metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20.47D8, C20.2Q16, C4.6Dic20, C42.4D10, C20.46SD16, C4⋊C8.4D5, C4⋊Dic5.2C4, C20⋊3C8.9C2, C4.19(D4⋊D5), (C2×C20).464D4, (C2×C4).122D20, C5⋊2(C4.10D8), C4.11(Q8⋊D5), C20⋊2Q8.9C2, C4.10(C40⋊C2), (C4×C20).40C22, C2.4(D20⋊6C4), C10.17(D4⋊C4), C10.15(Q8⋊C4), C2.5(C20.44D4), C2.4(C4.12D20), C10.8(C4.10D4), C22.61(D10⋊C4), (C5×C4⋊C8).4C2, (C2×C4).15(C4×D5), (C2×C20).200(C2×C4), (C2×C4).228(C5⋊D4), (C2×C10).108(C22⋊C4), SmallGroup(320,40)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20.47D8
G = < a,b,c | a20=b8=1, c2=a10, bab-1=cac-1=a-1, cbc-1=a5b-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, C4.10D8, C2×C5⋊2C8, C4⋊Dic5, C4⋊Dic5, C4×C20, C2×C40, C2×Dic10, C20⋊3C8, C5×C4⋊C8, C20⋊2Q8, C20.47D8
Quotients: C1, C2, C4, C22, C2×C4, D4, D5, C22⋊C4, D8, SD16, Q16, D10, C4.10D4, D4⋊C4, Q8⋊C4, C4×D5, D20, C5⋊D4, C4.10D8, C40⋊C2, Dic20, D10⋊C4, D4⋊D5, Q8⋊D5, D20⋊6C4, C20.44D4, C4.12D20, C20.47D8
►Regular action on 320 points
Generators in S320
(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)
(1 212 75 128 193 276 258 289)(2 211 76 127 194 275 259 288)(3 210 77 126 195 274 260 287)(4 209 78 125 196 273 241 286)(5 208 79 124 197 272 242 285)(6 207 80 123 198 271 243 284)(7 206 61 122 199 270 244 283)(8 205 62 121 200 269 245 282)(9 204 63 140 181 268 246 281)(10 203 64 139 182 267 247 300)(11 202 65 138 183 266 248 299)(12 201 66 137 184 265 249 298)(13 220 67 136 185 264 250 297)(14 219 68 135 186 263 251 296)(15 218 69 134 187 262 252 295)(16 217 70 133 188 261 253 294)(17 216 71 132 189 280 254 293)(18 215 72 131 190 279 255 292)(19 214 73 130 191 278 256 291)(20 213 74 129 192 277 257 290)(21 118 302 90 175 222 156 45)(22 117 303 89 176 221 157 44)(23 116 304 88 177 240 158 43)(24 115 305 87 178 239 159 42)(25 114 306 86 179 238 160 41)(26 113 307 85 180 237 141 60)(27 112 308 84 161 236 142 59)(28 111 309 83 162 235 143 58)(29 110 310 82 163 234 144 57)(30 109 311 81 164 233 145 56)(31 108 312 100 165 232 146 55)(32 107 313 99 166 231 147 54)(33 106 314 98 167 230 148 53)(34 105 315 97 168 229 149 52)(35 104 316 96 169 228 150 51)(36 103 317 95 170 227 151 50)(37 102 318 94 171 226 152 49)(38 101 319 93 172 225 153 48)(39 120 320 92 173 224 154 47)(40 119 301 91 174 223 155 46)
(1 113 11 103)(2 112 12 102)(3 111 13 101)(4 110 14 120)(5 109 15 119)(6 108 16 118)(7 107 17 117)(8 106 18 116)(9 105 19 115)(10 104 20 114)(21 202 31 212)(22 201 32 211)(23 220 33 210)(24 219 34 209)(25 218 35 208)(26 217 36 207)(27 216 37 206)(28 215 38 205)(29 214 39 204)(30 213 40 203)(41 64 51 74)(42 63 52 73)(43 62 53 72)(44 61 54 71)(45 80 55 70)(46 79 56 69)(47 78 57 68)(48 77 58 67)(49 76 59 66)(50 75 60 65)(81 252 91 242)(82 251 92 241)(83 250 93 260)(84 249 94 259)(85 248 95 258)(86 247 96 257)(87 246 97 256)(88 245 98 255)(89 244 99 254)(90 243 100 253)(121 143 131 153)(122 142 132 152)(123 141 133 151)(124 160 134 150)(125 159 135 149)(126 158 136 148)(127 157 137 147)(128 156 138 146)(129 155 139 145)(130 154 140 144)(161 280 171 270)(162 279 172 269)(163 278 173 268)(164 277 174 267)(165 276 175 266)(166 275 176 265)(167 274 177 264)(168 273 178 263)(169 272 179 262)(170 271 180 261)(181 229 191 239)(182 228 192 238)(183 227 193 237)(184 226 194 236)(185 225 195 235)(186 224 196 234)(187 223 197 233)(188 222 198 232)(189 221 199 231)(190 240 200 230)(281 310 291 320)(282 309 292 319)(283 308 293 318)(284 307 294 317)(285 306 295 316)(286 305 296 315)(287 304 297 314)(288 303 298 313)(289 302 299 312)(290 301 300 311)
