metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20.1Q16, C4.5Dic20, C42.3D10, C20.35SD16, C4⋊C8.3D5, C20⋊3C8.8C2, (C2×C4).121D20, (C2×C20).463D4, C4.9(C40⋊C2), C4.9(D4.D5), C20⋊2Q8.8C2, C4.9(C5⋊Q16), C5⋊2(C4.6Q16), (C4×C20).39C22, (C2×Dic10).2C4, C2.4(C10.Q16), C10.14(Q8⋊C4), C10.10(C4.D4), C2.4(C20.46D4), C2.4(C20.44D4), C22.60(D10⋊C4), (C5×C4⋊C8).3C2, (C2×C4).14(C4×D5), (C2×C20).199(C2×C4), (C2×C4).227(C5⋊D4), (C2×C10).107(C22⋊C4), SmallGroup(320,39)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4.Dic20
G = < a,b,c | a4=b40=1, c2=ab20, bab-1=a-1, ac=ca, cbc-1=a-1b-1 >
Subgroups: 254 in 64 conjugacy classes, 33 normal (31 characteristic)
C1, C2, C4, C4, C22, C5, C8, C2×C4, C2×C4, Q8, C10, C42, C4⋊C4, C2×C8, C2×Q8, Dic5, C20, C20, C2×C10, C4⋊C8, C4⋊C8, C4⋊Q8, C5⋊2C8, C40, Dic10, C2×Dic5, C2×C20, C4.6Q16, C2×C5⋊2C8, C4⋊Dic5, C4×C20, C2×C40, C2×Dic10, C20⋊3C8, C5×C4⋊C8, C20⋊2Q8, C4.Dic20
Quotients: C1, C2, C4, C22, C2×C4, D4, D5, C22⋊C4, SD16, Q16, D10, C4.D4, Q8⋊C4, C4×D5, D20, C5⋊D4, C4.6Q16, C40⋊C2, Dic20, D10⋊C4, D4.D5, C5⋊Q16, C10.Q16, C20.44D4, C20.46D4, C4.Dic20
►Regular action on 320 points
Generators in S320
(1 244 197 309)(2 310 198 245)(3 246 199 311)(4 312 200 247)(5 248 161 313)(6 314 162 249)(7 250 163 315)(8 316 164 251)(9 252 165 317)(10 318 166 253)(11 254 167 319)(12 320 168 255)(13 256 169 281)(14 282 170 257)(15 258 171 283)(16 284 172 259)(17 260 173 285)(18 286 174 261)(19 262 175 287)(20 288 176 263)(21 264 177 289)(22 290 178 265)(23 266 179 291)(24 292 180 267)(25 268 181 293)(26 294 182 269)(27 270 183 295)(28 296 184 271)(29 272 185 297)(30 298 186 273)(31 274 187 299)(32 300 188 275)(33 276 189 301)(34 302 190 277)(35 278 191 303)(36 304 192 279)(37 280 193 305)(38 306 194 241)(39 242 195 307)(40 308 196 243)(41 105 223 139)(42 140 224 106)(43 107 225 141)(44 142 226 108)(45 109 227 143)(46 144 228 110)(47 111 229 145)(48 146 230 112)(49 113 231 147)(50 148 232 114)(51 115 233 149)(52 150 234 116)(53 117 235 151)(54 152 236 118)(55 119 237 153)(56 154 238 120)(57 81 239 155)(58 156 240 82)(59 83 201 157)(60 158 202 84)(61 85 203 159)(62 160 204 86)(63 87 205 121)(64 122 206 88)(65 89 207 123)(66 124 208 90)(67 91 209 125)(68 126 210 92)(69 93 211 127)(70 128 212 94)(71 95 213 129)(72 130 214 96)(73 97 215 131)(74 132 216 98)(75 99 217 133)(76 134 218 100)(77 101 219 135)(78 136 220 102)(79 103 221 137)(80 138 222 104)
(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)
(1 217 264 153 197 75 289 119)(2 132 290 236 198 98 265 54)(3 215 266 151 199 73 291 117)(4 130 292 234 200 96 267 52)(5 213 268 149 161 71 293 115)(6 128 294 232 162 94 269 50)(7 211 270 147 163 69 295 113)(8 126 296 230 164 92 271 48)(9 209 272 145 165 67 297 111)(10 124 298 228 166 90 273 46)(11 207 274 143 167 65 299 109)(12 122 300 226 168 88 275 44)(13 205 276 141 169 63 301 107)(14 160 302 224 170 86 277 42)(15 203 278 139 171 61 303 105)(16 158 304 222 172 84 279 80)(17 201 280 137 173 59 305 103)(18 156 306 220 174 82 241 78)(19 239 242 135 175 57 307 101)(20 154 308 218 176 120 243 76)(21 237 244 133 177 55 309 99)(22 152 310 216 178 118 245 74)(23 235 246 131 179 53 311 97)(24 150 312 214 180 116 247 72)(25 233 248 129 181 51 313 95)(26 148 314 212 182 114 249 70)(27 231 250 127 183 49 315 93)(28 146 316 210 184 112 251 68)(29 229 252 125 185 47 317 91)(30 144 318 208 186 110 253 66)(31 227 254 123 187 45 319 89)(32 142 320 206 188 108 255 64)(33 225 256 121 189 43 281 87)(34 140 282 204 190 106 257 62)(35 223 258 159 191 41 283 85)(36 138 284 202 192 104 259 60)(37 221 260 157 193 79 285 83)(38 136 286 240 194 102 261 58)(39 219 262 155 195 77 287 81)(40 134 288 238 196 100 263 56)
