metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20.2D8, C4.10D40, C20.22Q16, C20.1SD16, C42.6D10, C4⋊C8.6D5, C4⋊Dic5.3C4, (C2×C20).466D4, (C2×C4).124D20, C4.7(C40⋊C2), C5⋊3(C4.10D8), C20⋊3C8.10C2, C4.10(D4.D5), (C4×C20).44C22, C20⋊2Q8.10C2, C4.10(C5⋊Q16), C2.5(D20⋊5C4), C2.5(C10.Q16), C10.28(D4⋊C4), C10.10(Q8⋊C4), C2.5(C4.12D20), C10.9(C4.10D4), C22.63(D10⋊C4), (C5×C4⋊C8).6C2, (C2×C4).17(C4×D5), (C2×C20).202(C2×C4), (C2×C4).230(C5⋊D4), (C2×C10).112(C22⋊C4), SmallGroup(320,44)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20.2D8
G = < a,b,c | a20=b8=1, c2=a15, bab-1=a11, cac-1=a9, 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, C20.2D8
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, D40, D10⋊C4, D4.D5, C5⋊Q16, C10.Q16, D20⋊5C4, C4.12D20, C20.2D8
►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)
(1 175 183 157 45 96 108 228)(2 166 184 148 46 87 109 239)(3 177 185 159 47 98 110 230)(4 168 186 150 48 89 111 221)(5 179 187 141 49 100 112 232)(6 170 188 152 50 91 113 223)(7 161 189 143 51 82 114 234)(8 172 190 154 52 93 115 225)(9 163 191 145 53 84 116 236)(10 174 192 156 54 95 117 227)(11 165 193 147 55 86 118 238)(12 176 194 158 56 97 119 229)(13 167 195 149 57 88 120 240)(14 178 196 160 58 99 101 231)(15 169 197 151 59 90 102 222)(16 180 198 142 60 81 103 233)(17 171 199 153 41 92 104 224)(18 162 200 144 42 83 105 235)(19 173 181 155 43 94 106 226)(20 164 182 146 44 85 107 237)(21 302 267 130 247 208 282 74)(22 313 268 121 248 219 283 65)(23 304 269 132 249 210 284 76)(24 315 270 123 250 201 285 67)(25 306 271 134 251 212 286 78)(26 317 272 125 252 203 287 69)(27 308 273 136 253 214 288 80)(28 319 274 127 254 205 289 71)(29 310 275 138 255 216 290 62)(30 301 276 129 256 207 291 73)(31 312 277 140 257 218 292 64)(32 303 278 131 258 209 293 75)(33 314 279 122 259 220 294 66)(34 305 280 133 260 211 295 77)(35 316 261 124 241 202 296 68)(36 307 262 135 242 213 297 79)(37 318 263 126 243 204 298 70)(38 309 264 137 244 215 299 61)(39 320 265 128 245 206 300 72)(40 311 266 139 246 217 281 63)
(1 75 16 70 11 65 6 80)(2 64 17 79 12 74 7 69)(3 73 18 68 13 63 8 78)(4 62 19 77 14 72 9 67)(5 71 20 66 15 61 10 76)(21 239 36 234 31 229 26 224)(22 228 37 223 32 238 27 233)(23 237 38 232 33 227 28 222)(24 226 39 221 34 236 29 231)(25 235 40 230 35 225 30 240)(41 135 56 130 51 125 46 140)(42 124 57 139 52 134 47 129)(43 133 58 128 53 123 48 138)(44 122 59 137 54 132 49 127)(45 131 60 126 55 121 50 136)(81 268 96 263 91 278 86 273)(82 277 97 272 92 267 87 262)(83 266 98 261 93 276 88 271)(84 275 99 270 94 265 89 280)(85 264 100 279 95 274 90 269)(101 320 116 315 111 310 106 305)(102 309 117 304 112 319 107 314)(103 318 118 313 113 308 108 303)(104 307 119 302 114 317 109 312)(105 316 120 311 115 306 110 301)(141 259 156 254 151 249 146 244)(142 248 157 243 152 258 147 253)(143 257 158 252 153 247 148 242)(144 246 159 241 154 256 149 251)(145 255 160 250 155 245 150 260)(161 292 176 287 171 282 166 297)(162 281 177 296 172 291 167 286)(163 290 178 285 173 300 168 295)(164 299 179 294 174 289 169 284)(165 288 180 283 175 298 170 293)(181 211 196 206 191 201 186 216)(182 220 197 215 192 210 187 205)(183 209 198 204 193 219 188 214)(184 218 199 213 194 208 189 203)(185 207 200 202 195 217 190 212)