G:=sub<Sym(320)| (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), (1,212,75,128,193,276,258,289)(2,211,76,127,194,275,259,288)(3,210,77,126,195,274,260,287)(4,209,78,125,196,273,241,286)(5,208,79,124,197,272,242,285)(6,207,80,123,198,271,243,284)(7,206,61,122,199,270,244,283)(8,205,62,121,200,269,245,282)(9,204,63,140,181,268,246,281)(10,203,64,139,182,267,247,300)(11,202,65,138,183,266,248,299)(12,201,66,137,184,265,249,298)(13,220,67,136,185,264,250,297)(14,219,68,135,186,263,251,296)(15,218,69,134,187,262,252,295)(16,217,70,133,188,261,253,294)(17,216,71,132,189,280,254,293)(18,215,72,131,190,279,255,292)(19,214,73,130,191,278,256,291)(20,213,74,129,192,277,257,290)(21,118,302,90,175,222,156,45)(22,117,303,89,176,221,157,44)(23,116,304,88,177,240,158,43)(24,115,305,87,178,239,159,42)(25,114,306,86,179,238,160,41)(26,113,307,85,180,237,141,60)(27,112,308,84,161,236,142,59)(28,111,309,83,162,235,143,58)(29,110,310,82,163,234,144,57)(30,109,311,81,164,233,145,56)(31,108,312,100,165,232,146,55)(32,107,313,99,166,231,147,54)(33,106,314,98,167,230,148,53)(34,105,315,97,168,229,149,52)(35,104,316,96,169,228,150,51)(36,103,317,95,170,227,151,50)(37,102,318,94,171,226,152,49)(38,101,319,93,172,225,153,48)(39,120,320,92,173,224,154,47)(40,119,301,91,174,223,155,46), (1,113,11,103)(2,112,12,102)(3,111,13,101)(4,110,14,120)(5,109,15,119)(6,108,16,118)(7,107,17,117)(8,106,18,116)(9,105,19,115)(10,104,20,114)(21,202,31,212)(22,201,32,211)(23,220,33,210)(24,219,34,209)(25,218,35,208)(26,217,36,207)(27,216,37,206)(28,215,38,205)(29,214,39,204)(30,213,40,203)(41,64,51,74)(42,63,52,73)(43,62,53,72)(44,61,54,71)(45,80,55,70)(46,79,56,69)(47,78,57,68)(48,77,58,67)(49,76,59,66)(50,75,60,65)(81,252,91,242)(82,251,92,241)(83,250,93,260)(84,249,94,259)(85,248,95,258)(86,247,96,257)(87,246,97,256)(88,245,98,255)(89,244,99,254)(90,243,100,253)(121,143,131,153)(122,142,132,152)(123,141,133,151)(124,160,134,150)(125,159,135,149)(126,158,136,148)(127,157,137,147)(128,156,138,146)(129,155,139,145)(130,154,140,144)(161,280,171,270)(162,279,172,269)(163,278,173,268)(164,277,174,267)(165,276,175,266)(166,275,176,265)(167,274,177,264)(168,273,178,263)(169,272,179,262)(170,271,180,261)(181,229,191,239)(182,228,192,238)(183,227,193,237)(184,226,194,236)(185,225,195,235)(186,224,196,234)(187,223,197,233)(188,222,198,232)(189,221,199,231)(190,240,200,230)(281,310,291,320)(282,309,292,319)(283,308,293,318)(284,307,294,317)(285,306,295,316)(286,305,296,315)(287,304,297,314)(288,303,298,313)(289,302,299,312)(290,301,300,311)>;
