metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20.53D8, C20.24Q16, C42.190D10, C20.15M4(2), C5⋊2C8⋊1C8, C4⋊C8.1D5, C5⋊4(C8⋊1C8), C4.11(C8×D5), C20.25(C2×C8), C10.15(C4⋊C8), (C2×C20).31Q8, C20⋊3C8.6C2, C4.26(D4⋊D5), (C2×C20).485D4, C4.7(C8⋊D5), C10.8(C2.D8), (C4×C20).37C22, (C2×C4).18Dic10, C4.12(C5⋊Q16), C10.9(C8.C4), C2.1(C10.D8), C2.3(C20.8Q8), C2.1(C20.53D4), C22.18(C10.D4), (C5×C4⋊C8).1C2, (C2×C5⋊2C8).7C4, (C4×C5⋊2C8).1C2, (C2×C4).133(C4×D5), (C2×C10).59(C4⋊C4), (C2×C20).219(C2×C4), (C2×C4).263(C5⋊D4), SmallGroup(320,37)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20.53D8
G = < a,b,c | a20=b8=1, c2=a5, bab-1=cac-1=a9, cbc-1=b-1 >
Smallest permutation representation of C20.53D8
►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)
(1 319 82 131 57 226 70 212)(2 308 83 140 58 235 71 201)(3 317 84 129 59 224 72 210)(4 306 85 138 60 233 73 219)(5 315 86 127 41 222 74 208)(6 304 87 136 42 231 75 217)(7 313 88 125 43 240 76 206)(8 302 89 134 44 229 77 215)(9 311 90 123 45 238 78 204)(10 320 91 132 46 227 79 213)(11 309 92 121 47 236 80 202)(12 318 93 130 48 225 61 211)(13 307 94 139 49 234 62 220)(14 316 95 128 50 223 63 209)(15 305 96 137 51 232 64 218)(16 314 97 126 52 221 65 207)(17 303 98 135 53 230 66 216)(18 312 99 124 54 239 67 205)(19 301 100 133 55 228 68 214)(20 310 81 122 56 237 69 203)(21 141 264 190 260 172 285 110)(22 150 265 199 241 161 286 119)(23 159 266 188 242 170 287 108)(24 148 267 197 243 179 288 117)(25 157 268 186 244 168 289 106)(26 146 269 195 245 177 290 115)(27 155 270 184 246 166 291 104)(28 144 271 193 247 175 292 113)(29 153 272 182 248 164 293 102)(30 142 273 191 249 173 294 111)(31 151 274 200 250 162 295 120)(32 160 275 189 251 171 296 109)(33 149 276 198 252 180 297 118)(34 158 277 187 253 169 298 107)(35 147 278 196 254 178 299 116)(36 156 279 185 255 167 300 105)(37 145 280 194 256 176 281 114)(38 154 261 183 257 165 282 103)(39 143 262 192 258 174 283 112)(40 152 263 181 259 163 284 101)
(1 285 6 290 11 295 16 300)(2 294 7 299 12 284 17 289)(3 283 8 288 13 293 18 298)(4 292 9 297 14 282 19 287)(5 281 10 286 15 291 20 296)(21 75 26 80 31 65 36 70)(22 64 27 69 32 74 37 79)(23 73 28 78 33 63 38 68)(24 62 29 67 34 72 39 77)(25 71 30 76 35 61 40 66)(41 280 46 265 51 270 56 275)(42 269 47 274 52 279 57 264)(43 278 48 263 53 268 58 273)(44 267 49 272 54 277 59 262)(45 276 50 261 55 266 60 271)(81 251 86 256 91 241 96 246)(82 260 87 245 92 250 97 255)(83 249 88 254 93 259 98 244)(84 258 89 243 94 248 99 253)(85 247 90 252 95 257 100 242)(101 216 106 201 111 206 116 211)(102 205 107 210 112 215 117 220)(103 214 108 219 113 204 118 209)(104 203 109 208 114 213 119 218)(105 212 110 217 115 202 120 207)(121 200 126 185 131 190 136 195)(122 189 127 194 132 199 137 184)(123 198 128 183 133 188 138 193)(124 187 129 192 134 197 139 182)(125 196 130 181 135 186 140 191)(141 231 146 236 151 221 156 226)(142 240 147 225 152 230 157 235)(143 229 148 234 153 239 158 224)(144 238 149 223 154 228 159 233)(145 227 150 232 155 237 160 222)(161 305 166 310 171 315 176 320)(162 314 167 319 172 304 177 309)(163 303 168 308 173 313 178 318)(164 312 169 317 174 302 179 307)(165 301 170 306 175 311 180 316)
