metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.4Q8, C42.32D4, Dic21⋊1C4, C2.1Dic42, C6.4Dic14, C14.4Dic6, C22.4D42, C21⋊4(C4⋊C4), C6.8(C4×D7), C14.8(C4×S3), (C2×C84).3C2, (C2×C28).2S3, C2.4(C4×D21), (C2×C4).1D21, (C2×C12).2D7, C42.17(C2×C4), C3⋊3(Dic7⋊C4), C7⋊3(Dic3⋊C4), (C2×C14).22D6, (C2×C6).22D14, C6.14(C7⋊D4), C2.1(C21⋊7D4), C14.14(C3⋊D4), (C2×C42).23C22, (C2×Dic21).1C2, SmallGroup(336,98)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.4Q8
G = < a,b,c | a42=b4=1, c2=a21b2, ab=ba, cac-1=a-1, cbc-1=a21b-1 >
Smallest permutation representation of C42.4Q8
►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)
(1 145 216 120)(2 146 217 121)(3 147 218 122)(4 148 219 123)(5 149 220 124)(6 150 221 125)(7 151 222 126)(8 152 223 85)(9 153 224 86)(10 154 225 87)(11 155 226 88)(12 156 227 89)(13 157 228 90)(14 158 229 91)(15 159 230 92)(16 160 231 93)(17 161 232 94)(18 162 233 95)(19 163 234 96)(20 164 235 97)(21 165 236 98)(22 166 237 99)(23 167 238 100)(24 168 239 101)(25 127 240 102)(26 128 241 103)(27 129 242 104)(28 130 243 105)(29 131 244 106)(30 132 245 107)(31 133 246 108)(32 134 247 109)(33 135 248 110)(34 136 249 111)(35 137 250 112)(36 138 251 113)(37 139 252 114)(38 140 211 115)(39 141 212 116)(40 142 213 117)(41 143 214 118)(42 144 215 119)(43 262 180 314)(44 263 181 315)(45 264 182 316)(46 265 183 317)(47 266 184 318)(48 267 185 319)(49 268 186 320)(50 269 187 321)(51 270 188 322)(52 271 189 323)(53 272 190 324)(54 273 191 325)(55 274 192 326)(56 275 193 327)(57 276 194 328)(58 277 195 329)(59 278 196 330)(60 279 197 331)(61 280 198 332)(62 281 199 333)(63 282 200 334)(64 283 201 335)(65 284 202 336)(66 285 203 295)(67 286 204 296)(68 287 205 297)(69 288 206 298)(70 289 207 299)(71 290 208 300)(72 291 209 301)(73 292 210 302)(74 293 169 303)(75 294 170 304)(76 253 171 305)(77 254 172 306)(78 255 173 307)(79 256 174 308)(80 257 175 309)(81 258 176 310)(82 259 177 311)(83 260 178 312)(84 261 179 313)
(1 51 237 209)(2 50 238 208)(3 49 239 207)(4 48 240 206)(5 47 241 205)(6 46 242 204)(7 45 243 203)(8 44 244 202)(9 43 245 201)(10 84 246 200)(11 83 247 199)(12 82 248 198)(13 81 249 197)(14 80 250 196)(15 79 251 195)(16 78 252 194)(17 77 211 193)(18 76 212 192)(19 75 213 191)(20 74 214 190)(21 73 215 189)(22 72 216 188)(23 71 217 187)(24 70 218 186)(25 69 219 185)(26 68 220 184)(27 67 221 183)(28 66 222 182)(29 65 223 181)(30 64 224 180)(31 63 225 179)(32 62 226 178)(33 61 227 177)(34 60 228 176)(35 59 229 175)(36 58 230 174)(37 57 231 173)(38 56 232 172)(39 55 233 171)(40 54 234 170)(41 53 235 169)(42 52 236 210)(85 284 131 315)(86 283 132 314)(87 282 133 313)(88 281 134 312)(89 280 135 311)(90 279 136 310)(91 278 137 309)(92 277 138 308)(93 276 139 307)(94 275 140 306)(95 274 141 305)(96 273 142 304)(97 272 143 303)(98 271 144 302)(99 270 145 301)(100 269 146 300)(101 268 147 299)(102 267 148 298)(103 266 149 297)(104 265 150 296)(105 264 151 295)(106 263 152 336)(107 262 153 335)(108 261 154 334)(109 260 155 333)(110 259 156 332)(111 258 157 331)(112 257 158 330)(113 256 159 329)(114 255 160 328)(115 254 161 327)(116 253 162 326)(117 294 163 325)(118 293 164 324)(119 292 165 323)(120 291 166 322)(121 290 167 321)(122 289 168 320)(123 288 127 319)(124 287 128 318)(125 286 129 317)(126 285 130 316)
