direct product, metacyclic, nilpotent (class 3), monomial, 2-elementary
Aliases: C5×C8⋊2C8, C8⋊2C40, C40⋊10C8, C20.56SD16, C20.54M4(2), C4⋊C8.4C10, C4.6(C2×C40), (C4×C40).29C2, C20.80(C2×C8), (C4×C8).11C10, (C2×C40).37C4, (C2×C8).10C20, C10.20(C4⋊C8), (C2×C20).47Q8, (C2×C20).530D4, C4.15(C5×SD16), C4.4(C5×M4(2)), C42.64(C2×C10), C10.13(C4.Q8), (C4×C20).348C22, C10.12(C8.C4), C2.3(C5×C4⋊C8), (C5×C4⋊C8).10C2, (C2×C4).8(C5×Q8), C2.1(C5×C4.Q8), (C2×C4).61(C2×C20), C2.1(C5×C8.C4), (C2×C4).139(C5×D4), C22.13(C5×C4⋊C4), (C2×C10).84(C4⋊C4), (C2×C20).495(C2×C4), SmallGroup(320,139)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C5×C8⋊2C8
G = < a,b,c | a5=b8=c8=1, ab=ba, ac=ca, cbc-1=b3 >
Smallest permutation representation of C5×C8⋊2C8
►Regular action on 320 points
Generators in S320
(1 247 153 145 137)(2 248 154 146 138)(3 241 155 147 139)(4 242 156 148 140)(5 243 157 149 141)(6 244 158 150 142)(7 245 159 151 143)(8 246 160 152 144)(9 318 308 302 292)(10 319 309 303 293)(11 320 310 304 294)(12 313 311 297 295)(13 314 312 298 296)(14 315 305 299 289)(15 316 306 300 290)(16 317 307 301 291)(17 119 126 33 104)(18 120 127 34 97)(19 113 128 35 98)(20 114 121 36 99)(21 115 122 37 100)(22 116 123 38 101)(23 117 124 39 102)(24 118 125 40 103)(25 130 49 41 110)(26 131 50 42 111)(27 132 51 43 112)(28 133 52 44 105)(29 134 53 45 106)(30 135 54 46 107)(31 136 55 47 108)(32 129 56 48 109)(57 161 169 73 65)(58 162 170 74 66)(59 163 171 75 67)(60 164 172 76 68)(61 165 173 77 69)(62 166 174 78 70)(63 167 175 79 71)(64 168 176 80 72)(81 228 236 212 89)(82 229 237 213 90)(83 230 238 214 91)(84 231 239 215 92)(85 232 240 216 93)(86 225 233 209 94)(87 226 234 210 95)(88 227 235 211 96)(177 185 217 193 201)(178 186 218 194 202)(179 187 219 195 203)(180 188 220 196 204)(181 189 221 197 205)(182 190 222 198 206)(183 191 223 199 207)(184 192 224 200 208)(249 281 279 265 263)(250 282 280 266 264)(251 283 273 267 257)(252 284 274 268 258)(253 285 275 269 259)(254 286 276 270 260)(255 287 277 271 261)(256 288 278 272 262)
(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)
(1 185 26 256 22 212 62 289)(2 188 27 251 23 215 63 292)(3 191 28 254 24 210 64 295)(4 186 29 249 17 213 57 290)(5 189 30 252 18 216 58 293)(6 192 31 255 19 211 59 296)(7 187 32 250 20 214 60 291)(8 190 25 253 21 209 61 294)(9 248 220 132 283 117 92 167)(10 243 221 135 284 120 93 162)(11 246 222 130 285 115 94 165)(12 241 223 133 286 118 95 168)(13 244 224 136 287 113 96 163)(14 247 217 131 288 116 89 166)(15 242 218 134 281 119 90 161)(16 245 219 129 282 114 91 164)(33 229 73 306 148 202 45 265)(34 232 74 309 149 205 46 268)(35 227 75 312 150 208 47 271)(36 230 76 307 151 203 48 266)(37 225 77 310 152 206 41 269)(38 228 78 305 145 201 42 272)(39 231 79 308 146 204 43 267)(40 226 80 311 147 207 44 270)(49 275 122 86 173 320 160 198)(50 278 123 81 174 315 153 193)(51 273 124 84 175 318 154 196)(52 276 125 87 176 313 155 199)(53 279 126 82 169 316 156 194)(54 274 127 85 170 319 157 197)(55 277 128 88 171 314 158 200)(56 280 121 83 172 317 159 195)(65 300 140 178 106 263 104 237)(66 303 141 181 107 258 97 240)(67 298 142 184 108 261 98 235)(68 301 143 179 109 264 99 238)(69 304 144 182 110 259 100 233)(70 299 137 177 111 262 101 236)(71 302 138 180 112 257 102 239)(72 297 139 183 105 260 103 234)