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), (1,319,82,131,57,226,70,212)(2,308,83,140,58,235,71,201)(3,317,84,129,59,224,72,210)(4,306,85,138,60,233,73,219)(5,315,86,127,41,222,74,208)(6,304,87,136,42,231,75,217)(7,313,88,125,43,240,76,206)(8,302,89,134,44,229,77,215)(9,311,90,123,45,238,78,204)(10,320,91,132,46,227,79,213)(11,309,92,121,47,236,80,202)(12,318,93,130,48,225,61,211)(13,307,94,139,49,234,62,220)(14,316,95,128,50,223,63,209)(15,305,96,137,51,232,64,218)(16,314,97,126,52,221,65,207)(17,303,98,135,53,230,66,216)(18,312,99,124,54,239,67,205)(19,301,100,133,55,228,68,214)(20,310,81,122,56,237,69,203)(21,141,264,190,260,172,285,110)(22,150,265,199,241,161,286,119)(23,159,266,188,242,170,287,108)(24,148,267,197,243,179,288,117)(25,157,268,186,244,168,289,106)(26,146,269,195,245,177,290,115)(27,155,270,184,246,166,291,104)(28,144,271,193,247,175,292,113)(29,153,272,182,248,164,293,102)(30,142,273,191,249,173,294,111)(31,151,274,200,250,162,295,120)(32,160,275,189,251,171,296,109)(33,149,276,198,252,180,297,118)(34,158,277,187,253,169,298,107)(35,147,278,196,254,178,299,116)(36,156,279,185,255,167,300,105)(37,145,280,194,256,176,281,114)(38,154,261,183,257,165,282,103)(39,143,262,192,258,174,283,112)(40,152,263,181,259,163,284,101), (1,285,6,290,11,295,16,300)(2,294,7,299,12,284,17,289)(3,283,8,288,13,293,18,298)(4,292,9,297,14,282,19,287)(5,281,10,286,15,291,20,296)(21,75,26,80,31,65,36,70)(22,64,27,69,32,74,37,79)(23,73,28,78,33,63,38,68)(24,62,29,67,34,72,39,77)(25,71,30,76,35,61,40,66)(41,280,46,265,51,270,56,275)(42,269,47,274,52,279,57,264)(43,278,48,263,53,268,58,273)(44,267,49,272,54,277,59,262)(45,276,50,261,55,266,60,271)(81,251,86,256,91,241,96,246)(82,260,87,245,92,250,97,255)(83,249,88,254,93,259,98,244)(84,258,89,243,94,248,99,253)(85,247,90,252,95,257,100,242)(101,216,106,201,111,206,116,211)(102,205,107,210,112,215,117,220)(103,214,108,219,113,204,118,209)(104,203,109,208,114,213,119,218)(105,212,110,217,115,202,120,207)(121,200,126,185,131,190,136,195)(122,189,127,194,132,199,137,184)(123,198,128,183,133,188,138,193)(124,187,129,192,134,197,139,182)(125,196,130,181,135,186,140,191)(141,231,146,236,151,221,156,226)(142,240,147,225,152,230,157,235)(143,229,148,234,153,239,158,224)(144,238,149,223,154,228,159,233)(145,227,150,232,155,237,160,222)(161,305,166,310,171,315,176,320)(162,314,167,319,172,304,177,309)(163,303,168,308,173,313,178,318)(164,312,169,317,174,302,179,307)(165,301,170,306,175,311,180,316)>;
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), (1,319,82,131,57,226,70,212)(2,308,83,140,58,235,71,201)(3,317,84,129,59,224,72,210)(4,306,85,138,60,233,73,219)(5,315,86,127,41,222,74,208)(6,304,87,136,42,231,75,217)(7,313,88,125,43,240,76,206)(8,302,89,134,44,229,77,215)(9,311,90,123,45,238,78,204)(10,320,91,132,46,227,79,213)(11,309,92,121,47,236,80,202)(12,318,93,130,48,225,61,211)(13,307,94,139,49,234,62,220)(14,316,95,128,50,223,63,209)(15,305,96,137,51,232,64,218)(16,314,97,126,52,221,65,207)(17,303,98,135,53,230,66,216)(18,312,99,124,54,239,67,205)(19,301,100,133,55,228,68,214)(20,310,81,122,56,237,69,203)(21