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), (1,145,216,120)(2,146,217,121)(3,147,218,122)(4,148,219,123)(5,149,220,124)(6,150,221,125)(7,151,222,126)(8,152,223,85)(9,153,224,86)(10,154,225,87)(11,155,226,88)(12,156,227,89)(13,157,228,90)(14,158,229,91)(15,159,230,92)(16,160,231,93)(17,161,232,94)(18,162,233,95)(19,163,234,96)(20,164,235,97)(21,165,236,98)(22,166,237,99)(23,167,238,100)(24,168,239,101)(25,127,240,102)(26,128,241,103)(27,129,242,104)(28,130,243,105)(29,131,244,106)(30,132,245,107)(31,133,246,108)(32,134,247,109)(33,135,248,110)(34,136,249,111)(35,137,250,112)(36,138,251,113)(37,139,252,114)(38,140,211,115)(39,141,212,116)(40,142,213,117)(41,143,214,118)(42,144,215,119)(43,262,180,314)(44,263,181,315)(45,264,182,316)(46,265,183,317)(47,266,184,318)(48,267,185,319)(49,268,186,320)(50,269,187,321)(51,270,188,322)(52,271,189,323)(53,272,190,324)(54,273,191,325)(55,274,192,326)(56,275,193,327)(57,276,194,328)(58,277,195,329)(59,278,196,330)(60,279,197,331)(61,280,198,332)(62,281,199,333)(63,282,200,334)(64,283,201,335)(65,284,202,336)(66,285,203,295)(67,286,204,296)(68,287,205,297)(69,288,206,298)(70,289,207,299)(71,290,208,300)(72,291,209,301)(73,292,210,302)(74,293,169,303)(75,294,170,304)(76,253,171,305)(77,254,172,306)(78,255,173,307)(79,256,174,308)(80,257,175,309)(81,258,176,310)(82,259,177,311)(83,260,178,312)(84,261,179,313), (1,51,237,209)(2,50,238,208)(3,49,239,207)(4,48,240,206)(5,47,241,205)(6,46,242,204)(7,45,243,203)(8,44,244,202)(9,43,245,201)(10,84,246,200)(11,83,247,199)(12,82,248,198)(13,81,249,197)(14,80,250,196)(15,79,251,195)(16,78,252,194)(17,77,211,193)(18,76,212,192)(19,75,213,191)(20,74,214,190)(21,73,215,189)(22,72,216,188)(23,71,217,187)(24,70,218,186)(25,69,219,185)(26,68,220,184)(27,67,221,183)(28,66,222,182)(29,65,223,181)(30,64,224,180)(31,63,225,179)(32,62,226,178)(33,61,227,177)(34,60,228,176)(35,59,229,175)(36,58,230,174)(37,57,231,173)(38,56,232,172)(39,55,233,171)(40,54,234,170)(41,53,235,169)(42,52,236,210)(85,284,131,315)(86,283,132,314)(87,282,133,313)(88,281,134,312)(89,280,135,311)(90,279,136,310)(91,278,137,309)(92,277,138,308)(93,276,139,307)(94,275,140,306)(95,274,141,305)(96,273,142,304)(97,272,143,303)(98,271,144,302)(99,270,145,301)(100,269,146,300)(101,268,147,299)(102,267,148,298)(103,266,149,297)(104,265,150,296)(105,264,151,295)(106,263,152,336)(107,262,153,335)(108,261,154,334)(109,260,155,333)(110,259,156,332)(111,258,157,331)(112,257,158,330)(113,256,159,329)(114,255,160,328)(115,254,161,327)(116,253,162,326)(117,294,163,325)(118,293,164,324)(119,292,165,323)(120,291,166,322)(121,290,167,321)(122,289,168,320)(123,288,127,319)(124,287,128,318)(125,286,129,317)(126,285,130,316)>;
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), (1,145,216,120)(2,146,217,121)(3,147,218,122)(4,148,219,123)(5,149,220,124)(6,150,221,125)(7,151,222,126)(8,152,223,85)(9,153,224,86)(10,154,225,87)(11,155,226,88)(12,156,227,89)(13,157,228,90)(14,158,229,91)(15,159,230,92)(16,160,231,93)(17,161,232,94)(18,162,233,95)(19,163,234,96)(20,164,235,97)(21,165,236,98)(22,166,237,99)(23,167,238,100)(24,168,239,101)(25,127,240,102)(26,128,241,103)(27,129,242,104)(28,130,243,105)(29,131,244,106)(30,132,245,107)(31,133,246,108)(32,134,247,109)(33,135,248,110)(34,136,249,111)(35,137,250,112)(36,138,251,113)(37,139,252,114)(38,140,211,115)(39,141,212,116)(40,142,213,117)(41,143,214,118)(42,144,215,119)(43,262,180,314)(44,263,181,315)(45,264,182,316)(46,265