G:=sub<Sym(320)| (1,247,153,145,137)(2,248,154,146,138)(3,241,155,147,139)(4,242,156,148,140)(5,243,157,149,141)(6,244,158,150,142)(7,245,159,151,143)(8,246,160,152,144)(9,318,308,302,292)(10,319,309,303,293)(11,320,310,304,294)(12,313,311,297,295)(13,314,312,298,296)(14,315,305,299,289)(15,316,306,300,290)(16,317,307,301,291)(17,119,126,33,104)(18,120,127,34,97)(19,113,128,35,98)(20,114,121,36,99)(21,115,122,37,100)(22,116,123,38,101)(23,117,124,39,102)(24,118,125,40,103)(25,130,49,41,110)(26,131,50,42,111)(27,132,51,43,112)(28,133,52,44,105)(29,134,53,45,106)(30,135,54,46,107)(31,136,55,47,108)(32,129,56,48,109)(57,161,169,73,65)(58,162,170,74,66)(59,163,171,75,67)(60,164,172,76,68)(61,165,173,77,69)(62,166,174,78,70)(63,167,175,79,71)(64,168,176,80,72)(81,228,236,212,89)(82,229,237,213,90)(83,230,238,214,91)(84,231,239,215,92)(85,232,240,216,93)(86,225,233,209,94)(87,226,234,210,95)(88,227,235,211,96)(177,185,217,193,201)(178,186,218,194,202)(179,187,219,195,203)(180,188,220,196,204)(181,189,221,197,205)(182,190,222,198,206)(183,191,223,199,207)(184,192,224,200,208)(249,281,279,265,263)(250,282,280,266,264)(251,283,273,267,257)(252,284,274,268,258)(253,285,275,269,259)(254,286,276,270,260)(255,287,277,271,261)(256,288,278,272,262), (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), (1,185,26,256,22,212,62,289)(2,188,27,251,23,215,63,292)(3,191,28,254,24,210,64,295)(4,186,29,249,17,213,57,290)(5,189,30,252,18,216,58,293)(6,192,31,255,19,211,59,296)(7,187,32,250,20,214,60,291)(8,190,25,253,21,209,61,294)(9,248,220,132,283,117,92,167)(10,243,221,135,284,120,93,162)(11,246,222,130,285,115,94,165)(12,241,223,133,286,118,95,168)(13,244,224,136,287,113,96,163)(14,247,217,131,288,116,89,166)(15,242,218,134,281,119,90,161)(16,245,219,129,282,114,91,164)(33,229,73,306,148,202,45,265)(34,232,74,309,149,205,46,268)(35,227,75,312,150,208,47,271)(36,230,76,307,151,203,48,266)(37,225,77,310,152,206,41,269)(38,228,78,305,145,201,42,272)(39,231,79,308,146,204,43,267)(40,226,80,311,147,207,44,270)(49,275,122,86,173,320,160,198)(50,278,123,81,174,315,153,193)(51,273,124,84,175,318,154,196)(52,276,125,87,176,313,155,199)(53,279,126,82,169,316,156,194)(54,274,127,85,170,319,157,197)(55,277,128,88,171,314,158,200)(56,280,121,83,172,317,159,195)(65,300,140,178,106,263,104,237)(66,303,141,181,107,258,97,240)(67,298,142,184,108,261,98,235)(68,301,143,179,109,264,99,238)(69,304,144,182,110,259,100,233)(70,299,137,177,111,262,101,236)(71,302,138,180,112,257,102,239)(72,297,139,183,105,260,103,234)>;
G:=Group( (1,247,153,145,137)(2,248,154,146,138)(3,241,155,147,139)(4,242,156,148,140)(5,243,157,149,141)(6,244,158,150,142)(7,245,159,151,143)(8,246,160,152,144)(9,318,308,302,292)(10,319,309,303,293)(11,320,310,304,294)(12,313,311,297,295)(13,314,312,298,296)(14,315,305,299,289)(15,316,306,300,290)(16,317,307,301,291)(17,119,126,33,104)(18,120,127,34,97)(19,113,128,35,98)(20,114,121,36,99)(21,115,122,37,100)(22,116,123,38,101)(23,117,124,39,102)(24,118,125,40,103)(25,130,49,41,110)(26,131,50,42,111)(27,132,51,43,112