metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.1Q8, Dic7⋊Dic3, C42.16D4, C14.12D12, C6.1Dic14, C14.1Dic6, C21⋊1(C4⋊C4), C7⋊1(C4⋊Dic3), (C2×C14).9D6, C6.14(C4×D7), (C2×C6).9D14, C2.1(C21⋊Q8), C42.11(C2×C4), C3⋊1(Dic7⋊C4), (C3×Dic7)⋊2C4, C6.6(C7⋊D4), C2.5(Dic3×D7), C22.8(S3×D7), C2.3(C7⋊D12), (C2×C42).6C22, (C6×Dic7).2C2, (C2×Dic3).1D7, (C2×Dic7).1S3, C14.5(C2×Dic3), (Dic3×C14).2C2, (C2×Dic21).5C2, SmallGroup(336,45)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.Q8
G = < a,b,c | a42=b4=1, c2=a21b2, bab-1=a29, cac-1=a13, cbc-1=a21b-1 >
Smallest permutation representation of C42.Q8
►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)
(1 162 48 121)(2 149 49 108)(3 136 50 95)(4 165 51 124)(5 152 52 111)(6 139 53 98)(7 168 54 85)(8 155 55 114)(9 142 56 101)(10 129 57 88)(11 158 58 117)(12 145 59 104)(13 132 60 91)(14 161 61 120)(15 148 62 107)(16 135 63 94)(17 164 64 123)(18 151 65 110)(19 138 66 97)(20 167 67 126)(21 154 68 113)(22 141 69 100)(23 128 70 87)(24 157 71 116)(25 144 72 103)(26 131 73 90)(27 160 74 119)(28 147 75 106)(29 134 76 93)(30 163 77 122)(31 150 78 109)(32 137 79 96)(33 166 80 125)(34 153 81 112)(35 140 82 99)(36 127 83 86)(37 156 84 115)(38 143 43 102)(39 130 44 89)(40 159 45 118)(41 146 46 105)(42 133 47 92)(169 310 234 269)(170 297 235 256)(171 326 236 285)(172 313 237 272)(173 300 238 259)(174 329 239 288)(175 316 240 275)(176 303 241 262)(177 332 242 291)(178 319 243 278)(179 306 244 265)(180 335 245 294)(181 322 246 281)(182 309 247 268)(183 296 248 255)(184 325 249 284)(185 312 250 271)(186 299 251 258)(187 328 252 287)(188 315 211 274)(189 302 212 261)(190 331 213 290)(191 318 214 277)(192 305 215 264)(193 334 216 293)(194 321 217 280)(195 308 218 267)(196 295 219 254)(197 324 220 283)(198 311 221 270)(199 298 222 257)(200 327 223 286)(201 314 224 273)(202 301 225 260)(203 330 226 289)(204 317 227 276)(205 304 228 263)(206 333 229 292)(207 320 230 279)(208 307 231 266)(209 336 232 253)(210 323 233 282)
(1 199 69 243)(2 170 70 214)(3 183 71 227)(4 196 72 240)(5 209 73 211)(6 180 74 224)(7 193 75 237)(8 206 76 250)(9 177 77 221)(10 190 78 234)(11 203 79 247)(12 174 80 218)(13 187 81 231)(14 200 82 244)(15 171 83 215)(16 184 84 228)(17 197 43 241)(18 210 44 212)(19 181 45 225)(20 194 46 238)(21 207 47 251)(22 178 48 222)(23 191 49 235)(24 204 50 248)(25 175 51 219)(26 188 52 232)(27 201 53 245)(28 172 54 216)(29 185 55 229)(30 198 56 242)(31 169 57 213)(32 182 58 226)(33 195 59 239)(34 208 60 252)(35 179 61 223)(36 192 62 236)(37 205 63 249)(38 176 64 220)(39 189 65 233)(40 202 66 246)(41 173 67 217)(42 186 68 230)(85 313 147 293)(86 326 148 264)(87 297 149 277)(88 310 150 290)(89 323 151 261)(90 336 152 274)(91 307 153 287)(92 320 154 258)(93 333 155 271)(94 304 156 284)(95 317 157 255)(96 330 158 268)(97 301 159 281)(98 314 160 294)(99 327 161 265)(100 298 162 278)(101 311 163 291)(102 324 164 262)(103 295 165 275)(104 308 166 288)(105 321 167 259)(106 334 168 272)(107 305 127 285)(108 318 128 256)(109 331 129 269)(110 302 130 282)(111 315 131 253)(112 328 132 266)(113 299 133 279)(114 312 134 292)(115 325 135 263)(116 296 136 276)(117 309 137 289)(118 322 138 260)(119 335 139 273)(120 306 140 286)(121 319 141 257)(122 332 142 270)(123 303 143 283)(124 316 144 254)(125 329 145 267)(126 300 146 280)