,141,264,190,260,172,285,110)(22,150,265,199,241,161,286,119)(23,159,266,188,242,170,287,108)(24,148,267,197,243,179,288,117)(25,157,268,186,244,168,289,106)(26,146,269,195,245,177,290,115)(27,155,270,184,246,166,291,104)(28,144,271,193,247,175,292,113)(29,153,272,182,248,164,293,102)(30,142,273,191,249,173,294,111)(31,151,274,200,250,162,295,120)(32,160,275,189,251,171,296,109)(33,149,276,198,252,180,297,118)(34,158,277,187,253,169,298,107)(35,147,278,196,254,178,299,116)(36,156,279,185,255,167,300,105)(37,145,280,194,256,176,281,114)(38,154,261,183,257,165,282,103)(39,143,262,192,258,174,283,112)(40,152,263,181,259,163,284,101), (1,285,6,290,11,295,16,300)(2,294,7,299,12,284,17,289)(3,283,8,288,13,293,18,298)(4,292,9,297,14,282,19,287)(5,281,10,286,15,291,20,296)(21,75,26,80,31,65,36,70)(22,64,27,69,32,74,37,79)(23,73,28,78,33,63,38,68)(24,62,29,67,34,72,39,77)(25,71,30,76,35,61,40,66)(41,280,46,265,51,270,56,275)(42,269,47,274,52,279,57,264)(43,278,48,263,53,268,58,273)(44,267,49,272,54,277,59,262)(45,276,50,261,55,266,60,271)(81,251,86,256,91,241,96,246)(82,260,87,245,92,250,97,255)(83,249,88,254,93,259,98,244)(84,258,89,243,94,248,99,253)(85,247,90,252,95,257,100,242)(101,216,106,201,111,206,116,211)(102,205,107,210,112,215,117,220)(103,214,108,219,113,204,118,209)(104,203,109,208,114,213,119,218)(105,212,110,217,115,202,120,207)(121,200,126,185,131,190,136,195)(122,189,127,194,132,199,137,184)(123,198,128,183,133,188,138,193)(124,187,129,192,134,197,139,182)(125,196,130,181,135,186,140,191)(141,231,146,236,151,221,156,226)(142,240,147,225,152,230,157,235)(143,229,148,234,153,239,158,224)(144,238,149,223,154,228,159,233)(145,227,150,232,155,237,160,222)(161,305,166,310,171,315,176,320)(162,314,167,319,172,304,177,309)(163,303,168,308,173,313,178,318)(164,312,169,317,174,302,179,307)(165,301,170,306,175,311,180,316) );
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)], [(1,319,82,131,57,226,70,212),(2,308,83,140,58,235,71,201),(3,317,84,129,59,224,72,210),(4,306,85,138,60,233,73,219),(5,315,86,127,41,222,74,208),(6,304,87,136,42,231,75,217),(7,313,88,125,43,240,76,206),(8,302,89,134,44,229,77,215),(9,311,90,123,45,238,78,204),(10,320,91,132,46,227,79,213),(11,309,92,121,47,236,80,202),(12,318,93,130,48,225,61,211),(13,307,94,139,49,234,62,220),(14,316,95,128,50,223,63,209),(15,305,96,137,51,232,64,218),(16,314,97,126,52,221,65,207),(17,303,98,135,53,230,66,216),(18,312,99,124,54,239,67,205),(19,301,100,133,55,228,68,214),(20,310,81,122,56,237,69,203),(21,141,264,190,260,172,285,110),(22,150,265,199,241,161,286,119),(23,159,266,188,242,170,287,108),(24,148,267,197,243,179,288,117),(25,157,268,186,244,168,289,106),(26,146,269,195,245,177,290,115),(27,155,270,184,246,166,291,104),(28,144,271,193,247,175,292,113),(29,153,272,182,248,164,293,102),(30,142,273,191,249,173,294,111),(31,151,274,200,250,162,295,120),(32,160,275,189,251,171,296,109),(33,149,276,198,252,180,297,118),(34,158,277,187,253,169,298,107),(35,147,278,196,254,178,299,116),(36,156,279,185,255,167,300,105),(37,145,280,194,256,176,281,114),(38,154,261,183,257,165,282,103),(39,143,262,192,258,174,283,112),(40,152,263,181,259