G:=sub<Sym(320)| (1,244,197,309)(2,310,198,245)(3,246,199,311)(4,312,200,247)(5,248,161,313)(6,314,162,249)(7,250,163,315)(8,316,164,251)(9,252,165,317)(10,318,166,253)(11,254,167,319)(12,320,168,255)(13,256,169,281)(14,282,170,257)(15,258,171,283)(16,284,172,259)(17,260,173,285)(18,286,174,261)(19,262,175,287)(20,288,176,263)(21,264,177,289)(22,290,178,265)(23,266,179,291)(24,292,180,267)(25,268,181,293)(26,294,182,269)(27,270,183,295)(28,296,184,271)(29,272,185,297)(30,298,186,273)(31,274,187,299)(32,300,188,275)(33,276,189,301)(34,302,190,277)(35,278,191,303)(36,304,192,279)(37,280,193,305)(38,306,194,241)(39,242,195,307)(40,308,196,243)(41,105,223,139)(42,140,224,106)(43,107,225,141)(44,142,226,108)(45,109,227,143)(46,144,228,110)(47,111,229,145)(48,146,230,112)(49,113,231,147)(50,148,232,114)(51,115,233,149)(52,150,234,116)(53,117,235,151)(54,152,236,118)(55,119,237,153)(56,154,238,120)(57,81,239,155)(58,156,240,82)(59,83,201,157)(60,158,202,84)(61,85,203,159)(62,160,204,86)(63,87,205,121)(64,122,206,88)(65,89,207,123)(66,124,208,90)(67,91,209,125)(68,126,210,92)(69,93,211,127)(70,128,212,94)(71,95,213,129)(72,130,214,96)(73,97,215,131)(74,132,216,98)(75,99,217,133)(76,134,218,100)(77,101,219,135)(78,136,220,102)(79,103,221,137)(80,138,222,104), (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), (1,217,264,153,197,75,289,119)(2,132,290,236,198,98,265,54)(3,215,266,151,199,73,291,117)(4,130,292,234,200,96,267,52)(5,213,268,149,161,71,293,115)(6,128,294,232,162,94,269,50)(7,211,270,147,163,69,295,113)(8,126,296,230,164,92,271,48)(9,209,272,145,165,67,297,111)(10,124,298,228,166,90,273,46)(11,207,274,143,167,65,299,109)(12,122,300,226,168,88,275,44)(13,205,276,141,169,63,301,107)(14,160,302,224,170,86,277,42)(15,203,278,139,171,61,303,105)(16,158,304,222,172,84,279,80)(17,201,280,137,173,59,305,103)(18,156,306,220,174,82,241,78)(19,239,242,135,175,57,307,101)(20,154,308,218,176,120,243,76)(21,237,244,133,177,55,309,99)(22,152,310,216,178,118,245,74)(23,235,246,131,179,53,311,97)(24,150,312,214,180,116,247,72)(25,233,248,129,181,51,313,95)(26,148,314,212,182,114,249,70)(27,231,250,127,183,49,315,93)(28,146,316,210,184,112,251,68)(29,229,252,125,185,47,317,91)(30,144,318,208,186,110,253,66)(31,227,254,123,187,45,319,89)(32,142,320,206,188,108,255,64)(33,225,256,121,189,43,281,87)(34,140,282,204,190,106,257,62)(35,223,258,159,191,41,283,85)(36,138,284,202,192,104,259,60)(37,221,260,157,193,79,285,83)(38,136,286,240,194,102,261,58)(39,219,262,155,195,77,287,81)(40,134,288,238,196,100,263,56)>;