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), (1,212,75,128,193,276,258,289)(2,211,76,127,194,275,259,288)(3,210,77,126,195,274,260,287)(4,209,78,125,196,273,241,286)(5,208,79,124,197,272,242,285)(6,207,80,123,198,271,243,284)(7,206,61,122,199,270,244,283)(8,205,62,121,200,269,245,282)(9,204,63,140,181,268,246,281)(10,203,64,139,182,267,247,300)(11,202,65,138,183,266,248,299)(12,201,66,137,184,265,249,298)(13,220,67,136,185,264,250,297)(14,219,68,135,186,263,251,296)(15,218,69,134,187,262,252,295)(16,217,70,133,188,261,253,294)(17,216,71,132,189,280,254,293)(18,215,72,131,190,279,255,292)(19,214,73,130,191,278,256,291)(20,213,74,129,192,277,257,290)(21,118,302,90,175,222,156,45)(22,117,303,89,176,221,157,44)(23,116,304,88,177,240,158,43)(24,115,305,87,178,239,159,42)(25,114,306,86,179,238,160,41)(26,113,307,85,180,237,141,60)(27,112,308,84,161,236,142,59)(28,111,309,83,162,235,143,58)(29,110,310,82,163,234,144,57)(30,109,311,81,164,233,145,56)(31,108,312,100,165,232,146,55)(32,107,313,99,166,231,147,54)(33,106,314,98,167,230,148,53)(34,105,315,97,168,229,149,52)(35,104,316,96,169,228,150,51)(36,103,317,95,170,227,151,50)(37,102,318,94,171,226,152,49)(38,101,319,93,172,225,153,48)(39,120,320,92,173,224,154,47)(40,119,301,91,174,223,155,46), (1,113,11,103)(2,112,12,102)(3,111,13,101)(4,110,14,120)(5,109,15,119)(6,108,16,118)(7,107,17,117)(8,106,18,116)(9,105,19,115)(10,104,20,114)(21,202,31,212)(22,201,32,211)(23,220,33,210)(24,219,34,209)(25,218,35,208)(26,217,36,207)(27,216,37,206)(28,215,38,205)(29,214,39,204)(30,213,40,203)(41,64,51,74)(42,63,52,73)(43,62,53,72)(44,61,54,71)(45,80,55,70)(46,79,56,69)(47,78,57,68)(48,77,58,67)(49,76,59,66)(50,75,60,65)(81,252,91,242)(82,251,92,241)(83,250,93,260)(84,249,94,259)(85,248,95,258)(86,247,96,257)(87,246,97,256)(88,245,98,255)(89,244,99,254)(90,243,100,253)(121,143,131,153)(122,142,132,152)(123,141,133,151)(124,160,134,150)(125,159,135,149)(126,158,136,148)(127,157,137,147)(128,156,138,146)(129,155,139,145)(130,154,140,144)(161,280,171,270)(162,279,172,269)(163,278,173,268)(164,277,174,267)(165,276,175,266)(166,275,176,265)(167,274,177,264)(168,273,178,263)(169,272,179,262)(170,271,180,261)(181,229,191,239)(182,228,192,238)(183,227,193,237)(184,226,194,236)(185,225,195,235)(186,224,196,234)(187,223,197,233)(188,222,198,232)(189,221,199,231)(190,240,200,230)(281,310,291,320)(282,309,292,319)(283,308,293,318)(284,307,294,317)(285,306,295,316)(286,305,296,315)(287,304,297,314)(288,303,298,313)(289,302,299,312)(290,301,300,311) );
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)], [(1,212,75,128,193,276,258,289),(2,211,76,127,194,275,259,288),(3,210,77,126,195,274,260,287),(4,209,78,125,196,273,241,286),(5,208,79,124,197,272,242,285),(6,207,80,123,198,271,243,284),(7,206,61,122,199,270,244,283),(8,205,62,121,200,269,245,282),(9,204,63,140,181,268,246,281),(10,203,64,139,182,267,247,300),(11,202,65,138,183,266,248,299),(12,201,66,137,184,265,249,298),(13,220,67,136,185,264,250,297),(14,219,68,135,186,263,251,296),(15,218,69,134,187,262,252,295),(16,217,70,133,188,261,253,294),(17,216,71,132,189,280,254,293),(18,215,72,131,190,279,255,292),(19,214,73,130,191,278,256,291),(20,213,74,129,192,277,257,290),(21,118,302,90,175,222,156,45),(22,117,303,89,176,221,157,44),(23,116,304,88,177,240,158,43),(24,115,305,87,178,239,159,42),(25,114,306,86,179,238,160,41),(26,113,307,85,180,237,141,60),(27,112,308,84,161,236,142,59),(28,111,309,83,162,235,143,58),(29,110,310,82,163,234,144,57),(30,109,311,81,164,233,145,56),(31,108,312,100,165,232,146,55),(32,107,313,99,166,231,147,54),(33,106,314,98,167,230,148,53),(34,105,315,97,168,229,149,52),(35,104,316,96,169,228,150,51),(36,103,317,95,170,227