direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: Q8×C42, C42.59C23, C84.80C22, (C2×C4).3C42, C4.4(C2×C42), (C2×C84).21C2, (C2×C12).9C14, C28.43(C2×C6), (C2×C28).20C6, C12.20(C2×C14), C22.4(C2×C42), C2.2(C22×C42), C6.12(C22×C14), C14.26(C22×C6), (C2×C42).54C22, (C2×C6).15(C2×C14), (C2×C14).32(C2×C6), SmallGroup(336,206)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Q8×C42
G = < a,b,c | a42=b4=1, c2=b2, ab=ba, ac=ca, cbc-1=b-1 >
Subgroups: 76, all normal (16 characteristic)
C1, C2, C2, C3, C4, C22, C6, C6, C7, C2×C4, Q8, C12, C2×C6, C14, C14, C2×Q8, C21, C2×C12, C3×Q8, C28, C2×C14, C42, C42, C6×Q8, C2×C28, C7×Q8, C84, C2×C42, Q8×C14, C2×C84, Q8×C21, Q8×C42
Quotients: C1, C2, C3, C22, C6, C7, Q8, C23, C2×C6, C14, C2×Q8, C21, C3×Q8, C22×C6, C2×C14, C42, C6×Q8, C7×Q8, C22×C14, C2×C42, Q8×C14, Q8×C21, C22×C42, Q8×C42
►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)
(1 128 58 185)(2 129 59 186)(3 130 60 187)(4 131 61 188)(5 132 62 189)(6 133 63 190)(7 134 64 191)(8 135 65 192)(9 136 66 193)(10 137 67 194)(11 138 68 195)(12 139 69 196)(13 140 70 197)(14 141 71 198)(15 142 72 199)(16 143 73 200)(17 144 74 201)(18 145 75 202)(19 146 76 203)(20 147 77 204)(21 148 78 205)(22 149 79 206)(23 150 80 207)(24 151 81 208)(25 152 82 209)(26 153 83 210)(27 154 84 169)(28 155 43 170)(29 156 44 171)(30 157 45 172)(31 158 46 173)(32 159 47 174)(33 160 48 175)(34 161 49 176)(35 162 50 177)(36 163 51 178)(37 164 52 179)(38 165 53 180)(39 166 54 181)(40 167 55 182)(41 168 56 183)(42 127 57 184)(85 216 255 327)(86 217 256 328)(87 218 257 329)(88 219 258 330)(89 220 259 331)(90 221 260 332)(91 222 261 333)(92 223 262 334)(93 224 263 335)(94 225 264 336)(95 226 265 295)(96 227 266 296)(97 228 267 297)(98 229 268 298)(99 230 269 299)(100 231 270 300)(101 232 271 301)(102 233 272 302)(103 234 273 303)(104 235 274 304)(105 236 275 305)(106 237 276 306)(107 238 277 307)(108 239 278 308)(109 240 279 309)(110 241 280 310)(111 242 281 311)(112 243 282 312)(113 244 283 313)(114 245 284 314)(115 246 285 315)(116 247 286 316)(117 248 287 317)(118 249 288 318)(119 250 289 319)(120 251 290 320)(121 252 291 321)(122 211 292 322)(123 212 293 323)(124 213 294 324)(125 214 253 325)(126 215 254 326)
(1 315 58 246)(2 316 59 247)(3 317 60 248)(4 318 61 249)(5 319 62 250)(6 320 63 251)(7 321 64 252)(8 322 65 211)(9 323 66 212)(10 324 67 213)(11 325 68 214)(12 326 69 215)(13 327 70 216)(14 328 71 217)(15 329 72 218)(16 330 73 219)(17 331 74 220)(18 332 75 221)(19 333 76 222)(20 334 77 223)(21 335 78 224)(22 336 79 225)(23 295 80 226)(24 296 81 227)(25 297 82 228)(26 298 83 229)(27 299 84 230)(28 300 43 231)(29 301 44 232)(30 302 45 233)(31 303 46 234)(32 304 47 235)(33 305 48 236)(34 306 49 237)(35 307 50 238)(36 308 51 239)(37 309 52 240)(38 310 53 241)(39 311 54 242)(40 312 55 243)(41 313 56 244)(42 314 57 245)(85 140 255 197)(86 141 256 198)(87 142 257 199)(88 143 258 200)(89 144 259 201)(90 145 260 202)(91 146 261 203)(92 147 262 204)(93 148 263 205)(94 149 264 206)(95 150 265 207)(96 151 266 208)(97 152 267 209)(98 153 268 210)(99 154 269 169)(100 155 270 170)(101 156 271 171)(102 157 272 172)(103 158 273 173)(104 159 274 174)(105 160 275 175)(106 161 276 176)(107 162 277 177)(108 163 278 178)(109 164 279 179)(110 165 280 180)(111 166 281 181)(112 167 282 182)(113 168 283 183)(114 127 284 184)(115 128 285 185)(116 129 286 186)(117 130 287 187)(118 131 288 188)(119 132 289 189)(120 133 290 190)(121 134 291 191)(122 135 292 192)(123 136 293 193)(124 137 294 194)(125 138 253 195)(126 139 254 196)