G:=Group( (1,244,197,309)(2,310,198,245)(3,246,199,311)(4,312,200,247)(5,248,161,313)(6,314,162,249)(7,250,163,315)(8,316,164,251)(9,252,165,317)(10,318,166,253)(11,254,167,319)(12,320,168,255)(13,256,169,281)(14,282,170,257)(15,258,171,283)(16,284,172,259)(17,260,173,285)(18,286,174,261)(19,262,175,287)(20,288,176,263)(21,264,177,289)(22,290,178,265)(23,266,179,291)(24,292,180,267)(25,268,181,293)(26,294,182,269)(27,270,183,295)(28,296,184,271)(29,272,185,297)(30,298,186,273)(31,274,187,299)(32,300,188,275)(33,276,189,301)(34,302,190,277)(35,278,191,303)(36,304,192,279)(37,280,193,305)(38,306,194,241)(39,242,195,307)(40,308,196,243)(41,105,223,139)(42,140,224,106)(43,107,225,141)(44,142,226,108)(45,109,227,143)(46,144,228,110)(47,111,229,145)(48,146,230,112)(49,113,231,147)(50,148,232,114)(51,115,233,149)(52,150,234,116)(53,117,235,151)(54,152,236,118)(55,119,237,153)(56,154,238,120)(57,81,239,155)(58,156,240,82)(59,83,201,157)(60,158,202,84)(61,85,203,159)(62,160,204,86)(63,87,205,121)(64,122,206,88)(65,89,207,123)(66,124,208,90)(67,91,209,125)(68,126,210,92)(69,93,211,127)(70,128,212,94)(71,95,213,129)(72,130,214,96)(73,97,215,131)(74,132,216,98)(75,99,217,133)(76,134,218,100)(77,101,219,135)(78,136,220,102)(79,103,221,137)(80,138,222,104), (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), (1,217,264,153,197,75,289,119)(2,132,290,236,198,98,265,54)(3,215,266,151,199,73,291,117)(4,130,292,234,200,96,267,52)(5,213,268,149,161,71,293,115)(6,128,294,232,162,94,269,50)(7,211,270,147,163,69,295,113)(8,126,296,230,164,92,271,48)(9,209,272,145,165,67,297,111)(10,124,298,228,166,90,273,46)(11,207,274,143,167,65,299,109)(12,122,300,226,168,88,275,44)(13,205,276,141,169,63,301,107)(14,160,302,224,170,86,277,42)(15,203,278,139,171,61,303,105)(16,158,304,222,172,84,279,80)(17,201,280,137,173,59,305,103)(18,156,306,220,174,82,241,78)(19,239,242,135,175,57,307,101)(20,154,308,218,176,120,243,76)(21,237,244,133,177,55,309,99)(22,152,310,216,178,118,245,74)(23,235,246,131,179,53,311,97)(24,150,312,214,180,116,247,72)(25,233,248,129,181,51,313,95)(26,148,314,212,182,114,249,70)(27,231,250,127,183,49,315,93)(28,146,316,210,184,112,251,68)(29,229,252,125,185,47,317,91)(30,144,318,208,186,110,253,66)(31,227,254,123,187,45,319,89)(32,142,320,206,188,108,255,64)(33,225,256,121,189,43,281,87)(34,140,282,204,190,106,257,62)(35,223,258,159,191,41,283,85)(36,138,284,202,192,104,259,60)(37,221,260,157,193,79,285,83)(38,136,286,240,194,102,261,58)(39,219,262,155,195,77,287,81)(40,134,288,238,196,100,263,56) );
G=PermutationGroup([[(1,244,197,309),(2,310,198,245),(3,246,199,311),(4,312,200,247),(5,248,161,313),(6,314,162,249),(7,250,163,315),(8,316,164,251),(9,252,165,317),(10,318,166,253),(11,254,167,319),(12,320,168,255),(13,256,169,281),(14,282,170,257),(15,258,171,283),(16,284,172,259),(17,260,173,285),(18,286,174,261),(19,262,175,287),(20,288,176,263),(21,264,177,289),(22,290,178,265),(23,266,179,291),(24,292,180,267),(25,268,181,293),(26,294,182,269),(27,270,183,295),(28,296,184,271),(29,272,185,297),(30,298,186,273),(31,274,187,299),(32,300,188,275),(33,276,189,301),(34,302,190,277),(35,278,191,303),(36,304,192,279),(37,280,193,305),(38,306,194,241),(39,242,195,307),(40,308,196,243),(41,105,223,139),(42,140,224,106),(43,107,225,141),(44,142,226,108),(45,109,227,143),(46,144,228,110),(47,111,229,145),(48,146,230,112),(49,113,231,147),(50,148,232,114),(51,115,233,149),(52,150,234,116),(53,117,235,151),(54,152,236,118),(55,119,237,153),(56,154,238,120),(57,81,239,155),(58,156,240,82),(59,83,201,157),(60,158,202,84),(61,85,203,159),