,163,284,101)], [(1,285,6,290,11,295,16,300),(2,294,7,299,12,284,17,289),(3,283,8,288,13,293,18,298),(4,292,9,297,14,282,19,287),(5,281,10,286,15,291,20,296),(21,75,26,80,31,65,36,70),(22,64,27,69,32,74,37,79),(23,73,28,78,33,63,38,68),(24,62,29,67,34,72,39,77),(25,71,30,76,35,61,40,66),(41,280,46,265,51,270,56,275),(42,269,47,274,52,279,57,264),(43,278,48,263,53,268,58,273),(44,267,49,272,54,277,59,262),(45,276,50,261,55,266,60,271),(81,251,86,256,91,241,96,246),(82,260,87,245,92,250,97,255),(83,249,88,254,93,259,98,244),(84,258,89,243,94,248,99,253),(85,247,90,252,95,257,100,242),(101,216,106,201,111,206,116,211),(102,205,107,210,112,215,117,220),(103,214,108,219,113,204,118,209),(104,203,109,208,114,213,119,218),(105,212,110,217,115,202,120,207),(121,200,126,185,131,190,136,195),(122,189,127,194,132,199,137,184),(123,198,128,183,133,188,138,193),(124,187,129,192,134,197,139,182),(125,196,130,181,135,186,140,191),(141,231,146,236,151,221,156,226),(142,240,147,225,152,230,157,235),(143,229,148,234,153,239,158,224),(144,238,149,223,154,228,159,233),(145,227,150,232,155,237,160,222),(161,305,166,310,171,315,176,320),(162,314,167,319,172,304,177,309),(163,303,168,308,173,313,178,318),(164,312,169,317,174,302,179,307),(165,301,170,306,175,311,180,316)]])
68 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5A | 5B | 8A | 8B | 8C | 8D | 8E | ··· | 8L | 8M | 8N | 8O | 8P | 10A | ··· | 10F | 20A | ··· | 20H | 20I | ··· | 20P | 40A | ··· | 40P |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 8 | ··· | 8 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
68 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | - | + | + | - | + | - | + | - | |||||||||
| image | C1 | C2 | C2 | C2 | C4 | C8 | D4 | Q8 | D5 | M4(2) | D8 | Q16 | D10 | C8.C4 | Dic10 | C4×D5 | C5⋊D4 | C8×D5 | C8⋊D5 | D4⋊D5 | C5⋊Q16 | C20.53D4 |
| kernel | C20.53D8 | C4×C5⋊2C8 | C20⋊3C8 | C5×C4⋊C8 | C2×C5⋊2C8 | C5⋊2C8 | C2×C20 | C2×C20 | C4⋊C8 | C20 | C20 | C20 | C42 | C10 | C2×C4 | C2×C4 | C2×C4 | C4 | C4 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 4 | 8 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 2 | 2 | 4 |
Matrix representation of C20.53D8 ►in GL5(𝔽41)
| 9 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 7 | 40 |
| 0 | 0 | 0 | 8 | 40 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 24 | 17 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 29 | 39 |
| 0 | 0 | 0 | 11 | 12 |
| 38 | 0 | 0 | 0 | 0 |
| 0 | 30 | 9 | 0 | 0 |
| 0 | 14 | 11 | 0 | 0 |
| 0 | 0 | 0 | 26 | 38 |
| 0 | 0 | 0 | 20 | 15 |
G:=sub<GL(5,GF(41))| [9,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,7,8,0,0,0,40,40],[40,0,0,0,0,0,24,12,0,0,0,17,0,0,0,0,0,0,29,11,0,0,0,39,12],[38,0,0,0,0,0,30,14,0,0,0,9,11,0,0,0,0,0,26,20,0,0,0,38,15] >;
C20.53D8 in GAP, Magma, Sage, TeX
C_{20}._{53}D_8 % in TeX
G:=Group("C20.53D8"); // GroupNames label
G:=SmallGroup(320,37);
// by ID
G=gap.SmallGroup(320,37);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,141,36,100,570,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=a^5,b*a*b^-1=c*a*c^-1=a^9,c*b*c^-1=b^-1>;
// generators/relations
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