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), (1,128,58,185)(2,129,59,186)(3,130,60,187)(4,131,61,188)(5,132,62,189)(6,133,63,190)(7,134,64,191)(8,135,65,192)(9,136,66,193)(10,137,67,194)(11,138,68,195)(12,139,69,196)(13,140,70,197)(14,141,71,198)(15,142,72,199)(16,143,73,200)(17,144,74,201)(18,145,75,202)(19,146,76,203)(20,147,77,204)(21,148,78,205)(22,149,79,206)(23,150,80,207)(24,151,81,208)(25,152,82,209)(26,153,83,210)(27,154,84,169)(28,155,43,170)(29,156,44,171)(30,157,45,172)(31,158,46,173)(32,159,47,174)(33,160,48,175)(34,161,49,176)(35,162,50,177)(36,163,51,178)(37,164,52,179)(38,165,53,180)(39,166,54,181)(40,167,55,182)(41,168,56,183)(42,127,57,184)(85,216,255,327)(86,217,256,328)(87,218,257,329)(88,219,258,330)(89,220,259,331)(90,221,260,332)(91,222,261,333)(92,223,262,334)(93,224,263,335)(94,225,264,336)(95,226,265,295)(96,227,266,296)(97,228,267,297)(98,229,268,298)(99,230,269,299)(100,231,270,300)(101,232,271,301)(102,233,272,302)(103,234,273,303)(104,235,274,304)(105,236,275,305)(106,237,276,306)(107,238,277,307)(108,239,278,308)(109,240,279,309)(110,241,280,310)(111,242,281,311)(112,243,282,312)(113,244,283,313)(114,245,284,314)(115,246,285,315)(116,247,286,316)(117,248,287,317)(118,249,288,318)(119,250,289,319)(120,251,290,320)(121,252,291,321)(122,211,292,322)(123,212,293,323)(124,213,294,324)(125,214,253,325)(126,215,254,326), (1,315,58,246)(2,316,59,247)(3,317,60,248)(4,318,61,249)(5,319,62,250)(6,320,63,251)(7,321,64,252)(8,322,65,211)(9,323,66,212)(10,324,67,213)(11,325,68,214)(12,326,69,215)(13,327,70,216)(14,328,71,217)(15,329,72,218)(16,330,73,219)(17,331,74,220)(18,332,75,221)(19,333,76,222)(20,334,77,223)(21,335,78,224)(22,336,79,225)(23,295,80,226)(24,296,81,227)(25,297,82,228)(26,298,83,229)(27,299,84,230)(28,300,43,231)(29,301,44,232)(30,302,45,233)(31,303,46,234)(32,304,47,235)(33,305,48,236)(34,306,49,237)(35,307,50,238)(36,308,51,239)(37,309,52,240)(38,310,53,241)(39,311,54,242)(40,312,55,243)(41,313,56,244)(42,314,57,245)(85,140,255,197)(86,141,256,198)(87,142,257,199)(88,143,258,200)(89,144,259,201)(90,145,260,202)(91,146,261,203)(92,147,262,204)(93,148,263,205)(94,149,264,206)(95,150,265,207)(96,151,266,208)(97,152,267,209)(98,153,268,210)(99,154,269,169)(100,155,270,170)(101,156,271,171)(102,157,272,172)(103,158,273,173)(104,159,274,174)(105,160,275,175)(106,161,276,176)(107,162,277,177)(108,163,278,178)(109,164,279,179)(110,165,280,180)(111,166,281,181)(112,167,282,182)(113,168,283,183)(114,127,284,184)(115,128,285,185)(116,129,286,186)(117,130,287,187)(118,131,288,188)(119,132,289,189)(120,133,290,190)(121,134,291,191)(122,135,292,192)(123,136,293,193)(124,137,294,194)(125,138,253,195)(126,139,254,196)>;
