215,125,136,47,281)(32,282,48,129,126,216,218)(33,289,49,297,141,231,157)(34,158,232,142,298,50,290)(35,291,51,299,143,225,159)(36,160,226,144,300,52,292)(37,293,53,301,137,227,153)(38,154,228,138,302,54,294)(39,295,55,303,139,229,155)(40,156,230,140,304,56,296)(57,308,245,165,237,149,313)(58,314,150,238,166,246,309)(59,310,247,167,239,151,315)(60,316,152,240,168,248,311)(61,312,241,161,233,145,317)(62,318,146,234,162,242,305)(63,306,243,163,235,147,319)(64,320,148,236,164,244,307), (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) );
G=PermutationGroup([[(1,139,196,28,333,309),(2,140,197,29,334,310),(3,141,198,30,335,311),(4,142,199,31,336,312),(5,143,200,32,329,305),(6,144,193,25,330,306),(7,137,194,26,331,307),(8,138,195,27,332,308),(9,317,102,158,204,47),(10,318,103,159,205,48),(11,319,104,160,206,41),(12,320,97,153,207,42),(13,313,98,154,208,43),(14,314,99,155,201,44),(15,315,100,156,202,45),(16,316,101,157,203,46),(17,212,110,166,325,55),(18,213,111,167,326,56),(19,214,112,168,327,49),(20,215,105,161,328,50),(21,216,106,162,321,51),(22,209,107,163,322,52),(23,210,108,164,323,53),(24,211,109,165,324,54),(33,270,135,96,152,80),(34,271,136,89,145,73),(35,272,129,90,146,74),(36,265,130,91,147,75),(37,266,131,92,148,76),(38,267,132,93,149,77),(39,268,133,94,150,78),(40,269,134,95,151,79),(57,172,228,120,285,255),(58,173,229,113,286,256),(59,174,230,114,287,249),(60,175,231,115,288,250),(61,176,232,116,281,251),(62,169,225,117,282,252),(63,170,226,118,283,253),(64,171,227,119,284,254),(65,293,263,128,180,236),(66,294,264,121,181,237),(67,295,257,122,182,238),(68,296,258,123,183,239),(69,289,259,124,184,240),(70,290,260,125,177,233),(71,291,261,126,178,234),(72,292,262,127,179,235),(81,301,279,220,188,244),(82,302,280,221,189,245),(83,303,273,222,190,246),(84,304,274,223,191,247),(85,297,275,224,192,248),(86,298,276,217,185,241),(87,299,277,218,186,242),(88,300,278,219,187,243)], [(1,173,99,78,67,325,83),(2,84,326,68,79,100,174),(3,175,101,80,69,327,85),(4,86,328,70,73,102,176),(5,169,103,74,71,321,87),(6,88,322,72,75,104,170),(7,171,97,76,65,323,81),(8,82,324,66,77,98,172),(9,251,336,185,105,177,89),(10,90,178,106,186,329,252),(11,253,330,187,107,179,91),(12,92,180,108,188,331,254),(13,255,332,189,109,181,93),(14,94,182,110,190,333,256),(15,249,334,191,111,183,95),(16,96,184,112,192,335,250),(17,273,196,113,201,268,257),(18,258,269,202,114,197,274),(19,275,198,115,203,270,259),(20,260,271,204,116,199,276),(21,277,200,117,205,272,261),(22,262,265,206,118,193,278),(23,279,194,119,207,266,263),(24,264,267,208,120,195,280),(25,219,209,127,130,41,283),(26,284,42,131,128,210,220),(27,221,211,121,132,43,285),(28,286,44,133,122,212,222),(29,223,213,123,134,45,287),(30,288,46,135,124,214,224),(31,217,215,125,136,47,281),(32,282,48,129,126,216,218),(33,289,49,297,141,231,157),(34,158,232,142,298,50,290),(35,291,51,299,143,225,159),(36,160,226,144,300,52,292),(37,293,53,301,137,227,153),(38,154,228,138,302,54,294),(39,295,55,303,139,229,155),(40,156,230,140,304,56,296),(57,308,245,165,237,149,313),(58,314,150,238,166,246,309),(59,310,247,167,239,151,315),(60,316,152,240,168,248,311),(61,312,241,161,233,145,317),(62,318,146,234,162,242,305),(63,306,243,163,235,147,319),(64,320,148,236,164,244,307)], [(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)]])
120 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 4A | 4B | 4C | 4D | 6A | ··· | 6F | 7A | 7B | 7C | 8A | ··· | 8H | 12A | ··· | 12H | 14A | ··· | 14I | 21A | ··· | 21F | 24A | ··· | 24P | 28A | ··· | 28L | 42A | ··· | 42R | 84A | ··· | 84X |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 7 | 7 | 7 | 8 | ··· | 8 | 12 | ··· | 12 | 14 | ··· | 14 | 21 | ··· | 21 | 24 | ··· | 24 | 28 | ··· | 28 | 42 | ··· | 42 | 84 | ··· | 84 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 7 | ··· | 7 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 7 | ··· | 7 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
120 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | |||||||||||||||
| image | C1 | C2 | C2 | C3 | C4 | C4 | C6 | C6 | C8 | C12 | C12 | C24 | D7 | Dic7 | D14 | Dic7 | C3×D7 | C7⋊C8 | C3×Dic7 | C6×D7 | C3×Dic7 | C3×C7⋊C8 |
| kernel | C6×C7⋊C8 | C3×C7⋊C8 | C2×C84 | C2×C7⋊C8 | C84 | C2×C42 | C7⋊C8 | C2×C28 | C42 | C28 | C2×C14 | C14 | C2×C12 | C12 | C12 | C2×C6 | C2×C4 | C6 | C4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 2 | 8 | 4 | 4 | 16 | 3 | 3 | 3 | 3 | 6 | 12 | 6 | 6 | 6 | 24 |
Matrix representation of C6×C7⋊C8 ►in GL3(𝔽337) generated by
| 336 | 0 | 0 |
| 0 | 209 | 0 |
| 0 | 0 | 209 |
| 1 | 0 | 0 |
| 0 | 304 | 336 |
| 0 | 305 | 336 |
| 252 | 0 | 0 |
| 0 | 104 | 314 |
| 0 | 104 | 233 |
G:=sub<GL(3,GF(337))| [336,0,0,0,209,0,0,0,209],[1,0,0,0,304,305,0,336,336],[252,0,0,0,104,104,0,314,233] >;
C6×C7⋊C8 in GAP, Magma, Sage, TeX
C_6\times C_7\rtimes C_8
% in TeX
G:=Group("C6xC7:C8"); // GroupNames label
G:=SmallGroup(336,63);
// by ID
G=gap.SmallGroup(336,63);
# by ID
G:=PCGroup([6,-2,-2,-3,-2,-2,-7,72,69,10373]);
// Polycyclic
G:=Group<a,b,c|a^6=b^7=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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