metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20.39SD16, C42.191D10, C20.16M4(2), C5⋊2C8⋊2C8, C4⋊C8.2D5, C5⋊4(C8⋊2C8), C4.12(C8×D5), C20.26(C2×C8), C10.16(C4⋊C8), (C2×C20).32Q8, C20⋊3C8.7C2, (C2×C20).486D4, C4.8(C8⋊D5), C4.14(Q8⋊D5), C10.6(C4.Q8), C4.14(D4.D5), (C4×C20).38C22, (C2×C4).19Dic10, C2.4(C20.8Q8), C2.1(C20.Q8), C10.10(C8.C4), C2.2(C20.53D4), C22.19(C10.D4), (C5×C4⋊C8).2C2, (C4×C5⋊2C8).2C2, (C2×C5⋊2C8).8C4, (C2×C4).134(C4×D5), (C2×C10).60(C4⋊C4), (C2×C20).220(C2×C4), (C2×C4).264(C5⋊D4), SmallGroup(320,38)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20.39SD16
G = < a,b,c | a20=b8=1, c2=a5, bab-1=a9, ac=ca, cbc-1=b3 >
Smallest permutation representation of C20.39SD16
►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)
(1 307 125 191 149 111 80 97)(2 316 126 200 150 120 61 86)(3 305 127 189 151 109 62 95)(4 314 128 198 152 118 63 84)(5 303 129 187 153 107 64 93)(6 312 130 196 154 116 65 82)(7 301 131 185 155 105 66 91)(8 310 132 194 156 114 67 100)(9 319 133 183 157 103 68 89)(10 308 134 192 158 112 69 98)(11 317 135 181 159 101 70 87)(12 306 136 190 160 110 71 96)(13 315 137 199 141 119 72 85)(14 304 138 188 142 108 73 94)(15 313 139 197 143 117 74 83)(16 302 140 186 144 106 75 92)(17 311 121 195 145 115 76 81)(18 320 122 184 146 104 77 90)(19 309 123 193 147 113 78 99)(20 318 124 182 148 102 79 88)(21 173 267 51 215 291 226 252)(22 162 268 60 216 300 227 241)(23 171 269 49 217 289 228 250)(24 180 270 58 218 298 229 259)(25 169 271 47 219 287 230 248)(26 178 272 56 220 296 231 257)(27 167 273 45 201 285 232 246)(28 176 274 54 202 294 233 255)(29 165 275 43 203 283 234 244)(30 174 276 52 204 292 235 253)(31 163 277 41 205 281 236 242)(32 172 278 50 206 290 237 251)(33 161 279 59 207 299 238 260)(34 170 280 48 208 288 239 249)(35 179 261 57 209 297 240 258)(36 168 262 46 210 286 221 247)(37 177 263 55 211 295 222 256)(38 166 264 44 212 284 223 245)(39 175 265 53 213 293 224 254)(40 164 266 42 214 282 225 243)
(1 238 6 223 11 228 16 233)(2 239 7 224 12 229 17 234)(3 240 8 225 13 230 18 235)(4 221 9 226 14 231 19 236)(5 222 10 227 15 232 20 237)(21 73 26 78 31 63 36 68)(22 74 27 79 32 64 37 69)(23 75 28 80 33 65 38 70)(24 76 29 61 34 66 39 71)(25 77 30 62 35 67 40 72)(41 84 46 89 51 94 56 99)(42 85 47 90 52 95 57 100)(43 86 48 91 53 96 58 81)(44 87 49 92 54 97 59 82)(45 88 50 93 55 98 60 83)(101 289 106 294 111 299 116 284)(102 290 107 295 112 300 117 285)(103 291 108 296 113 281 118 286)(104 292 109 297 114 282 119 287)(105 293 110 298 115 283 120 288)(121 203 126 208 131 213 136 218)(122 204 127 209 132 214 137 219)(123 205 128 210 133 215 138 220)(124 206 129 211 134 216 139 201)(125 207 130 212 135 217 140 202)(141 271 146 276 151 261 156 266)(142 272 147 277 152 262 157 267)(143 273 148 278 153 263 158 268)(144 274 149 279 154 264 159 269)(145 275 150 280 155 265 160 270)(161 312 166 317 171 302 176 307)(162 313 167 318 172 303 177 308)(163 314 168 319 173 304 178 309)(164 315 169 320 174 305 179 310)(165 316 170 301 175 306 180 311)(181 250 186 255 191 260 196 245)(182 251 187 256 192 241 197 246)(183 252 188 257 193 242 198 247)(184 253 189 258 194 243 199 248)(185 254 190 259 195 244 200 249)