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), (1,162,48,121)(2,149,49,108)(3,136,50,95)(4,165,51,124)(5,152,52,111)(6,139,53,98)(7,168,54,85)(8,155,55,114)(9,142,56,101)(10,129,57,88)(11,158,58,117)(12,145,59,104)(13,132,60,91)(14,161,61,120)(15,148,62,107)(16,135,63,94)(17,164,64,123)(18,151,65,110)(19,138,66,97)(20,167,67,126)(21,154,68,113)(22,141,69,100)(23,128,70,87)(24,157,71,116)(25,144,72,103)(26,131,73,90)(27,160,74,119)(28,147,75,106)(29,134,76,93)(30,163,77,122)(31,150,78,109)(32,137,79,96)(33,166,80,125)(34,153,81,112)(35,140,82,99)(36,127,83,86)(37,156,84,115)(38,143,43,102)(39,130,44,89)(40,159,45,118)(41,146,46,105)(42,133,47,92)(169,310,234,269)(170,297,235,256)(171,326,236,285)(172,313,237,272)(173,300,238,259)(174,329,239,288)(175,316,240,275)(176,303,241,262)(177,332,242,291)(178,319,243,278)(179,306,244,265)(180,335,245,294)(181,322,246,281)(182,309,247,268)(183,296,248,255)(184,325,249,284)(185,312,250,271)(186,299,251,258)(187,328,252,287)(188,315,211,274)(189,302,212,261)(190,331,213,290)(191,318,214,277)(192,305,215,264)(193,334,216,293)(194,321,217,280)(195,308,218,267)(196,295,219,254)(197,324,220,283)(198,311,221,270)(199,298,222,257)(200,327,223,286)(201,314,224,273)(202,301,225,260)(203,330,226,289)(204,317,227,276)(205,304,228,263)(206,333,229,292)(207,320,230,279)(208,307,231,266)(209,336,232,253)(210,323,233,282), (1,199,69,243)(2,170,70,214)(3,183,71,227)(4,196,72,240)(5,209,73,211)(6,180,74,224)(7,193,75,237)(8,206,76,250)(9,177,77,221)(10,190,78,234)(11,203,79,247)(12,174,80,218)(13,187,81,231)(14,200,82,244)(15,171,83,215)(16,184,84,228)(17,197,43,241)(18,210,44,212)(19,181,45,225)(20,194,46,238)(21,207,47,251)(22,178,48,222)(23,191,49,235)(24,204,50,248)(25,175,51,219)(26,188,52,232)(27,201,53,245)(28,172,54,216)(29,185,55,229)(30,198,56,242)(31,169,57,213)(32,182,58,226)(33,195,59,239)(34,208,60,252)(35,179,61,223)(36,192,62,236)(37,205,63,249)(38,176,64,220)(39,189,65,233)(40,202,66,246)(41,173,67,217)(42,186,68,230)(85,313,147,293)(86,326,148,264)(87,297,149,277)(88,310,150,290)(89,323,151,261)(90,336,152,274)(91,307,153,287)(92,320,154,258)(93,333,155,271)(94,304,156,284)(95,317,157,255)(96,330,158,268)(97,301,159,281)(98,314,160,294)(99,327,161,265)(100,298,162,278)(101,311,163,291)(102,324,164,262)(103,295,165,275)(104,308,166,288)(105,321,167,259)(106,334,168,272)(107,305,127,285)(108,318,128,256)(109,331,129,269)(110,302,130,282)(111,315,131,253)(112,328,132,266)(113,299,133,279)(114,312,134,292)(115,325,135,263)(116,296,136,276)(117,309,137,289)(118,322,138,260)(119,335,139,273)(120,306,140,286)(121,319,141,257)(122,332,142,270)(123,303,143,283)(124,316,144,254)(125,329,145,267)(126,300,146,280)>;
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), (1,162,48,121)(2,149,49,108)(3,136,50,95)(4,165,51,124)(5,152,52,111)(6,139,53,98)(7,168,54,85)(8,155,55,114)(9,142,56,101)(10,129,57,88)(11,158,58,117)(12,145,59,104)(13,132,60,91)(14,161,61,120)(15,148,62,107)(16,135,63,94)(17,164,64,123)(18,151,65,110)(19,138,66,97)(20,167,67,126)(21,154,68,113)(22,141,69,100)(23,128,70,87)(24,157,71,116)(25,144,72,103)(26,131,73,90)(27,160,74,119)(28,147,75,106)(29,134,76,93)(30,163,77,122)(31,150,78,109)(32,137,79,96)(33,166,80,125)(34,153,81,112)(35,140,82,99)(36,127,83,86)(37,156,84,115)(38,143,43,102)(39,130,44,89)(40,159,45,118)(41,146,46,105)(42,133,47,92)(169,310,234