,183,317)(47,266,184,318)(48,267,185,319)(49,268,186,320)(50,269,187,321)(51,270,188,322)(52,271,189,323)(53,272,190,324)(54,273,191,325)(55,274,192,326)(56,275,193,327)(57,276,194,328)(58,277,195,329)(59,278,196,330)(60,279,197,331)(61,280,198,332)(62,281,199,333)(63,282,200,334)(64,283,201,335)(65,284,202,336)(66,285,203,295)(67,286,204,296)(68,287,205,297)(69,288,206,298)(70,289,207,299)(71,290,208,300)(72,291,209,301)(73,292,210,302)(74,293,169,303)(75,294,170,304)(76,253,171,305)(77,254,172,306)(78,255,173,307)(79,256,174,308)(80,257,175,309)(81,258,176,310)(82,259,177,311)(83,260,178,312)(84,261,179,313), (1,51,237,209)(2,50,238,208)(3,49,239,207)(4,48,240,206)(5,47,241,205)(6,46,242,204)(7,45,243,203)(8,44,244,202)(9,43,245,201)(10,84,246,200)(11,83,247,199)(12,82,248,198)(13,81,249,197)(14,80,250,196)(15,79,251,195)(16,78,252,194)(17,77,211,193)(18,76,212,192)(19,75,213,191)(20,74,214,190)(21,73,215,189)(22,72,216,188)(23,71,217,187)(24,70,218,186)(25,69,219,185)(26,68,220,184)(27,67,221,183)(28,66,222,182)(29,65,223,181)(30,64,224,180)(31,63,225,179)(32,62,226,178)(33,61,227,177)(34,60,228,176)(35,59,229,175)(36,58,230,174)(37,57,231,173)(38,56,232,172)(39,55,233,171)(40,54,234,170)(41,53,235,169)(42,52,236,210)(85,284,131,315)(86,283,132,314)(87,282,133,313)(88,281,134,312)(89,280,135,311)(90,279,136,310)(91,278,137,309)(92,277,138,308)(93,276,139,307)(94,275,140,306)(95,274,141,305)(96,273,142,304)(97,272,143,303)(98,271,144,302)(99,270,145,301)(100,269,146,300)(101,268,147,299)(102,267,148,298)(103,266,149,297)(104,265,150,296)(105,264,151,295)(106,263,152,336)(107,262,153,335)(108,261,154,334)(109,260,155,333)(110,259,156,332)(111,258,157,331)(112,257,158,330)(113,256,159,329)(114,255,160,328)(115,254,161,327)(116,253,162,326)(117,294,163,325)(118,293,164,324)(119,292,165,323)(120,291,166,322)(121,290,167,321)(122,289,168,320)(123,288,127,319)(124,287,128,318)(125,286,129,317)(126,285,130,316) );
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)], [(1,145,216,120),(2,146,217,121),(3,147,218,122),(4,148,219,123),(5,149,220,124),(6,150,221,125),(7,151,222,126),(8,152,223,85),(9,153,224,86),(10,154,225,87),(11,155,226,88),(12,156,227,89),(13,157,228,90),(14,158,229,91),(15,159,230,92),(16,160,231,93),(17,161,232,94),(18,162,233,95),(19,163,234,96),(20,164,235,97),(21,165,236,98),(22,166,237,99),(23,167,238,100),(24,168,239,101),(25,127,240,102),(26,128,241,103),(27,129,242,104),(28,130,243,105),(29,131,244,106),(30,132,245,107),(31,133,246,108),(32,134,247,109),(33,135,248,110),(34,136,249,111),(35,137,250,112),(36,138,251,113),(37,139,252,114),(38,140,211,115),(39,141,212,116),(40,142,213,117),(41,143,214,118),(42,144,215,119),(43,262,180,314),(44,263,181,315),(45,264,182,316),(46,265,183,317),(47,266,184,318),(48,267,185,319),(49,268,186,320),(50,269,187,321),(51,270,188,322),(52,271,189,323),(53,272,190,324),(54,273,191,325),(55,274,192,326),(56,275,193,327),(57,276,194,328),(58,277,195,329),(59,278,196,330),(60,279,197,331),(61,280,198,332),(62,281,199,333),(63,282,200,334),(64,283,201,335),(65,284,202,336),(66,285,203,295),(67,286,204,296),(68,287,205,297),(69,288,206,298),(70,289,207,299),(71,290,208,300),(72,291,209,301),(73,292,210,302),(74,293,169,303),(75,294,170,304),(76,253,171,305),(77,254,172,306),(78,255,173,307),(79,256,174,308),(80,257,175,309),(81,258,176,310),(82,259,177