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), (1,307,125,191,149,111,80,97)(2,316,126,200,150,120,61,86)(3,305,127,189,151,109,62,95)(4,314,128,198,152,118,63,84)(5,303,129,187,153,107,64,93)(6,312,130,196,154,116,65,82)(7,301,131,185,155,105,66,91)(8,310,132,194,156,114,67,100)(9,319,133,183,157,103,68,89)(10,308,134,192,158,112,69,98)(11,317,135,181,159,101,70,87)(12,306,136,190,160,110,71,96)(13,315,137,199,141,119,72,85)(14,304,138,188,142,108,73,94)(15,313,139,197,143,117,74,83)(16,302,140,186,144,106,75,92)(17,311,121,195,145,115,76,81)(18,320,122,184,146,104,77,90)(19,309,123,193,147,113,78,99)(20,318,124,182,148,102,79,88)(21,173,267,51,215,291,226,252)(22,162,268,60,216,300,227,241)(23,171,269,49,217,289,228,250)(24,180,270,58,218,298,229,259)(25,169,271,47,219,287,230,248)(26,178,272,56,220,296,231,257)(27,167,273,45,201,285,232,246)(28,176,274,54,202,294,233,255)(29,165,275,43,203,283,234,244)(30,174,276,52,204,292,235,253)(31,163,277,41,205,281,236,242)(32,172,278,50,206,290,237,251)(33,161,279,59,207,299,238,260)(34,170,280,48,208,288,239,249)(35,179,261,57,209,297,240,258)(36,168,262,46,210,286,221,247)(37,177,263,55,211,295,222,256)(38,166,264,44,212,284,223,245)(39,175,265,53,213,293,224,254)(40,164,266,42,214,282,225,243), (1,238,6,223,11,228,16,233)(2,239,7,224,12,229,17,234)(3,240,8,225,13,230,18,235)(4,221,9,226,14,231,19,236)(5,222,10,227,15,232,20,237)(21,73,26,78,31,63,36,68)(22,74,27,79,32,64,37,69)(23,75,28,80,33,65,38,70)(24,76,29,61,34,66,39,71)(25,77,30,62,35,67,40,72)(41,84,46,89,51,94,56,99)(42,85,47,90,52,95,57,100)(43,86,48,91,53,96,58,81)(44,87,49,92,54,97,59,82)(45,88,50,93,55,98,60,83)(101,289,106,294,111,299,116,284)(102,290,107,295,112,300,117,285)(103,291,108,296,113,281,118,286)(104,292,109,297,114,282,119,287)(105,293,110,298,115,283,120,288)(121,203,126,208,131,213,136,218)(122,204,127,209,132,214,137,219)(123,205,128,210,133,215,138,220)(124,206,129,211,134,216,139,201)(125,207,130,212,135,217,140,202)(141,271,146,276,151,261,156,266)(142,272,147,277,152,262,157,267)(143,273,148,278,153,263,158,268)(144,274,149,279,154,264,159,269)(145,275,150,280,155,265,160,270)(161,312,166,317,171,302,176,307)(162,313,167,318,172,303,177,308)(163,314,168,319,173,304,178,309)(164,315,169,320,174,305,179,310)(165,316,170,301,175,306,180,311)(181,250,186,255,191,260,196,245)(182,251,187,256,192,241,197,246)(183,252,188,257,193,242,198,247)(184,253,189,258,194,243,199,248)(185,254,190,259,195,244,200,249)>;
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), (1,307,125,191,149,111,80,97)(2,316,126,200,150,120,61,86)(3,305,127,189,151,109,62,95)(4,314,128,198,152,118,63,84)(5,303,129,187,153,107,64,93)(6,312,130,196,154,116,65,82)(7,301,131,185,155,105,66,91)(8,310,132,194,156,114,67,100)(9,319,133,183,157,103,68,89)(10,308,134,192,158,112,69,98)(11,317,135,181,159,101,70,87)(12,306,136,190,160,110,71,96)(13,315,137,199,141,119,72,85)(14,304,138,188,142,108,73,94)(15,313,139,197,143,117,74,83)(16,302,140,186,144,106,75,92)(17,311,121,195,145,115,76,