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), (1,175,183,157,45,96,108,228)(2,166,184,148,46,87,109,239)(3,177,185,159,47,98,110,230)(4,168,186,150,48,89,111,221)(5,179,187,141,49,100,112,232)(6,170,188,152,50,91,113,223)(7,161,189,143,51,82,114,234)(8,172,190,154,52,93,115,225)(9,163,191,145,53,84,116,236)(10,174,192,156,54,95,117,227)(11,165,193,147,55,86,118,238)(12,176,194,158,56,97,119,229)(13,167,195,149,57,88,120,240)(14,178,196,160,58,99,101,231)(15,169,197,151,59,90,102,222)(16,180,198,142,60,81,103,233)(17,171,199,153,41,92,104,224)(18,162,200,144,42,83,105,235)(19,173,181,155,43,94,106,226)(20,164,182,146,44,85,107,237)(21,302,267,130,247,208,282,74)(22,313,268,121,248,219,283,65)(23,304,269,132,249,210,284,76)(24,315,270,123,250,201,285,67)(25,306,271,134,251,212,286,78)(26,317,272,125,252,203,287,69)(27,308,273,136,253,214,288,80)(28,319,274,127,254,205,289,71)(29,310,275,138,255,216,290,62)(30,301,276,129,256,207,291,73)(31,312,277,140,257,218,292,64)(32,303,278,131,258,209,293,75)(33,314,279,122,259,220,294,66)(34,305,280,133,260,211,295,77)(35,316,261,124,241,202,296,68)(36,307,262,135,242,213,297,79)(37,318,263,126,243,204,298,70)(38,309,264,137,244,215,299,61)(39,320,265,128,245,206,300,72)(40,311,266,139,246,217,281,63), (1,75,16,70,11,65,6,80)(2,64,17,79,12,74,7,69)(3,73,18,68,13,63,8,78)(4,62,19,77,14,72,9,67)(5,71,20,66,15,61,10,76)(21,239,36,234,31,229,26,224)(22,228,37,223,32,238,27,233)(23,237,38,232,33,227,28,222)(24,226,39,221,34,236,29,231)(25,235,40,230,35,225,30,240)(41,135,56,130,51,125,46,140)(42,124,57,139,52,134,47,129)(43,133,58,128,53,123,48,138)(44,122,59,137,54,132,49,127)(45,131,60,126,55,121,50,136)(81,268,96,263,91,278,86,273)(82,277,97,272,92,267,87,262)(83,266,98,261,93,276,88,271)(84,275,99,270,94,265,89,280)(85,264,100,279,95,274,90,269)(101,320,116,315,111,310,106,305)(102,309,117,304,112,319,107,314)(103,318,118,313,113,308,108,303)(104,307,119,302,114,317,109,312)(105,316,120,311,115,306,110,301)(141,259,156,254,151,249,146,244)(142,248,157,243,152,258,147,253)(143,257,158,252,153,247,148,242)(144,246,159,241,154,256,149,251)(145,255,160,250,155,245,150,260)(161,292,176,287,171,282,166,297)(162,281,177,296,172,291,167,286)(163,290,178,285,173,300,168,295)(164,299,179,294,174,289,169,284)(165,288,180,283,175,298,170,293)(181,211,196,206,191,201,186,216)(182,220,197,215,192,210,187,205)(183,209,198,204,193,219,188,214)(184,218,199,213,194,208,189,203)(185,207,200,202,195,217,190,212)>;