(62,160,204,86),(63,87,205,121),(64,122,206,88),(65,89,207,123),(66,124,208,90),(67,91,209,125),(68,126,210,92),(69,93,211,127),(70,128,212,94),(71,95,213,129),(72,130,214,96),(73,97,215,131),(74,132,216,98),(75,99,217,133),(76,134,218,100),(77,101,219,135),(78,136,220,102),(79,103,221,137),(80,138,222,104)], [(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)], [(1,217,264,153,197,75,289,119),(2,132,290,236,198,98,265,54),(3,215,266,151,199,73,291,117),(4,130,292,234,200,96,267,52),(5,213,268,149,161,71,293,115),(6,128,294,232,162,94,269,50),(7,211,270,147,163,69,295,113),(8,126,296,230,164,92,271,48),(9,209,272,145,165,67,297,111),(10,124,298,228,166,90,273,46),(11,207,274,143,167,65,299,109),(12,122,300,226,168,88,275,44),(13,205,276,141,169,63,301,107),(14,160,302,224,170,86,277,42),(15,203,278,139,171,61,303,105),(16,158,304,222,172,84,279,80),(17,201,280,137,173,59,305,103),(18,156,306,220,174,82,241,78),(19,239,242,135,175,57,307,101),(20,154,308,218,176,120,243,76),(21,237,244,133,177,55,309,99),(22,152,310,216,178,118,245,74),(23,235,246,131,179,53,311,97),(24,150,312,214,180,116,247,72),(25,233,248,129,181,51,313,95),(26,148,314,212,182,114,249,70),(27,231,250,127,183,49,315,93),(28,146,316,210,184,112,251,68),(29,229,252,125,185,47,317,91),(30,144,318,208,186,110,253,66),(31,227,254,123,187,45,319,89),(32,142,320,206,188,108,255,64),(33,225,256,121,189,43,281,87),(34,140,282,204,190,106,257,62),(35,223,258,159,191,41,283,85),(36,138,284,202,192,104,259,60),(37,221,260,157,193,79,285,83),(38,136,286,240,194,102,261,58),(39,219,262,155,195,77,287,81),(40,134,288,238,196,100,263,56)]])
59 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 5A | 5B | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 10A | ··· | 10F | 20A | ··· | 20H | 20I | ··· | 20P | 40A | ··· | 40P |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 40 | 40 | 2 | 2 | 4 | 4 | 4 | 4 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
59 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | + | - | + | - | - | + | |||||
| image | C1 | C2 | C2 | C2 | C4 | D4 | D5 | SD16 | Q16 | D10 | C4×D5 | D20 | C5⋊D4 | C40⋊C2 | Dic20 | C4.D4 | D4.D5 | C5⋊Q16 | C20.46D4 |
| kernel | C4.Dic20 | C20⋊3C8 | C5×C4⋊C8 | C20⋊2Q8 | C2×Dic10 | C2×C20 | C4⋊C8 | C20 | C20 | C42 | C2×C4 | C2×C4 | C2×C4 | C4 | C4 | C10 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 4 | 2 | 2 | 4 | 4 | 2 | 4 | 4 | 4 | 8 | 8 | 1 | 2 | 2 | 4 |
Matrix representation of C4.Dic20 ►in GL4(𝔽41) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 40 | 39 |
| 0 | 0 | 1 | 1 |
| 6 | 29 | 0 | 0 |
| 14 | 20 | 0 | 0 |
| 0 | 0 | 12 | 22 |
| 0 | 0 | 40 | 29 |
| 28 | 26 | 0 | 0 |
| 25 | 13 | 0 | 0 |
| 0 | 0 | 0 | 24 |
| 0 | 0 | 29 | 17 |
G:=sub<GL(4,GF(41))| [1,0,0,0,0,1,0,0,0,0,40,1,0,0,39,1],[6,14,0,0,29,20,0,0,0,0,12,40,0,0,22,29],[28,25,0,0,26,13,0,0,0,0,0,29,0,0,24,17] >;
C4.Dic20 in GAP, Magma, Sage, TeX
C_4.{\rm Dic}_{20} % in TeX
G:=Group("C4.Dic20"); // GroupNames label
G:=SmallGroup(320,39);
// by ID
G=gap.SmallGroup(320,39);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,85,92,422,387,268,570,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^4=b^40=1,c^2=a*b^20,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=a^-1*b^-1>;
// generators/relations