81)(18,320,122,184,146,104,77,90)(19,309,123,193,147,113,78,99)(20,318,124,182,148,102,79,88)(21,173,267,51,215,291,226,252)(22,162,268,60,216,300,227,241)(23,171,269,49,217,289,228,250)(24,180,270,58,218,298,229,259)(25,169,271,47,219,287,230,248)(26,178,272,56,220,296,231,257)(27,167,273,45,201,285,232,246)(28,176,274,54,202,294,233,255)(29,165,275,43,203,283,234,244)(30,174,276,52,204,292,235,253)(31,163,277,41,205,281,236,242)(32,172,278,50,206,290,237,251)(33,161,279,59,207,299,238,260)(34,170,280,48,208,288,239,249)(35,179,261,57,209,297,240,258)(36,168,262,46,210,286,221,247)(37,177,263,55,211,295,222,256)(38,166,264,44,212,284,223,245)(39,175,265,53,213,293,224,254)(40,164,266,42,214,282,225,243), (1,238,6,223,11,228,16,233)(2,239,7,224,12,229,17,234)(3,240,8,225,13,230,18,235)(4,221,9,226,14,231,19,236)(5,222,10,227,15,232,20,237)(21,73,26,78,31,63,36,68)(22,74,27,79,32,64,37,69)(23,75,28,80,33,65,38,70)(24,76,29,61,34,66,39,71)(25,77,30,62,35,67,40,72)(41,84,46,89,51,94,56,99)(42,85,47,90,52,95,57,100)(43,86,48,91,53,96,58,81)(44,87,49,92,54,97,59,82)(45,88,50,93,55,98,60,83)(101,289,106,294,111,299,116,284)(102,290,107,295,112,300,117,285)(103,291,108,296,113,281,118,286)(104,292,109,297,114,282,119,287)(105,293,110,298,115,283,120,288)(121,203,126,208,131,213,136,218)(122,204,127,209,132,214,137,219)(123,205,128,210,133,215,138,220)(124,206,129,211,134,216,139,201)(125,207,130,212,135,217,140,202)(141,271,146,276,151,261,156,266)(142,272,147,277,152,262,157,267)(143,273,148,278,153,263,158,268)(144,274,149,279,154,264,159,269)(145,275,150,280,155,265,160,270)(161,312,166,317,171,302,176,307)(162,313,167,318,172,303,177,308)(163,314,168,319,173,304,178,309)(164,315,169,320,174,305,179,310)(165,316,170,301,175,306,180,311)(181,250,186,255,191,260,196,245)(182,251,187,256,192,241,197,246)(183,252,188,257,193,242,198,247)(184,253,189,258,194,243,199,248)(185,254,190,259,195,244,200,249) );
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)], [(1,307,125,191,149,111,80,97),(2,316,126,200,150,120,61,86),(3,305,127,189,151,109,62,95),(4,314,128,198,152,118,63,84),(5,303,129,187,153,107,64,93),(6,312,130,196,154,116,65,82),(7,301,131,185,155,105,66,91),(8,310,132,194,156,114,67,100),(9,319,133,183,157,103,68,89),(10,308,134,192,158,112,69,98),(11,317,135,181,159,101,70,87),(12,306,136,190,160,110,71,96),(13,315,137,199,141,119,72,85),(14,304,138,188,142,108,73,94),(15,313,139,197,143,117,74,83),(16,302,140,186,144,106,75,92),(17,311,121,195,145,115,76,81),(18,320,122,184,146,104,77,90),(19,309,123,193,147,113,78,99),(20,318,124,182,148,102,79,88),(21,173,267,51,215,291,226,252),(22,162,268,60,216,300,227,241),(23,171,269,49,217,289,228,250),(24,180,270,58,218,298,229,259),(25,169,271,47,219,287,230,248),(26,178,272,56,220,296,231,257),(27,167,273,45,201,285,232,246),(28,176,274,54,202,294,233,255),(29,165,275,43,203,283,234,244),(30,174,276,52,204,292,235,253),(31,163,277,41,205,281,236,242),(32,172,278,50,206,290,237,251),(33,161,279,59,207,299,238,260),(34,170,280,48,208,288,239,249),(35,179,261,57,209,297,240,258),(36,168,262,46,210,286,221,247),