)(28,133,52,44,105)(29,134,53,45,106)(30,135,54,46,107)(31,136,55,47,108)(32,129,56,48,109)(57,161,169,73,65)(58,162,170,74,66)(59,163,171,75,67)(60,164,172,76,68)(61,165,173,77,69)(62,166,174,78,70)(63,167,175,79,71)(64,168,176,80,72)(81,228,236,212,89)(82,229,237,213,90)(83,230,238,214,91)(84,231,239,215,92)(85,232,240,216,93)(86,225,233,209,94)(87,226,234,210,95)(88,227,235,211,96)(177,185,217,193,201)(178,186,218,194,202)(179,187,219,195,203)(180,188,220,196,204)(181,189,221,197,205)(182,190,222,198,206)(183,191,223,199,207)(184,192,224,200,208)(249,281,279,265,263)(250,282,280,266,264)(251,283,273,267,257)(252,284,274,268,258)(253,285,275,269,259)(254,286,276,270,260)(255,287,277,271,261)(256,288,278,272,262), (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), (1,185,26,256,22,212,62,289)(2,188,27,251,23,215,63,292)(3,191,28,254,24,210,64,295)(4,186,29,249,17,213,57,290)(5,189,30,252,18,216,58,293)(6,192,31,255,19,211,59,296)(7,187,32,250,20,214,60,291)(8,190,25,253,21,209,61,294)(9,248,220,132,283,117,92,167)(10,243,221,135,284,120,93,162)(11,246,222,130,285,115,94,165)(12,241,223,133,286,118,95,168)(13,244,224,136,287,113,96,163)(14,247,217,131,288,116,89,166)(15,242,218,134,281,119,90,161)(16,245,219,129,282,114,91,164)(33,229,73,306,148,202,45,265)(34,232,74,309,149,205,46,268)(35,227,75,312,150,208,47,271)(36,230,76,307,151,203,48,266)(37,225,77,310,152,206,41,269)(38,228,78,305,145,201,42,272)(39,231,79,308,146,204,43,267)(40,226,80,311,147,207,44,270)(49,275,122,86,173,320,160,198)(50,278,123,81,174,315,153,193)(51,273,124,84,175,318,154,196)(52,276,125,87,176,313,155,199)(53,279,126,82,169,316,156,194)(54,274,127,85,170,319,157,197)(55,277,128,88,171,314,158,200)(56,280,121,83,172,317,159,195)(65,300,140,178,106,263,104,237)(66,303,141,181,107,258,97,240)(67,298,142,184,108,261,98,235)(68,301,143,179,109,264,99,238)(69,304,144,182,110,259,100,233)(70,299,137,177,111,262,101,236)(71,302,138,180,112,257,102,239)(72,297,139,183,105,260,103,234) );
G=PermutationGroup([[(1,247,153,145,137),(2,248,154,146,138),(3,241,155,147,139),(4,242,156,148,140),(5,243,157,149,141),(6,244,158,150,142),(7,245,159,151,143),(8,246,160,152,144),(9,318,308,302,292),(10,319,309,303,293),(11,320,310,304,294),(12,313,311,297,295),(13,314,312,298,296),(14,315,305,299,289),(15,316,306,300,290),(16,317,307,301,291),(17,119,126,33,104),(18,120,127,34,97),(19,113,128,35,98),(20,114,121,36,99),(21,115,122,37,100),(22,116,123,38,101),(23,117,124,39,102),(24,118,125,40,103),(25,130,49,41,110),(26,131,50,42,111),(27,132,51,43,112),(28,133,52,44,105),(29,134,53,45,106),(30,135,54,46,107),(31,136,55,47,108),(32,129,56,48,109),(57,161,169,73,65),(58,162,170,74,66),(59,163,171,75,67),(60,164,172,76,68),(61,165,173,77,69),(62,166,174,78,70),(63,167,175,79,71),(64,168,176,80,72),(81,228,236,212,89),(82,229,237,213,90),(83,230,238,214,91),(84,231,239,215,92),(85,232,240,216,93),(86,225,233,209,94),(87,226,234,210,95),(88,227,235,211,96),(177,185,217,193,201),(178,186,218,194,202),(179,187,219,195,203),(180,188,220,196,204),(181,189,221,197,205),(182,190,222,198,206),(183,191,223,199,207),(184,192,224,200,208),(249,281,279,265,263),(250,282