,269)(170,297,235,256)(171,326,236,285)(172,313,237,272)(173,300,238,259)(174,329,239,288)(175,316,240,275)(176,303,241,262)(177,332,242,291)(178,319,243,278)(179,306,244,265)(180,335,245,294)(181,322,246,281)(182,309,247,268)(183,296,248,255)(184,325,249,284)(185,312,250,271)(186,299,251,258)(187,328,252,287)(188,315,211,274)(189,302,212,261)(190,331,213,290)(191,318,214,277)(192,305,215,264)(193,334,216,293)(194,321,217,280)(195,308,218,267)(196,295,219,254)(197,324,220,283)(198,311,221,270)(199,298,222,257)(200,327,223,286)(201,314,224,273)(202,301,225,260)(203,330,226,289)(204,317,227,276)(205,304,228,263)(206,333,229,292)(207,320,230,279)(208,307,231,266)(209,336,232,253)(210,323,233,282), (1,199,69,243)(2,170,70,214)(3,183,71,227)(4,196,72,240)(5,209,73,211)(6,180,74,224)(7,193,75,237)(8,206,76,250)(9,177,77,221)(10,190,78,234)(11,203,79,247)(12,174,80,218)(13,187,81,231)(14,200,82,244)(15,171,83,215)(16,184,84,228)(17,197,43,241)(18,210,44,212)(19,181,45,225)(20,194,46,238)(21,207,47,251)(22,178,48,222)(23,191,49,235)(24,204,50,248)(25,175,51,219)(26,188,52,232)(27,201,53,245)(28,172,54,216)(29,185,55,229)(30,198,56,242)(31,169,57,213)(32,182,58,226)(33,195,59,239)(34,208,60,252)(35,179,61,223)(36,192,62,236)(37,205,63,249)(38,176,64,220)(39,189,65,233)(40,202,66,246)(41,173,67,217)(42,186,68,230)(85,313,147,293)(86,326,148,264)(87,297,149,277)(88,310,150,290)(89,323,151,261)(90,336,152,274)(91,307,153,287)(92,320,154,258)(93,333,155,271)(94,304,156,284)(95,317,157,255)(96,330,158,268)(97,301,159,281)(98,314,160,294)(99,327,161,265)(100,298,162,278)(101,311,163,291)(102,324,164,262)(103,295,165,275)(104,308,166,288)(105,321,167,259)(106,334,168,272)(107,305,127,285)(108,318,128,256)(109,331,129,269)(110,302,130,282)(111,315,131,253)(112,328,132,266)(113,299,133,279)(114,312,134,292)(115,325,135,263)(116,296,136,276)(117,309,137,289)(118,322,138,260)(119,335,139,273)(120,306,140,286)(121,319,141,257)(122,332,142,270)(123,303,143,283)(124,316,144,254)(125,329,145,267)(126,300,146,280) );
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)], [(1,162,48,121),(2,149,49,108),(3,136,50,95),(4,165,51,124),(5,152,52,111),(6,139,53,98),(7,168,54,85),(8,155,55,114),(9,142,56,101),(10,129,57,88),(11,158,58,117),(12,145,59,104),(13,132,60,91),(14,161,61,120),(15,148,62,107),(16,135,63,94),(17,164,64,123),(18,151,65,110),(19,138,66,97),(20,167,67,126),(21,154,68,113),(22,141,69,100),(23,128,70,87),(24,157,71,116),(25,144,72,103),(26,131,73,90),(27,160,74,119),(28,147,75,106),(29,134,76,93),(30,163,77,122),(31,150,78,109),(32,137,79,96),(33,166,80,125),(34,153,81,112),(35,140,82,99),(36,127,83,86),(37,156,84,115),(38,143,43,102),(39,130,44,89),(40,159,45,118),(41,146,46,105),(42,133,47,92),(169,310,234,269),(170,297,235,256),(171,326,236,285),(172,313,237,272),(173,300,238,259),(174,329,239,288),(175,316,240,275),(176,303,241,262),(177,332,242,291),(178,319,243,278),(179,306,244,265),(180,335,245,294),(181,322,246,281),(182,309,247,268),(183,296,248,255),(184,325,249,284),(185,312,250,271),(186,299,251,258),(187,328,252,287),(188,315,211,274),(189,302,212,261),(190,331,213,290),(191,318,214,277),(192,305,215,264),(193,334,216,293),(194,321,217,280),(195,308,218,267),(196,295,219,254),(197,324,220,283),(198,311,221,270),(199,298,222,257),(200,327,223,286),(201,314,224,273),(202,301