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), (1,175,183,157,45,96,108,228)(2,166,184,148,46,87,109,239)(3,177,185,159,47,98,110,230)(4,168,186,150,48,89,111,221)(5,179,187,141,49,100,112,232)(6,170,188,152,50,91,113,223)(7,161,189,143,51,82,114,234)(8,172,190,154,52,93,115,225)(9,163,191,145,53,84,116,236)(10,174,192,156,54,95,117,227)(11,165,193,147,55,86,118,238)(12,176,194,158,56,97,119,229)(13,167,195,149,57,88,120,240)(14,178,196,160,58,99,101,231)(15,169,197,151,59,90,102,222)(16,180,198,142,60,81,103,233)(17,171,199,153,41,92,104,224)(18,162,200,144,42,83,105,235)(19,173,181,155,43,94,106,226)(20,164,182,146,44,85,107,237)(21,302,267,130,247,208,282,74)(22,313,268,121,248,219,283,65)(23,304,269,132,249,210,284,76)(24,315,270,123,250,201,285,67)(25,306,271,134,251,212,286,78)(26,317,272,125,252,203,287,69)(27,308,273,136,253,214,288,80)(28,319,274,127,254,205,289,71)(29,310,275,138,255,216,290,62)(30,301,276,129,256,207,291,73)(31,312,277,140,257,218,292,64)(32,303,278,131,258,209,293,75)(33,314,279,122,259,220,294,66)(34,305,280,133,260,211,295,77)(35,316,261,124,241,202,296,68)(36,307,262,135,242,213,297,79)(37,318,263,126,243,204,298,70)(38,309,264,137,244,215,299,61)(39,320,265,128,245,206,300,72)(40,311,266,139,246,217,281,63), (1,75,16,70,11,65,6,80)(2,64,17,79,12,74,7,69)(3,73,18,68,13,63,8,78)(4,62,19,77,14,72,9,67)(5,71,20,66,15,61,10,76)(21,239,36,234,31,229,26,224)(22,228,37,223,32,238,27,233)(23,237,38,232,33,227,28,222)(24,226,39,221,34,236,29,231)(25,235,40,230,35,225,30,240)(41,135,56,130,51,125,46,140)(42,124,57,139,52,134,47,129)(43,133,58,128,53,123,48,138)(44,122,59,137,54,132,49,127)(45,131,60,126,55,121,50,136)(81,268,96,263,91,278,86,273)(82,277,97,272,92,267,87,262)(83,266,98,261,93,276,88,271)(84,275,99,270,94,265,89,280)(85,264,100,279,95,274,90,269)(101,320,116,315,111,310,106,305)(102,309,117,304,112,319,107,314)(103,318,118,313,113,308,108,303)(104,307,119,302,114,317,109,312)(105,316,120,311,115,306,110,301)(141,259,156,254,151,249,146,244)(142,248,157,243,152,258,147,253)(143,257,158,252,153,247,148,242)(144,246,159,241,154,256,149,251)(145,255,160,250,155,245,150,260)(161,292,176,287,171,282,166,297)(162,281,177,296,172,291,167,286)(163,290,178,285,173,300,168,295)(164,299,179,294,174,289,169,284)(165,288,180,283,175,298,170,293)(181,211,196,206,191,201,186,216)(182,220,197,215,192,210,187,205)(183,209,198,204,193,219,188,214)(184,218,199,213,194,208,189,203)(185,207,200,202,195,217,190,212) );
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)], [(1,175,183,157,45,96,108,228),(2,166,184,148,46,87,109,239),(3,177,185,159,47,98,110,230),(4,168,186,150,48,89,111,221),(5,179,187,141,49,100,112,232),(6,170,188,152,50,91,113,223),(7,161,189,143,51,82,114,234),(8,172,190,154,52,93,115,225),(9,163,191,145,53,84,116,236),(10,174,192,156,54,95,117,227),(11,165,193,147,55,86,118,238),(12,176,194,158,56,97,119,229),(13,167,195,149,57,88,120,240),(14,178,196,160,58,99,101,231),(15,169,197,151,59,90,102,222),(16,180,198,142,60,81,103,233),(17,171,199,153,41,92,104,224),