,280,266,264),(251,283,273,267,257),(252,284,274,268,258),(253,285,275,269,259),(254,286,276,270,260),(255,287,277,271,261),(256,288,278,272,262)], [(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)], [(1,185,26,256,22,212,62,289),(2,188,27,251,23,215,63,292),(3,191,28,254,24,210,64,295),(4,186,29,249,17,213,57,290),(5,189,30,252,18,216,58,293),(6,192,31,255,19,211,59,296),(7,187,32,250,20,214,60,291),(8,190,25,253,21,209,61,294),(9,248,220,132,283,117,92,167),(10,243,221,135,284,120,93,162),(11,246,222,130,285,115,94,165),(12,241,223,133,286,118,95,168),(13,244,224,136,287,113,96,163),(14,247,217,131,288,116,89,166),(15,242,218,134,281,119,90,161),(16,245,219,129,282,114,91,164),(33,229,73,306,148,202,45,265),(34,232,74,309,149,205,46,268),(35,227,75,312,150,208,47,271),(36,230,76,307,151,203,48,266),(37,225,77,310,152,206,41,269),(38,228,78,305,145,201,42,272),(39,231,79,308,146,204,43,267),(40,226,80,311,147,207,44,270),(49,275,122,86,173,320,160,198),(50,278,123,81,174,315,153,193),(51,273,124,84,175,318,154,196),(52,276,125,87,176,313,155,199),(53,279,126,82,169,316,156,194),(54,274,127,85,170,319,157,197),(55,277,128,88,171,314,158,200),(56,280,121,83,172,317,159,195),(65,300,140,178,106,263,104,237),(66,303,141,181,107,258,97,240),(67,298,142,184,108,261,98,235),(68,301,143,179,109,264,99,238),(69,304,144,182,110,259,100,233),(70,299,137,177,111,262,101,236),(71,302,138,180,112,257,102,239),(72,297,139,183,105,260,103,234)]])
140 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5A | 5B | 5C | 5D | 8A | ··· | 8H | 8I | ··· | 8P | 10A | ··· | 10L | 20A | ··· | 20P | 20Q | ··· | 20AF | 40A | ··· | 40AF | 40AG | ··· | 40BL |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 8 | ··· | 8 | 8 | ··· | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 | 40 | ··· | 40 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
140 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | |||||||||||||||
| image | C1 | C2 | C2 | C4 | C5 | C8 | C10 | C10 | C20 | C40 | D4 | Q8 | M4(2) | SD16 | C8.C4 | C5×D4 | C5×Q8 | C5×M4(2) | C5×SD16 | C5×C8.C4 |
| kernel | C5×C8⋊2C8 | C4×C40 | C5×C4⋊C8 | C2×C40 | C8⋊2C8 | C40 | C4×C8 | C4⋊C8 | C2×C8 | C8 | C2×C20 | C2×C20 | C20 | C20 | C10 | C2×C4 | C2×C4 | C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 4 | 4 | 8 | 4 | 8 | 16 | 32 | 1 | 1 | 2 | 4 | 4 | 4 | 4 | 8 | 16 | 16 |
Matrix representation of C5×C8⋊2C8 ►in GL4(𝔽41) generated by
| 10 | 0 | 0 | 0 |
| 0 | 10 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 40 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 30 |
| 0 | 0 | 26 | 30 |
| 9 | 16 | 0 | 0 |
| 16 | 32 | 0 | 0 |
| 0 | 0 | 26 | 23 |
| 0 | 0 | 17 | 15 |
G:=sub<GL(4,GF(41))| [10,0,0,0,0,10,0,0,0,0,1,0,0,0,0,1],[0,1,0,0,40,0,0,0,0,0,0,26,0,0,30,30],[9,16,0,0,16,32,0,0,0,0,26,17,0,0,23,15] >;
C5×C8⋊2C8 in GAP, Magma, Sage, TeX
C_5\times C_8\rtimes_2C_8
% in TeX
G:=Group("C5xC8:2C8"); // GroupNames label
G:=SmallGroup(320,139);
// by ID
G=gap.SmallGroup(320,139);
# by ID
G:=PCGroup([7,-2,-2,-5,-2,-2,-2,-2,280,309,148,2803,136,172]);
// Polycyclic
G:=Group<a,b,c|a^5=b^8=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^3>;
// generators/relations
Export