metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic10⋊3C8, C20.16Q16, C4.8Dic20, C20.27SD16, C42.246D10, C20.35M4(2), C5⋊3(Q8⋊C8), C4.6(C8×D5), (C4×C8).2D5, (C4×C40).2C2, C10.15C4≀C2, C20.50(C2×C8), C20⋊3C8.1C2, (C2×C4).158D20, (C2×C20).435D4, C4.4(C8⋊D5), C4⋊Dic5.16C4, C4.14(C40⋊C2), (C4×Dic10).1C2, C2.1(D20⋊4C4), C2.3(D10⋊1C8), C10.16(C22⋊C8), (C4×C20).317C22, (C2×Dic10).17C4, C10.12(Q8⋊C4), C2.1(C20.44D4), C22.30(D10⋊C4), (C2×C4).95(C4×D5), (C2×C20).388(C2×C4), (C2×C4).204(C5⋊D4), (C2×C10).99(C22⋊C4), SmallGroup(320,14)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic10⋊3C8
G = < a,b,c | a20=c8=1, b2=a10, bab-1=a-1, ac=ca, cbc-1=a15b >
Subgroups: 230 in 70 conjugacy classes, 35 normal (33 characteristic)
C1, C2, C4, C4, C22, C5, C8, C2×C4, C2×C4, Q8, C10, C42, C42, C4⋊C4, C2×C8, C2×Q8, Dic5, C20, C20, C2×C10, C4×C8, C4⋊C8, C4×Q8, C5⋊2C8, C40, Dic10, Dic10, C2×Dic5, C2×C20, Q8⋊C8, C2×C5⋊2C8, C4×Dic5, C10.D4, C4⋊Dic5, C4×C20, C2×C40, C2×Dic10, C20⋊3C8, C4×C40, C4×Dic10, Dic10⋊3C8
Quotients: C1, C2, C4, C22, C8, C2×C4, D4, D5, C22⋊C4, C2×C8, M4(2), SD16, Q16, D10, C22⋊C8, Q8⋊C4, C4≀C2, C4×D5, D20, C5⋊D4, Q8⋊C8, C8×D5, C8⋊D5, C40⋊C2, Dic20, D10⋊C4, D20⋊4C4, C20.44D4, D10⋊1C8, Dic10⋊3C8
►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 50 11 60)(2 49 12 59)(3 48 13 58)(4 47 14 57)(5 46 15 56)(6 45 16 55)(7 44 17 54)(8 43 18 53)(9 42 19 52)(10 41 20 51)(21 97 31 87)(22 96 32 86)(23 95 33 85)(24 94 34 84)(25 93 35 83)(26 92 36 82)(27 91 37 81)(28 90 38 100)(29 89 39 99)(30 88 40 98)(61 101 71 111)(62 120 72 110)(63 119 73 109)(64 118 74 108)(65 117 75 107)(66 116 76 106)(67 115 77 105)(68 114 78 104)(69 113 79 103)(70 112 80 102)(121 189 131 199)(122 188 132 198)(123 187 133 197)(124 186 134 196)(125 185 135 195)(126 184 136 194)(127 183 137 193)(128 182 138 192)(129 181 139 191)(130 200 140 190)(141 306 151 316)(142 305 152 315)(143 304 153 314)(144 303 154 313)(145 302 155 312)(146 301 156 311)(147 320 157 310)(148 319 158 309)(149 318 159 308)(150 317 160 307)(161 241 171 251)(162 260 172 250)(163 259 173 249)(164 258 174 248)(165 257 175 247)(166 256 176 246)(167 255 177 245)(168 254 178 244)(169 253 179 243)(170 252 180 242)(201 230 211 240)(202 229 212 239)(203 228 213 238)(204 227 214 237)(205 226 215 236)(206 225 216 235)(207 224 217 234)(208 223 218 233)(209 222 219 232)(210 221 220 231)(261 289 271 299)(262 288 272 298)(263 287 273 297)(264 286 274 296)(265 285 275 295)(266 284 276 294)(267 283 277 293)(268 282 278 292)(269 281 279 291)(270 300 280 290)
(1 140 264 62 164 215 307 35)(2 121 265 63 165 216 308 36)(3 122 266 64 166 217 309 37)(4 123 267 65 167 218 310 38)(5 124 268 66 168 219 311 39)(6 125 269 67 169 220 312 40)(7 126 270 68 170 201 313 21)(8 127 271 69 171 202 314 22)(9 128 272 70 172 203 315 23)(10 129 273 71 173 204 316 24)(11 130 274 72 174 205 317 25)(12 131 275 73 175 206 318 26)(13 132 276 74 176 207 319 27)(14 133 277 75 177 208 320 28)(15 134 278 76 178 209 301 29)(16 135 279 77 179 210 302 30)(17 136 280 78 180 211 303 31)(18 137 261 79 161 212 304 32)(19 138 262 80 162 213 305 33)(20 139 263 61 163 214 306 34)(41 196 287 116 249 222 151 99)(42 197 288 117 250 223 152 100)(43 198 289 118 251 224 153 81)(44 