(37,177,263,55,211,295,222,256),(38,166,264,44,212,284,223,245),(39,175,265,53,213,293,224,254),(40,164,266,42,214,282,225,243)], [(1,238,6,223,11,228,16,233),(2,239,7,224,12,229,17,234),(3,240,8,225,13,230,18,235),(4,221,9,226,14,231,19,236),(5,222,10,227,15,232,20,237),(21,73,26,78,31,63,36,68),(22,74,27,79,32,64,37,69),(23,75,28,80,33,65,38,70),(24,76,29,61,34,66,39,71),(25,77,30,62,35,67,40,72),(41,84,46,89,51,94,56,99),(42,85,47,90,52,95,57,100),(43,86,48,91,53,96,58,81),(44,87,49,92,54,97,59,82),(45,88,50,93,55,98,60,83),(101,289,106,294,111,299,116,284),(102,290,107,295,112,300,117,285),(103,291,108,296,113,281,118,286),(104,292,109,297,114,282,119,287),(105,293,110,298,115,283,120,288),(121,203,126,208,131,213,136,218),(122,204,127,209,132,214,137,219),(123,205,128,210,133,215,138,220),(124,206,129,211,134,216,139,201),(125,207,130,212,135,217,140,202),(141,271,146,276,151,261,156,266),(142,272,147,277,152,262,157,267),(143,273,148,278,153,263,158,268),(144,274,149,279,154,264,159,269),(145,275,150,280,155,265,160,270),(161,312,166,317,171,302,176,307),(162,313,167,318,172,303,177,308),(163,314,168,319,173,304,178,309),(164,315,169,320,174,305,179,310),(165,316,170,301,175,306,180,311),(181,250,186,255,191,260,196,245),(182,251,187,256,192,241,197,246),(183,252,188,257,193,242,198,247),(184,253,189,258,194,243,199,248),(185,254,190,259,195,244,200,249)]])
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 | 4 | 4 | 4 |
| type | + | + | + | + | + | - | + | + | - | - | + | ||||||||||
| image | C1 | C2 | C2 | C2 | C4 | C8 | D4 | Q8 | D5 | M4(2) | SD16 | D10 | C8.C4 | Dic10 | C4×D5 | C5⋊D4 | C8×D5 | C8⋊D5 | D4.D5 | Q8⋊D5 | C20.53D4 |
| kernel | C20.39SD16 | C4×C5⋊2C8 | C20⋊3C8 | C5×C4⋊C8 | C2×C5⋊2C8 | C5⋊2C8 | C2×C20 | C2×C20 | C4⋊C8 | 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 | 4 | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 2 | 2 | 4 |
Matrix representation of C20.39SD16 ►in GL6(𝔽41)
| 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 40 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 33 | 23 | 0 | 0 | 0 | 0 |
| 15 | 8 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 13 | 0 | 0 |
| 0 | 0 | 16 | 23 | 0 | 0 |
| 0 | 0 | 0 | 0 | 26 | 15 |
| 0 | 0 | 0 | 0 | 26 | 26 |
| 12 | 5 | 0 | 0 | 0 | 0 |
| 14 | 29 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 32 | 0 | 0 |
| 0 | 0 | 9 | 30 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 28 |
| 0 | 0 | 0 | 0 | 28 | 23 |
G:=sub<GL(6,GF(41))| [9,0,0,0,0,0,0,9,0,0,0,0,0,0,0,40,0,0,0,0,1,7,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[33,15,0,0,0,0,23,8,0,0,0,0,0,0,18,16,0,0,0,0,13,23,0,0,0,0,0,0,26,26,0,0,0,0,15,26],[12,14,0,0,0,0,5,29,0,0,0,0,0,0,11,9,0,0,0,0,32,30,0,0,0,0,0,0,18,28,0,0,0,0,28,23] >;
C20.39SD16 in GAP, Magma, Sage, TeX
C_{20}._{39}{\rm SD}_{16} % in TeX
G:=Group("C20.39SD16"); // GroupNames label
G:=SmallGroup(320,38);
// by ID
G=gap.SmallGroup(320,38);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,589,36,100,570,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=a^5,b*a*b^-1=a^9,a*c=c*a,c*b*c^-1=b^3>;
// generators/relations
Export