,311),(83,260,178,312),(84,261,179,313)], [(1,51,237,209),(2,50,238,208),(3,49,239,207),(4,48,240,206),(5,47,241,205),(6,46,242,204),(7,45,243,203),(8,44,244,202),(9,43,245,201),(10,84,246,200),(11,83,247,199),(12,82,248,198),(13,81,249,197),(14,80,250,196),(15,79,251,195),(16,78,252,194),(17,77,211,193),(18,76,212,192),(19,75,213,191),(20,74,214,190),(21,73,215,189),(22,72,216,188),(23,71,217,187),(24,70,218,186),(25,69,219,185),(26,68,220,184),(27,67,221,183),(28,66,222,182),(29,65,223,181),(30,64,224,180),(31,63,225,179),(32,62,226,178),(33,61,227,177),(34,60,228,176),(35,59,229,175),(36,58,230,174),(37,57,231,173),(38,56,232,172),(39,55,233,171),(40,54,234,170),(41,53,235,169),(42,52,236,210),(85,284,131,315),(86,283,132,314),(87,282,133,313),(88,281,134,312),(89,280,135,311),(90,279,136,310),(91,278,137,309),(92,277,138,308),(93,276,139,307),(94,275,140,306),(95,274,141,305),(96,273,142,304),(97,272,143,303),(98,271,144,302),(99,270,145,301),(100,269,146,300),(101,268,147,299),(102,267,148,298),(103,266,149,297),(104,265,150,296),(105,264,151,295),(106,263,152,336),(107,262,153,335),(108,261,154,334),(109,260,155,333),(110,259,156,332),(111,258,157,331),(112,257,158,330),(113,256,159,329),(114,255,160,328),(115,254,161,327),(116,253,162,326),(117,294,163,325),(118,293,164,324),(119,292,165,323),(120,291,166,322),(121,290,167,321),(122,289,168,320),(123,288,127,319),(124,287,128,318),(125,286,129,317),(126,285,130,316)]])
90 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 6A | 6B | 6C | 7A | 7B | 7C | 12A | 12B | 12C | 12D | 14A | ··· | 14I | 21A | ··· | 21F | 28A | ··· | 28L | 42A | ··· | 42R | 84A | ··· | 84X |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 6 | 6 | 7 | 7 | 7 | 12 | 12 | 12 | 12 | 14 | ··· | 14 | 21 | ··· | 21 | 28 | ··· | 28 | 42 | ··· | 42 | 84 | ··· | 84 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 42 | 42 | 42 | 42 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
90 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | + | - | + | + | - | + | - | |||||||
| image | C1 | C2 | C2 | C4 | S3 | D4 | Q8 | D6 | D7 | Dic6 | C4×S3 | C3⋊D4 | D14 | D21 | Dic14 | C4×D7 | C7⋊D4 | D42 | Dic42 | C4×D21 | C21⋊7D4 |
| kernel | C42.4Q8 | C2×Dic21 | C2×C84 | Dic21 | C2×C28 | C42 | C42 | C2×C14 | C2×C12 | C14 | C14 | C14 | C2×C6 | C2×C4 | C6 | C6 | C6 | C22 | C2 | C2 | C2 |
| # reps | 1 | 2 | 1 | 4 | 1 | 1 | 1 | 1 | 3 | 2 | 2 | 2 | 3 | 6 | 6 | 6 | 6 | 6 | 12 | 12 | 12 |
Matrix representation of C42.4Q8 ►in GL4(𝔽337) generated by
| 336 | 336 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 193 | 1 |
| 0 | 0 | 192 | 1 |
| 15 | 30 | 0 | 0 |
| 307 | 322 | 0 | 0 |
| 0 | 0 | 122 | 247 |
| 0 | 0 | 244 | 215 |
| 205 | 28 | 0 | 0 |
| 160 | 132 | 0 | 0 |
| 0 | 0 | 236 | 56 |
| 0 | 0 | 215 | 101 |
G:=sub<GL(4,GF(337))| [336,1,0,0,336,0,0,0,0,0,193,192,0,0,1,1],[15,307,0,0,30,322,0,0,0,0,122,244,0,0,247,215],[205,160,0,0,28,132,0,0,0,0,236,215,0,0,56,101] >;
C42.4Q8 in GAP, Magma, Sage, TeX
C_{42}._4Q_8 % in TeX
G:=Group("C42.4Q8"); // GroupNames label
G:=SmallGroup(336,98);
// by ID
G=gap.SmallGroup(336,98);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-3,-7,48,121,31,964,10373]);
// Polycyclic
G:=Group<a,b,c|a^42=b^4=1,c^2=a^21*b^2,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=a^21*b^-1>;
// generators/relations
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