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), (1,128,58,185)(2,129,59,186)(3,130,60,187)(4,131,61,188)(5,132,62,189)(6,133,63,190)(7,134,64,191)(8,135,65,192)(9,136,66,193)(10,137,67,194)(11,138,68,195)(12,139,69,196)(13,140,70,197)(14,141,71,198)(15,142,72,199)(16,143,73,200)(17,144,74,201)(18,145,75,202)(19,146,76,203)(20,147,77,204)(21,148,78,205)(22,149,79,206)(23,150,80,207)(24,151,81,208)(25,152,82,209)(26,153,83,210)(27,154,84,169)(28,155,43,170)(29,156,44,171)(30,157,45,172)(31,158,46,173)(32,159,47,174)(33,160,48,175)(34,161,49,176)(35,162,50,177)(36,163,51,178)(37,164,52,179)(38,165,53,180)(39,166,54,181)(40,167,55,182)(41,168,56,183)(42,127,57,184)(85,216,255,327)(86,217,256,328)(87,218,257,329)(88,219,258,330)(89,220,259,331)(90,221,260,332)(91,222,261,333)(92,223,262,334)(93,224,263,335)(94,225,264,336)(95,226,265,295)(96,227,266,296)(97,228,267,297)(98,229,268,298)(99,230,269,299)(100,231,270,300)(101,232,271,301)(102,233,272,302)(103,234,273,303)(104,235,274,304)(105,236,275,305)(106,237,276,306)(107,238,277,307)(108,239,278,308)(109,240,279,309)(110,241,280,310)(111,242,281,311)(112,243,282,312)(113,244,283,313)(114,245,284,314)(115,246,285,315)(116,247,286,316)(117,248,287,317)(118,249,288,318)(119,250,289,319)(120,251,290,320)(121,252,291,321)(122,211,292,322)(123,212,293,323)(124,213,294,324)(125,214,253,325)(126,215,254,326), (1,315,58,246)(2,316,59,247)(3,317,60,248)(4,318,61,249)(5,319,62,250)(6,320,63,251)(7,321,64,252)(8,322,65,211)(9,323,66,212)(10,324,67,213)(11,325,68,214)(12,326,69,215)(13,327,70,216)(14,328,71,217)(15,329,72,218)(16,330,73,219)(17,331,74,220)(18,332,75,221)(19,333,76,222)(20,334,77,223)(21,335,78,224)(22,336,79,225)(23,295,80,226)(24,296,81,227)(25,297,82,228)(26,298,83,229)(27,299,84,230)(28,300,43,231)(29,301,44,232)(30,302,45,233)(31,303,46,234)(32,304,47,235)(33,305,48,236)(34,306,49,237)(35,307,50,238)(36,308,51,239)(37,309,52,240)(38,310,53,241)(39,311,54,242)(40,312,55,243)(41,313,56,244)(42,314,57,245)(85,140,255,197)(86,141,256,198)(87,142,257,199)(88,143,258,200)(89,144,259,201)(90,145,260,202)(91,146,261,203)(92,147,262,204)(93,148,263,205)(94,149,264,206)(95,150,265,207)(96,151,266,208)(97,152,267,209)(98,153,268,210)(99,154,269,169)(100,155,270,170)(101,156,271,171)(102,157,272,172)(103,158,273,173)(104,159,274,174)(105,160,275,175)(106,161,276,176)(107,162,277,177)(108,163,278,178)(109,164,279,179)(110,165,280,180)(111,166,281,181)(112,167,282,182)(113,168,283,183)(114,127,284,184)(115,128,285,185)(116,129,286,186)(117,130,287,187)(118,131,288,188)(119,132,289,189)(120,133,290,190)(121,134,291,191)(122,135,292,192)(123,136,293,193)(124,137,294,194)(125,138,253,195)(126,139,254,196) );
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)], [(1,128,58,185),(2,129,59,186),(3,130,60,187),(4,131,61,188),(5,132,62,189),(6,133,63,190),(7,134,64,191),(8,135,65,192),(9,136,66,193),(10,137,67,194),(11,138,68,195),(12,139,69,196),(13,140,70,197),(14,141,71,198),(15,142,72,199),(16,143,73,200),(17,144,74,201),(18,145,75,202),(19,146,76,203),(20,147,77,204),(21,148,78,205),(22,149,79,206),(23,150,80,207),(24,151,81,208),(25,152,82,209),(26,153,83,210),(27,154,84,169),(28,155,43,170),(29,156,44,171),(30,157,45,172),(31,158,46,173),(32,159,47,174),(33,160,48,175),(34,161,49,176),(35,162,50,177),(36,163,51,178),(37,164,52,179),(38,165,53,180),(39,166,54,181),(40,167,55,182),(41,168,56,183),(42,127,57,184),(85,216,255,327),(86,217,256,328),(87,218,257,329),(88,219,258,330),(89,220,259,331),(90,221,260,332),(91,222,261,333),(92,223,262,334),(93,224,263,335),(94,225,264,336),(95,226,265,295),(96,227,266,296),(97,228,267,297),(98,229,268,298),(99,230,269,299),(100,231,270,300),(101,232,271,301),(102,233,272,302),(103,234,273,303),(104,235,274,304),(105,236,275,305),(106,237,276,306),(107,238,277,307),(108,239,278,308),(109