,225,260),(203,330,226,289),(204,317,227,276),(205,304,228,263),(206,333,229,292),(207,320,230,279),(208,307,231,266),(209,336,232,253),(210,323,233,282)], [(1,199,69,243),(2,170,70,214),(3,183,71,227),(4,196,72,240),(5,209,73,211),(6,180,74,224),(7,193,75,237),(8,206,76,250),(9,177,77,221),(10,190,78,234),(11,203,79,247),(12,174,80,218),(13,187,81,231),(14,200,82,244),(15,171,83,215),(16,184,84,228),(17,197,43,241),(18,210,44,212),(19,181,45,225),(20,194,46,238),(21,207,47,251),(22,178,48,222),(23,191,49,235),(24,204,50,248),(25,175,51,219),(26,188,52,232),(27,201,53,245),(28,172,54,216),(29,185,55,229),(30,198,56,242),(31,169,57,213),(32,182,58,226),(33,195,59,239),(34,208,60,252),(35,179,61,223),(36,192,62,236),(37,205,63,249),(38,176,64,220),(39,189,65,233),(40,202,66,246),(41,173,67,217),(42,186,68,230),(85,313,147,293),(86,326,148,264),(87,297,149,277),(88,310,150,290),(89,323,151,261),(90,336,152,274),(91,307,153,287),(92,320,154,258),(93,333,155,271),(94,304,156,284),(95,317,157,255),(96,330,158,268),(97,301,159,281),(98,314,160,294),(99,327,161,265),(100,298,162,278),(101,311,163,291),(102,324,164,262),(103,295,165,275),(104,308,166,288),(105,321,167,259),(106,334,168,272),(107,305,127,285),(108,318,128,256),(109,331,129,269),(110,302,130,282),(111,315,131,253),(112,328,132,266),(113,299,133,279),(114,312,134,292),(115,325,135,263),(116,296,136,276),(117,309,137,289),(118,322,138,260),(119,335,139,273),(120,306,140,286),(121,319,141,257),(122,332,142,270),(123,303,143,283),(124,316,144,254),(125,329,145,267),(126,300,146,280)]])
54 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 | 21B | 21C | 28A | ··· | 28L | 42A | ··· | 42I |
| 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 | 21 | 28 | ··· | 28 | 42 | ··· | 42 |
| size | 1 | 1 | 1 | 1 | 2 | 6 | 6 | 14 | 14 | 42 | 42 | 2 | 2 | 2 | 2 | 2 | 2 | 14 | 14 | 14 | 14 | 2 | ··· | 2 | 4 | 4 | 4 | 6 | ··· | 6 | 4 | ··· | 4 |
54 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | - | + | + | - | + | + | - | + | - | + | - | |||
| image | C1 | C2 | C2 | C2 | C4 | S3 | D4 | Q8 | Dic3 | D6 | D7 | Dic6 | D12 | D14 | Dic14 | C4×D7 | C7⋊D4 | S3×D7 | Dic3×D7 | C7⋊D12 | C21⋊Q8 |
| kernel | C42.Q8 | C6×Dic7 | Dic3×C14 | C2×Dic21 | C3×Dic7 | C2×Dic7 | C42 | C42 | Dic7 | C2×C14 | C2×Dic3 | C14 | C14 | C2×C6 | C6 | C6 | C6 | C22 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 1 | 2 | 1 | 3 | 2 | 2 | 3 | 6 | 6 | 6 | 3 | 3 | 3 | 3 |
Matrix representation of C42.Q8 ►in GL4(𝔽337) generated by
| 303 | 336 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 336 | 196 |
| 0 | 0 | 294 | 2 |
| 195 | 289 | 0 | 0 |
| 48 | 142 | 0 | 0 |
| 0 | 0 | 71 | 199 |
| 0 | 0 | 227 | 266 |
| 123 | 36 | 0 | 0 |
| 235 | 214 | 0 | 0 |
| 0 | 0 | 45 | 186 |
| 0 | 0 | 279 | 292 |
G:=sub<GL(4,GF(337))| [303,1,0,0,336,0,0,0,0,0,336,294,0,0,196,2],[195,48,0,0,289,142,0,0,0,0,71,227,0,0,199,266],[123,235,0,0,36,214,0,0,0,0,45,279,0,0,186,292] >;
C42.Q8 in GAP, Magma, Sage, TeX
C_{42}.Q_8 % in TeX
G:=Group("C42.Q8"); // GroupNames label
G:=SmallGroup(336,45);
// by ID
G=gap.SmallGroup(336,45);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-3,-7,48,121,31,490,10373]);
// Polycyclic
G:=Group<a,b,c|a^42=b^4=1,c^2=a^21*b^2,b*a*b^-1=a^29,c*a*c^-1=a^13,c*b*c^-1=a^21*b^-1>;
// generators/relations
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