199 290 119 252 225 154 82)(45 200 291 120 253 226 155 83)(46 181 292 101 254 227 156 84)(47 182 293 102 255 228 157 85)(48 183 294 103 256 229 158 86)(49 184 295 104 257 230 159 87)(50 185 296 105 258 231 160 88)(51 186 297 106 259 232 141 89)(52 187 298 107 260 233 142 90)(53 188 299 108 241 234 143 91)(54 189 300 109 242 235 144 92)(55 190 281 110 243 236 145 93)(56 191 282 111 244 237 146 94)(57 192 283 112 245 238 147 95)(58 193 284 113 246 239 148 96)(59 194 285 114 247 240 149 97)(60 195 286 115 248 221 150 98)
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), (1,50,11,60)(2,49,12,59)(3,48,13,58)(4,47,14,57)(5,46,15,56)(6,45,16,55)(7,44,17,54)(8,43,18,53)(9,42,19,52)(10,41,20,51)(21,97,31,87)(22,96,32,86)(23,95,33,85)(24,94,34,84)(25,93,35,83)(26,92,36,82)(27,91,37,81)(28,90,38,100)(29,89,39,99)(30,88,40,98)(61,101,71,111)(62,120,72,110)(63,119,73,109)(64,118,74,108)(65,117,75,107)(66,116,76,106)(67,115,77,105)(68,114,78,104)(69,113,79,103)(70,112,80,102)(121,189,131,199)(122,188,132,198)(123,187,133,197)(124,186,134,196)(125,185,135,195)(126,184,136,194)(127,183,137,193)(128,182,138,192)(129,181,139,191)(130,200,140,190)(141,306,151,316)(142,305,152,315)(143,304,153,314)(144,303,154,313)(145,302,155,312)(146,301,156,311)(147,320,157,310)(148,319,158,309)(149,318,159,308)(150,317,160,307)(161,241,171,251)(162,260,172,250)(163,259,173,249)(164,258,174,248)(165,257,175,247)(166,256,176,246)(167,255,177,245)(168,254,178,244)(169,253,179,243)(170,252,180,242)(201,230,211,240)(202,229,212,239)(203,228,213,238)(204,227,214,237)(205,226,215,236)(206,225,216,235)(207,224,217,234)(208,223,218,233)(209,222,219,232)(210,221,220,231)(261,289,271,299)(262,288,272,298)(263,287,273,297)(264,286,274,296)(265,285,275,295)(266,284,276,294)(267,283,277,293)(268,282,278,292)(269,281,279,291)(270,300,280,290), (1,140,264,62,164,215,307,35)(2,121,265,63,165,216,308,36)(3,122,266,64,166,217,309,37)(4,123,267,65,167,218,310,38)(5,124,268,66,168,219,311,39)(6,125,269,67,169,220,312,40)(7,126,270,68,170,201,313,21)(8,127,271,69,171,202,314,22)(9,128,272,70,172,203,315,23)(10,129,273,71,173,204,316,24)(11,130,274,72,174,205,317,25)(12,131,275,73,175,206,318,26)(13,132,276,74,176,207,319,27)(14,133,277,75,177,208,320,28)(15,134,278,76,178,209,301,29)(16,135,279,77,179,210,302,30)(17,136,280,78,180,211,303,31)(18,137,261,79,161,212,304,32)(19,138,262,80,162,213,305,33)(20,139,263,61,163,214,306,34)(41,196,287,116,249,222,151,99)(42,197,288,117,250,223,152,100)(43,198,289,118,251,224,153,81)(44,199,290,119,252,225,154,82)(45,200,291,120,253,226,155,83)(46,181,292,101,254,227,156,84)(47,182,293,102,255,228,157,85)(48,183,294,103,256,229,158,86)(49,184,295,104,257,230,159,87)(50,185,296,105,258,231,160,88)(51,186,297,106,259,232,141,89)(52,187,298,107,260,233,142,90)(53,188,299,108,241,234,143,91)(54,189,300,109,242,235,144,92)(55,190,281,110,243,236,145,93)(56,191,282,111,244,237,146,94)(57,192,283,112,245,238,147,95)(58,193,284,113,246,239,148,96)(59,194,285,114,247,240,149,97)(60,195,286,115,248,221,150,98)>;
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), (1,50,11,60)(2,49,12,59)(3,48,13,58)(4,47,14,57)(5,46,15,56)(6,45,16,55)(7,44,17,54)(8,43,18,53)(9,42,19,52)(10,41,20,51)(21,97,31,87)(22,96,32,86)(23,95,33,85)(24,94,34,84)(25,93,35,83)(26,92,36,82)(27,91,37,81)(28,90,38,100)(29,89,39,99)(30,88,40,98)(61,101,71,111)(62,120,72,110)(63,119,73,109)(64,118,74,108)(65,117,75,107)(66,116,76,106)(67,115,77,105)(68,114,78,104)(69,113,79,103)(70,112,80,102)(121,189,131,199)(122,188,132,198)(123,187,133,197)(124,186,134,196)(125,185,135,195)(126,184,136,194)(127,183,137,193)(128,182,138,192)(129,181,139,191)(130,200,140,190)(141,306,151,316)(142,305,152,315)(143,304,153,314)(144,303,154,313)(145,302,155,312)(146,301,156,311)(147,320,157,310)(148,319,158,309)(149,318,159,308)(150,317,160,307)(161,241,171,251)(162,260,172,250)(163,259,173,249)(164,258,174,248)(165,257,175,247)(166,256,176,246)(167,255,177,245)(168,254,178,244)(169,253,179,243)(170,252,180,242)(201,230,211,240)(202,229,212,239)(203,228,213,238)(204,227,214,237)(205,226,215,236)(206,225,216,235)(207,224,217,234)(208,223,218,233)(209,222,219,232)(210,221,220,231)(261,289,271,299)(262,288,272,298)(263,287,273,297)(264,286,274,296)(265,285,275,295)(266,284,276,294)(267,283,277,293)(268,282,278,292)(269,281,279,291)(270,300,280,290), (1,140,264,62,164,215,307,35)(2,121,265,63,165,216,308,36)(3,122,266,64,166,217,309,37)(4,123,267,65,167,218,310,38)(5,124,268,66,168,219,311,39)(6,125,269,67,169,220,312,40)(7,126,270,68,170,201,313,21)(8,127,271,69,171,202,314,22)(9,128,272,70,172,203,315,23)(10,129,273,71,173,204,316,24)(11,130,274,72,174,205,317,25)(12,131,275,73,175,206,318,26)(13,132,276,74,176,207,319,27)(14,133,277,75,177,208,320,28)(15,134,278,76,178,209,301,29)(16,135,279,77,179,210,302,30)(17,136,280,78,180,211,303,31)(18,137,261,79,161,212,304,32)(19,138,262,80,162,213,305,33)(20,139,263,61,163,214,306,34)(41,196,287,116,249,222,151,99)(42,197,288,117,250,223,152,100)(43,198,289,118,251,224,153,81)(44,199,290,119,252,225,154,82)(45,200,291,120,253,226,155,83)(46,181,292,101,254,227,156,84)(47,182,293,102,255,228,157,85)(48,183,294,103,256,229,158,86)(49,184,295,104,257,230,159,87)(50,185,296,105,258,231,160,88)(51,186,297,106,259,232,141,89)(52,187,298,107,260,233,142,90)(53,188,299,108,241,234,143,91)(54,189,300,109,242,235,144,92)(55,190,281,110,243,236,145,93)(56,191,282,111,244,237,146,94)(57,192,283,112,245,238,147,95)(58,193,284,113,246,239,148,96)(59,194,285,114,247,240,149,97)(60,195,286,115,248,221,150,98) );
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)], [(1,50,11,60),(2,49,12,59),(3,48,13,58),(4,47,14,57),(5,46,15,56),(6,45,16,55),(7,44,17,54),(8,43,18,53),(9,42,19,52),(10,41,20,51),(21,97,31,87),(22,96,32,86),(23,95,33,85),(24,94,34,84),(25,93,35,83),(26,92,36,82),(27,91,37,81),(28,90,38,100),(29,89,39,99),(30,88,40,98),(61,101,71,111),(62,120,72,110),(63,119,73,109),(64,118,74,108),(65,117,75,107),(66,116,76,106),(67,115,77,105),(68,114,78,104),(69,113,79,103),(70,112,80,102),(121,189,131,199),(122,188,132,198),(123,187,133,197),(124,186,134,196),(125,185,135,195),(126,184,136,194),(127,183,137,193),(128,182,138,192),(129,181,139,191),(130,200,140,190),(141,306,151,316),(142,305,152,315),(143,304,153,314),(144,303,154,313),(145,302,155,312),(146,301,156,311),(147,320,157,310),(148,319,158,309),(149,318,159,308),(150,317,160,307),(161,241,171,251),(162,260,172,250),(163,259,173,249),(164,258,174,248),(165,257,175,247),(166,256,176,246),(167,255,177,245),(168,254,178,244),(169,253,179,243),(170,252,180,242),(201,230,211,240),(202,229,212,239),(203,228,213,238),(204,227,214,237),(205,226,215,236),(206,225,216,235),(207,224,217,234),(208,223,218,233),(209,222,219,232),(210,221,220,231),(261,289,271,299),(262,288,272,298),(263,287,273,297),(264,286,274,296),(265,285,275,295),(266,284,276,294),(267,283,277,293),(268,282,278,292),(269,281,279,291),(270,300,280,290)], [(1,140,264,62,164,215,307,35),(2,121,265,63,165,216,308,36),(3,122,266,64,166,217,309,37),(4,123,267,65,167,218,310,38),(5,124,268,66,168,219,311,39),(6,125,269,67,169,220,312,40),(7,126,270,68,170,201,313,21),(8,127,271,69,171,202,314,22),(9,128,272,70,172,203,315,23),(10,129,273,71,173,204,316,24),(11,130,274,72,174,205,317,25),(12,131,275,73,175,206,318,26),(13,132,276,74,176,207,319,27),(14,133,277,75,177,208,320,28),(15,134,278,76,178,209,301,29),(16,135,279,77,179,210,302,30),(17,136,280,78,180,211,303,31),(18,137,261,79,161,212,304,32),(19,138,262,80,162,213,305,33),(20,139,263,61,163,214,306,34),(41,196,287,116,249,222,151,99),(42,197,288,117,250,223,152,100),(43,198,289,118,251,224,153,81),(44,199,290,119,252,225,154,82),(45,200,291,120,253,226,155,83),(46,181,292,101,254,227,156,84),(47,182,293,102,255,228,157,85),(48,183,294,103,256,229,158,86),(49,184,295,104,257,230,159,87),(50,185,296,105,258,231,160,88),(51,186,297,106,259,232,141,89),(52,187,298,107,260,233,142,90),(53,188,299,108,241,234,143,91),(54,189,300,109,242,235,144,92),(55,190,281,110,243,236,145,93),(56,191,282,111,244,237,146,94),(57,192,283,112,245,238,147,95),(58,193,284,113,246,239,148,96),(59,194,285,114,247,240,149,97),(60,195,286,115,248,221,150,98)]])
92 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 5A | 5B | 8A | ··· | 8H | 8I | 8J | 8K | 8L | 10A | ··· | 10F | 20A | ··· | 20X | 40A | ··· | 40AF |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | ··· | 8 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
92 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | - | + | + | - | ||||||||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | C8 | D4 | D5 | M4(2) | SD16 | Q16 | D10 | C4≀C2 | C4×D5 | D20 | C5⋊D4 | C8×D5 | C8⋊D5 | C40⋊C2 | Dic20 | D20⋊4C4 |
| kernel | Dic10⋊3C8 | C20⋊3C8 | C4×C40 | C4×Dic10 | C4⋊Dic5 | C2×Dic10 | Dic10 | 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 | 2 | 2 | 8 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 16 |
Matrix representation of Dic10⋊3C8 ►in GL3(𝔽41) generated by
| 1 | 0 | 0 |
| 0 | 21 | 0 |
| 0 | 0 | 2 |
| 1 | 0 | 0 |
| 0 | 0 | 14 |
| 0 | 38 | 0 |
| 3 | 0 | 0 |
| 0 | 27 | 0 |
| 0 | 0 | 38 |
G:=sub<GL(3,GF(41))| [1,0,0,0,21,0,0,0,2],[1,0,0,0,0,38,0,14,0],[3,0,0,0,27,0,0,0,38] >;
Dic10⋊3C8 in GAP, Magma, Sage, TeX
{\rm Dic}_{10}\rtimes_3C_8 % in TeX
G:=Group("Dic10:3C8"); // GroupNames label
G:=SmallGroup(320,14);
// by ID
G=gap.SmallGroup(320,14);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,85,92,422,100,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=c^8=1,b^2=a^10,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=a^15*b>;
// generators/relations