,240,279,309),(110,241,280,310),(111,242,281,311),(112,243,282,312),(113,244,283,313),(114,245,284,314),(115,246,285,315),(116,247,286,316),(117,248,287,317),(118,249,288,318),(119,250,289,319),(120,251,290,320),(121,252,291,321),(122,211,292,322),(123,212,293,323),(124,213,294,324),(125,214,253,325),(126,215,254,326)], [(1,315,58,246),(2,316,59,247),(3,317,60,248),(4,318,61,249),(5,319,62,250),(6,320,63,251),(7,321,64,252),(8,322,65,211),(9,323,66,212),(10,324,67,213),(11,325,68,214),(12,326,69,215),(13,327,70,216),(14,328,71,217),(15,329,72,218),(16,330,73,219),(17,331,74,220),(18,332,75,221),(19,333,76,222),(20,334,77,223),(21,335,78,224),(22,336,79,225),(23,295,80,226),(24,296,81,227),(25,297,82,228),(26,298,83,229),(27,299,84,230),(28,300,43,231),(29,301,44,232),(30,302,45,233),(31,303,46,234),(32,304,47,235),(33,305,48,236),(34,306,49,237),(35,307,50,238),(36,308,51,239),(37,309,52,240),(38,310,53,241),(39,311,54,242),(40,312,55,243),(41,313,56,244),(42,314,57,245),(85,140,255,197),(86,141,256,198),(87,142,257,199),(88,143,258,200),(89,144,259,201),(90,145,260,202),(91,146,261,203),(92,147,262,204),(93,148,263,205),(94,149,264,206),(95,150,265,207),(96,151,266,208),(97,152,267,209),(98,153,268,210),(99,154,269,169),(100,155,270,170),(101,156,271,171),(102,157,272,172),(103,158,273,173),(104,159,274,174),(105,160,275,175),(106,161,276,176),(107,162,277,177),(108,163,278,178),(109,164,279,179),(110,165,280,180),(111,166,281,181),(112,167,282,182),(113,168,283,183),(114,127,284,184),(115,128,285,185),(116,129,286,186),(117,130,287,187),(118,131,288,188),(119,132,289,189),(120,133,290,190),(121,134,291,191),(122,135,292,192),(123,136,293,193),(124,137,294,194),(125,138,253,195),(126,139,254,196)]])
210 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 4A | ··· | 4F | 6A | ··· | 6F | 7A | ··· | 7F | 12A | ··· | 12L | 14A | ··· | 14R | 21A | ··· | 21L | 28A | ··· | 28AJ | 42A | ··· | 42AJ | 84A | ··· | 84BT |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | ··· | 4 | 6 | ··· | 6 | 7 | ··· | 7 | 12 | ··· | 12 | 14 | ··· | 14 | 21 | ··· | 21 | 28 | ··· | 28 | 42 | ··· | 42 | 84 | ··· | 84 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 |
210 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||||||||
| image | C1 | C2 | C2 | C3 | C6 | C6 | C7 | C14 | C14 | C21 | C42 | C42 | Q8 | C3×Q8 | C7×Q8 | Q8×C21 |
| kernel | Q8×C42 | C2×C84 | Q8×C21 | Q8×C14 | C2×C28 | C7×Q8 | C6×Q8 | C2×C12 | C3×Q8 | C2×Q8 | C2×C4 | Q8 | C42 | C14 | C6 | C2 |
| # reps | 1 | 3 | 4 | 2 | 6 | 8 | 6 | 18 | 24 | 12 | 36 | 48 | 2 | 4 | 12 | 24 |
Matrix representation of Q8×C42 ►in GL4(𝔽337) generated by
| 273 | 0 | 0 | 0 |
| 0 | 209 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 336 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 336 |
| 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 336 | 0 | 0 |
| 0 | 0 | 285 | 230 |
| 0 | 0 | 230 | 52 |
G:=sub<GL(4,GF(337))| [273,0,0,0,0,209,0,0,0,0,1,0,0,0,0,1],[336,0,0,0,0,1,0,0,0,0,0,1,0,0,336,0],[1,0,0,0,0,336,0,0,0,0,285,230,0,0,230,52] >;
Q8×C42 in GAP, Magma, Sage, TeX
Q_8\times C_{42} % in TeX
G:=Group("Q8xC42"); // GroupNames label
G:=SmallGroup(336,206);
// by ID
G=gap.SmallGroup(336,206);
# by ID
G:=PCGroup([6,-2,-2,-2,-3,-7,-2,1008,2041,1015]);
// Polycyclic
G:=Group<a,b,c|a^42=b^4=1,c^2=b^2,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations