direct product, metacyclic, nilpotent (class 2), monomial, 2-elementary
Aliases: C4⋊C4×C21, C4⋊C84, C84⋊7C4, C12⋊3C28, C28⋊7C12, C42.53D4, C42.10Q8, C2.(Q8×C21), C6.3(C7×Q8), (C2×C84).4C2, (C2×C4).1C42, C2.2(C2×C84), C2.2(D4×C21), C6.13(C7×D4), C14.6(C3×Q8), (C2×C12).2C14, C6.11(C2×C28), C42.42(C2×C4), (C2×C28).13C6, C14.29(C3×D4), C14.25(C2×C12), C22.3(C2×C42), (C2×C42).53C22, (C2×C14).31(C2×C6), (C2×C6).14(C2×C14), SmallGroup(336,108)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊C4×C21
G = < a,b,c | a21=b4=c4=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C4⋊C4×C21
►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)
(1 107 158 309)(2 108 159 310)(3 109 160 311)(4 110 161 312)(5 111 162 313)(6 112 163 314)(7 113 164 315)(8 114 165 295)(9 115 166 296)(10 116 167 297)(11 117 168 298)(12 118 148 299)(13 119 149 300)(14 120 150 301)(15 121 151 302)(16 122 152 303)(17 123 153 304)(18 124 154 305)(19 125 155 306)(20 126 156 307)(21 106 157 308)(22 322 144 245)(23 323 145 246)(24 324 146 247)(25 325 147 248)(26 326 127 249)(27 327 128 250)(28 328 129 251)(29 329 130 252)(30 330 131 232)(31 331 132 233)(32 332 133 234)(33 333 134 235)(34 334 135 236)(35 335 136 237)(36 336 137 238)(37 316 138 239)(38 317 139 240)(39 318 140 241)(40 319 141 242)(41 320 142 243)(42 321 143 244)(43 82 174 270)(44 83 175 271)(45 84 176 272)(46 64 177 273)(47 65 178 253)(48 66 179 254)(49 67 180 255)(50 68 181 256)(51 69 182 257)(52 70 183 258)(53 71 184 259)(54 72 185 260)(55 73 186 261)(56 74 187 262)(57 75 188 263)(58 76 189 264)(59 77 169 265)(60 78 170 266)(61 79 171 267)(62 80 172 268)(63 81 173 269)(85 208 220 294)(86 209 221 274)(87 210 222 275)(88 190 223 276)(89 191 224 277)(90 192 225 278)(91 193 226 279)(92 194 227 280)(93 195 228 281)(94 196 229 282)(95 197 230 283)(96 198 231 284)(97 199 211 285)(98 200 212 286)(99 201 213 287)(100 202 214 288)(101 203 215 289)(102 204 216 290)(103 205 217 291)(104 206 218 292)(105 207 219 293)
(1 254 317 231)(2 255 318 211)(3 256 319 212)(4 257 320 213)(5 258 321 214)(6 259 322 215)(7 260 323 216)(8 261 324 217)(9 262 325 218)(10 263 326 219)(11 264 327 220)(12 265 328 221)(13 266 329 222)(14 267 330 223)(15 268 331 224)(16 269 332 225)(17 270 333 226)(18 271 334 227)(19 272 335 228)(20 273 336 229)(21 253 316 230)(22 289 314 53)(23 290 315 54)(24 291 295 55)(25 292 296 56)(26 293 297 57)(27 294 298 58)(28 274 299 59)(29 275 300 60)(30 276 301 61)(31 277 302 62)(32 278 303 63)(33 279 304 43)(34 280 305 44)(35 281 306 45)(36 282 307 46)(37 283 308 47)(38 284 309 48)(39 285 310 49)(40 286 311 50)(41 287 312 51)(42 288 313 52)(64 238 94 156)(65 239 95 157)(66 240 96 158)(67 241 97 159)(68 242 98 160)(69 243 99 161)(70 244 100 162)(71 245 101 163)(72 246 102 164)(73 247 103 165)(74 248 104 166)(75 249 105 167)(76 250 85 168)(77 251 86 148)(78 252 87 149)(79 232 88 150)(80 233 89 151)(81 234 90 152)(82 235 91 153)(83 236 92 154)(84 237 93 155)(106 178 138 197)(107 179 139 198)(108 180 140 199)(109 181 141 200)(110 182 142 201)(111 183 143 202)(112 184 144 203)(113 185 145 204)(114 186 146 205)(115 187 147 206)(116 188 127 207)(117 189 128 208)(118 169 129 209)(119 170 130 210)(120 171 131 190)(121 172 132 191)(122 173 133 192)(123 174 134 193)(124 175 135 194)(125 176 136 195)(126 177 137 196)
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), (1,107,158,309)(2,108,159,310)(3,109,160,311)(4,110,161,312)(5,111,162,313)(6,112,163,314)(7,113,164,315)(8,114,165,295)(9,115,166,296)(10,116,167,297)(11,117,168,298)(12,118,148,299)(13,119,149,300)(14,120,150,301)(15,121,151,302)(16,122,152,303)(17,123,153,304)(18,124,154,305)(19,125,155,306)(20,126,156,307)(21,106,157,308)(22,322,144,245)(23,323,145,246)(24,324,146,247)(25,325,147,248)(26,326,127,249)(27,327,128,250)(28,328,129,251)(29,329,130,252)(30,330,131,232)(31,331,132,233)(32,332,133,234)(33,333,134,235)(34,334,135,236)(35,335,136,237)(36,336,137,238)(37,316,138,239)(38,317,139,240)(39,318,140,241)(40,319,141,242)(41,320,142,243)(42,321,143,244)(43,82,174,270)(44,83,175,271)(45,84,176,272)(46,64,177,273)(47,65,178,253)(48,66,179,254)(49,67,180,255)(50,68,181,256)(51,69,182,257)(52,70,183,258)(53,71,184,259)(54,72,185,260)(55,73,186,261)(56,74,187,262)(57,75,188,263)(58,76,189,264)(59,77,169,265)(60,78,170,266)(61,79,171,267)(62,80,172,268)(63,81,173,269)(85,208,220,294)(86,209,221,274)(87,210,222,275)(88,190,223,276)(89,191,224,277)(90,192,225,278)(91,193,226,279)(92,194,227,280)(93,195,228,281)(94,196,229,282)(95,197,230,283)(96,198,231,284)(97,199,211,285)(98,200,212,286)(99,201,213,287)(100,202,214,288)(101,203,215,289)(102,204,216,290)(103,205,217,291)(104,206,218,292)(105,207,219,293), (1,254,317,231)(2,255,318,211)(3,256,319,212)(4,257,320,213)(5,258,321,214)(6,259,322,215)(7,260,323,216)(8,261,324,217)(9,262,325,218)(10,263,326,219)(11,264,327,220)(12,265,328,221)(13,266,329,222)(14,267,330,223)(15,268,331,224)(16,269,332,225)(17,270,333,226)(18,271,334,227)(19,272,335,228)(20,273,336,229)(21,253,316,230)(22,289,314,53)(23,290,315,54)(24,291,295,55)(25,292,296,56)(26,293,297,57)(27,294,298,58)(28,274,299,59)(29,275,300,60)(30,276,301,61)(31,277,302,62)(32,278,303,63)(33,279,304,43)(34,280,305,44)(35,281,306,45)(36,282,307,46)(37,283,308,47)(38,284,309,48)(39,285,310,49)(40,286,311,50)(41,287,312,51)(42,288,313,52)(64,238,94,156)(65,239,95,157)(66,240,96,158)(67,241,97,159)(68,242,98,160)(69,243,99,161)(70,244,100,162)(71,245,101,163)(72,246,102,164)(73,247,103,165)(74,248,104,166)(75,249,105,167)(76,250,85,168)(77,251,86,148)(78,252,87,149)(79,232,88,150)(80,233,89,151)(81,234,90,152)(82,235,91,153)(83,236,92,154)(84,237,93,155)(106,178,138,197)(107,179,139,198)(108,180,140,199)(109,181,141,200)(110,182,142,201)(111,183,143,202)(112,184,144,203)(113,185,145,204)(114,186,146,205)(115,187,147,206)(116,188,127,207)(117,189,128,208)(118,169,129,209)(119,170,130,210)(120,171,131,190)(121,172,132,191)(122,173,133,192)(123,174,134,193)(124,175,135,194)(125,176,136,195)(126,177,137,196)>;
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), (1,107,158,309)(2,108,159,310)(3,109,160,311)(4,110,161,312)(5,111,162,313)(6,112,163,314)(7,113,164,315)(8,114,165,295)(9,115,166,296)(10,116,167,297)(11,117,168,298)(12,118,148,299)(13,119,149,300)(14,120,150,301)(15,121,151,302)(16,122,152,303)(17,123,153,304)(18,124,154,305)(19,125,155,306)(20,126,156,307)(21,106,157,308)(22,322,144,245)(23,323,145,246)(24,324,146,247)(25,325,147,248)(26,326,127,249)(27,327,128,250)(28,328,129,251)(29,329,130,252)(30,330,131,232)(31,331,132,233)(32,332,133,234)(33,333,134,235)(34,334,135,236)(35,335,136,237)(36,336,137,238)(37,316,138,239)(38,317,139,240)(39,318,140,241)(40,319,141,242)(41,320,142,243)(42,321,143,244)(43,82,174,270)(44,83,175,271)(45,84,176,272)(46,64,177,273)(47,65,178,253)(48,66,179,254)(49,67,180,255)(50,68,181,256)(51,69,182,257)(52,70,183,258)(53,71,184,259)(54,72,185,260)(55,73,186,261)(56,74,187,262)(57,75,188,263)(58,76,189,264)(59,77,169,265)(60,78,170,266)(61,79,171,267)(62,80,172,268)(63,81,173,269)(85,208,220,294)(86,209,221,274)(87,210,222,275)(88,190,223,276)(89,191,224,277)(90,192,225,278)(91,193,226,279)(92,194,227,280)(93,195,228,281)(94,196,229,282)(95,197,230,283)(96,198,231,284)(97,199,211,285)(98,200,212,286)(99,201,213,287)(100,202,214,288)(101,203,215,289)(102,204,216,290)(103,205,217,291)(104,206,218,292)(105,207,219,293), (1,254,317,231)(2,255,318,211)(3,256,319,212)(4,257,320,213)(5,258,321,214)(6,259,322,215)(7,260,323,216)(8,261,324,217)(9,262,325,218)(10,263,326,219)(11,264,327,220)(12,265,328,221)(13,266,329,222)(14,267,330,223)(15,268,331,224)(16,269,332,225)(17,270,333,226)(18,271,334,227)(19,272,335,228)(20,273,336,229)(21,253,316,230)(22,289,314,53)(23,290,315,54)(24,291,295,55)(25,292,296,56)(26,293,297,57)(27,294,298,58)(28,274,299,59)(29,275,300,60)(30,276,301,61)(31,277,302,62)(32,278,303,63)(33,279,304,43)(34,280,305,44)(35,281,306,45)(36,282,307,46)(37,283,308,47)(38,284,309,48)(39,285,310,49)(40,286,311,50)(41,287,312,51)(42,288,313,52)(64,238,94,156)(65,239,95,157)(66,240,96,158)(67,241,97,159)(68,242,98,160)(69,243,99,161)(70,244,100,162)(71,245,101,163)(72,246,102,164)(73,247,103,165)(74,248,104,166)(75,249,105,167)(76,250,85,168)(77,251,86,148)(78,252,87,149)(79,232,88,150)(80,233,89,151)(81,234,90,152)(82,235,91,153)(83,236,92,154)(84,237,93,155)(106,178,138,197)(107,179,139,198)(108,180,140,199)(109,181,141,200)(110,182,142,201)(111,183,143,202)(112,184,144,203)(113,185,145,204)(114,186,146,205)(115,187,147,206)(116,188,127,207)(117,189,128,208)(118,169,129,209)(119,170,130,210)(120,171,131,190)(121,172,132,191)(122,173,133,192)(123,174,134,193)(124,175,135,194)(125,176,136,195)(126,177,137,196) );
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)], [(1,107,158,309),(2,108,159,310),(3,109,160,311),(4,110,161,312),(5,111,162,313),(6,112,163,314),(7,113,164,315),(8,114,165,295),(9,115,166,296),(10,116,167,297),(11,117,168,298),(12,118,148,299),(13,119,149,300),(14,120,150,301),(15,121,151,302),(16,122,152,303),(17,123,153,304),(18,124,154,305),(19,125,155,306),(20,126,156,307),(21,106,157,308),(22,322,144,245),(23,323,145,246),(24,324,146,247),(25,325,147,248),(26,326,127,249),(27,327,128,250),(28,328,129,251),(29,329,130,252),(30,330,131,232),(31,331,132,233),(32,332,133,234),(33,333,134,235),(34,334,135,236),(35,335,136,237),(36,336,137,238),(37,316,138,239),(38,317,139,240),(39,318,140,241),(40,319,141,242),(41,320,142,243),(42,321,143,244),(43,82,174,270),(44,83,175,271),(45,84,176,272),(46,64,177,273),(47,65,178,253),(48,66,179,254),(49,67,180,255),(50,68,181,256),(51,69,182,257),(52,70,183,258),(53,71,184,259),(54,72,185,260),(55,73,186,261),(56,74,187,262),(57,75,188,263),(58,76,189,264),(59,77,169,265),(60,78,170,266),(61,79,171,267),(62,80,172,268),(63,81,173,269),(85,208,220,294),(86,209,221,274),(87,210,222,275),(88,190,223,276),(89,191,224,277),(90,192,225,278),(91,193,226,279),(92,194,227,280),(93,195,228,281),(94,196,229,282),(95,197,230,283),(96,198,231,284),(97,199,211,285),(98,200,212,286),(99,201,213,287),(100,202,214,288),(101,203,215,289),(102,204,216,290),(103,205,217,291),(104,206,218,292),(105,207,219,293)], [(1,254,317,231),(2,255,318,211),(3,256,319,212),(4,257,320,213),(5,258,321,214),(6,259,322,215),(7,260,323,216),(8,261,324,217),(9,262,325,218),(10,263,326,219),(11,264,327,220),(12,265,328,221),(13,266,329,222),(14,267,330,223),(15,268,331,224),(16,269,332,225),(17,270,333,226),(18,271,334,227),(19,272,335,228),(20,273,336,229),(21,253,316,230),(22,289,314,53),(23,290,315,54),(24,291,295,55),(25,292,296,56),(26,293,297,57),(27,294,298,58),(28,274,299,59),(29,275,300,60),(30,276,301,61),(31,277,302,62),(32,278,303,63),(33,279,304,43),(34,280,305,44),(35,281,306,45),(36,282,307,46),(37,283,308,47),(38,284,309,48),(39,285,310,49),(40,286,311,50),(41,287,312,51),(42,288,313,52),(64,238,94,156),(65,239,95,157),(66,240,96,158),(67,241,97,159),(68,242,98,160),(69,243,99,161),(70,244,100,162),(71,245,101,163),(72,246,102,164),(73,247,103,165),(74,248,104,166),(75,249,105,167),(76,250,85,168),(77,251,86,148),(78,252,87,149),(79,232,88,150),(80,233,89,151),(81,234,90,152),(82,235,91,153),(83,236,92,154),(84,237,93,155),(106,178,138,197),(107,179,139,198),(108,180,140,199),(109,181,141,200),(110,182,142,201),(111,183,143,202),(112,184,144,203),(113,185,145,204),(114,186,146,205),(115,187,147,206),(116,188,127,207),(117,189,128,208),(118,169,129,209),(119,170,130,210),(120,171,131,190),(121,172,132,191),(122,173,133,192),(123,174,134,193),(124,175,135,194),(125,176,136,195),(126,177,137,196)]])
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 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||||||||||||
| image | C1 | C2 | C3 | C4 | C6 | C7 | C12 | C14 | C21 | C28 | C42 | C84 | D4 | Q8 | C3×D4 | C3×Q8 | C7×D4 | C7×Q8 | D4×C21 | Q8×C21 |
| kernel | C4⋊C4×C21 | C2×C84 | C7×C4⋊C4 | C84 | C2×C28 | C3×C4⋊C4 | C28 | C2×C12 | C4⋊C4 | C12 | C2×C4 | C4 | C42 | C42 | C14 | C14 | C6 | C6 | C2 | C2 |
| # reps | 1 | 3 | 2 | 4 | 6 | 6 | 8 | 18 | 12 | 24 | 36 | 48 | 1 | 1 | 2 | 2 | 6 | 6 | 12 | 12 |
Matrix representation of C4⋊C4×C21 ►in GL3(𝔽337) generated by
| 208 | 0 | 0 |
| 0 | 52 | 0 |
| 0 | 0 | 52 |
| 336 | 0 | 0 |
| 0 | 0 | 336 |
| 0 | 1 | 0 |
| 148 | 0 | 0 |
| 0 | 175 | 190 |
| 0 | 190 | 162 |
G:=sub<GL(3,GF(337))| [208,0,0,0,52,0,0,0,52],[336,0,0,0,0,1,0,336,0],[148,0,0,0,175,190,0,190,162] >;
C4⋊C4×C21 in GAP, Magma, Sage, TeX
C_4\rtimes C_4\times C_{21} % in TeX
G:=Group("C4:C4xC21"); // GroupNames label
G:=SmallGroup(336,108);
// by ID
G=gap.SmallGroup(336,108);
# by ID
G:=PCGroup([6,-2,-2,-3,-7,-2,-2,1008,1033,511]);
// Polycyclic
G:=Group<a,b,c|a^21=b^4=c^4=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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