,151,50),(37,102,318,94,171,226,152,49),(38,101,319,93,172,225,153,48),(39,120,320,92,173,224,154,47),(40,119,301,91,174,223,155,46)], [(1,113,11,103),(2,112,12,102),(3,111,13,101),(4,110,14,120),(5,109,15,119),(6,108,16,118),(7,107,17,117),(8,106,18,116),(9,105,19,115),(10,104,20,114),(21,202,31,212),(22,201,32,211),(23,220,33,210),(24,219,34,209),(25,218,35,208),(26,217,36,207),(27,216,37,206),(28,215,38,205),(29,214,39,204),(30,213,40,203),(41,64,51,74),(42,63,52,73),(43,62,53,72),(44,61,54,71),(45,80,55,70),(46,79,56,69),(47,78,57,68),(48,77,58,67),(49,76,59,66),(50,75,60,65),(81,252,91,242),(82,251,92,241),(83,250,93,260),(84,249,94,259),(85,248,95,258),(86,247,96,257),(87,246,97,256),(88,245,98,255),(89,244,99,254),(90,243,100,253),(121,143,131,153),(122,142,132,152),(123,141,133,151),(124,160,134,150),(125,159,135,149),(126,158,136,148),(127,157,137,147),(128,156,138,146),(129,155,139,145),(130,154,140,144),(161,280,171,270),(162,279,172,269),(163,278,173,268),(164,277,174,267),(165,276,175,266),(166,275,176,265),(167,274,177,264),(168,273,178,263),(169,272,179,262),(170,271,180,261),(181,229,191,239),(182,228,192,238),(183,227,193,237),(184,226,194,236),(185,225,195,235),(186,224,196,234),(187,223,197,233),(188,222,198,232),(189,221,199,231),(190,240,200,230),(281,310,291,320),(282,309,292,319),(283,308,293,318),(284,307,294,317),(285,306,295,316),(286,305,296,315),(287,304,297,314),(288,303,298,313),(289,302,299,312),(290,301,300,311)]])
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 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | - | - | + | + | - | |||||
| image | C1 | C2 | C2 | C2 | C4 | D4 | D5 | D8 | SD16 | Q16 | D10 | C4×D5 | D20 | C5⋊D4 | C40⋊C2 | Dic20 | C4.10D4 | D4⋊D5 | Q8⋊D5 | C4.12D20 |
| kernel | C20.47D8 | C20⋊3C8 | C5×C4⋊C8 | C20⋊2Q8 | C4⋊Dic5 | C2×C20 | C4⋊C8 | C20 | C20 | C20 | C42 | C2×C4 | C2×C4 | C2×C4 | C4 | C4 | C10 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 4 | 2 | 2 | 2 | 4 | 2 | 2 | 4 | 4 | 4 | 8 | 8 | 1 | 2 | 2 | 4 |
Matrix representation of C20.47D8 ►in GL6(𝔽41)
| 40 | 2 | 0 | 0 | 0 | 0 |
| 40 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 40 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 20 | 28 | 0 | 0 | 0 | 0 |
| 34 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 14 | 14 | 0 | 0 |
| 0 | 0 | 30 | 27 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 26 |
| 0 | 0 | 0 | 0 | 15 | 15 |
| 37 | 12 | 0 | 0 | 0 | 0 |
| 2 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 7 | 0 | 0 |
| 0 | 0 | 40 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 18 |
| 0 | 0 | 0 | 0 | 18 | 28 |
G:=sub<GL(6,GF(41))| [40,40,0,0,0,0,2,1,0,0,0,0,0,0,0,40,0,0,0,0,1,7,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[20,34,0,0,0,0,28,21,0,0,0,0,0,0,14,30,0,0,0,0,14,27,0,0,0,0,0,0,15,15,0,0,0,0,26,15],[37,2,0,0,0,0,12,4,0,0,0,0,0,0,34,40,0,0,0,0,7,7,0,0,0,0,0,0,13,18,0,0,0,0,18,28] >;
C20.47D8 in GAP, Magma, Sage, TeX
C_{20}._{47}D_8 % in TeX
G:=Group("C20.47D8"); // GroupNames label
G:=SmallGroup(320,40);
// by ID
G=gap.SmallGroup(320,40);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,85,316,422,387,268,570,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=a^10,b*a*b^-1=c*a*c^-1=a^-1,c*b*c^-1=a^5*b^-1>;
// generators/relations