(18,162,200,144,42,83,105,235),(19,173,181,155,43,94,106,226),(20,164,182,146,44,85,107,237),(21,302,267,130,247,208,282,74),(22,313,268,121,248,219,283,65),(23,304,269,132,249,210,284,76),(24,315,270,123,250,201,285,67),(25,306,271,134,251,212,286,78),(26,317,272,125,252,203,287,69),(27,308,273,136,253,214,288,80),(28,319,274,127,254,205,289,71),(29,310,275,138,255,216,290,62),(30,301,276,129,256,207,291,73),(31,312,277,140,257,218,292,64),(32,303,278,131,258,209,293,75),(33,314,279,122,259,220,294,66),(34,305,280,133,260,211,295,77),(35,316,261,124,241,202,296,68),(36,307,262,135,242,213,297,79),(37,318,263,126,243,204,298,70),(38,309,264,137,244,215,299,61),(39,320,265,128,245,206,300,72),(40,311,266,139,246,217,281,63)], [(1,75,16,70,11,65,6,80),(2,64,17,79,12,74,7,69),(3,73,18,68,13,63,8,78),(4,62,19,77,14,72,9,67),(5,71,20,66,15,61,10,76),(21,239,36,234,31,229,26,224),(22,228,37,223,32,238,27,233),(23,237,38,232,33,227,28,222),(24,226,39,221,34,236,29,231),(25,235,40,230,35,225,30,240),(41,135,56,130,51,125,46,140),(42,124,57,139,52,134,47,129),(43,133,58,128,53,123,48,138),(44,122,59,137,54,132,49,127),(45,131,60,126,55,121,50,136),(81,268,96,263,91,278,86,273),(82,277,97,272,92,267,87,262),(83,266,98,261,93,276,88,271),(84,275,99,270,94,265,89,280),(85,264,100,279,95,274,90,269),(101,320,116,315,111,310,106,305),(102,309,117,304,112,319,107,314),(103,318,118,313,113,308,108,303),(104,307,119,302,114,317,109,312),(105,316,120,311,115,306,110,301),(141,259,156,254,151,249,146,244),(142,248,157,243,152,258,147,253),(143,257,158,252,153,247,148,242),(144,246,159,241,154,256,149,251),(145,255,160,250,155,245,150,260),(161,292,176,287,171,282,166,297),(162,281,177,296,172,291,167,286),(163,290,178,285,173,300,168,295),(164,299,179,294,174,289,169,284),(165,288,180,283,175,298,170,293),(181,211,196,206,191,201,186,216),(182,220,197,215,192,210,187,205),(183,209,198,204,193,219,188,214),(184,218,199,213,194,208,189,203),(185,207,200,202,195,217,190,212)]])
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 | D40 | C4.10D4 | D4.D5 | C5⋊Q16 | C4.12D20 |
| kernel | C20.2D8 | 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 C20.2D8 ►in GL4(𝔽41) generated by
| 35 | 1 | 0 | 0 |
| 40 | 0 | 0 | 0 |
| 0 | 0 | 1 | 39 |
| 0 | 0 | 1 | 40 |
| 4 | 31 | 0 | 0 |
| 10 | 26 | 0 | 0 |
| 0 | 0 | 25 | 38 |
| 0 | 0 | 3 | 16 |
| 13 | 32 | 0 | 0 |
| 28 | 28 | 0 | 0 |
| 0 | 0 | 11 | 30 |
| 0 | 0 | 26 | 0 |
G:=sub<GL(4,GF(41))| [35,40,0,0,1,0,0,0,0,0,1,1,0,0,39,40],[4,10,0,0,31,26,0,0,0,0,25,3,0,0,38,16],[13,28,0,0,32,28,0,0,0,0,11,26,0,0,30,0] >;
C20.2D8 in GAP, Magma, Sage, TeX
C_{20}._2D_8 % in TeX
G:=Group("C20.2D8"); // GroupNames label
G:=SmallGroup(320,44);
// by ID
G=gap.SmallGroup(320,44);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,141,36,1094,268,1123,346,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=a^15,b*a*b^-1=a^11,c*a*c^-1=a^9,c*b*c^-1=a^5*b^-1>;
// generators/relations