metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic10⋊4C8, C20.25Q16, C20.40SD16, C42.193D10, C20.18M4(2), C5⋊4(Q8⋊C8), C4⋊C8.5D5, C4.2(C8×D5), C10.23C4≀C2, C20.28(C2×C8), (C2×C20).226D4, (C2×C4).110D20, C4.2(C8⋊D5), C4⋊Dic5.27C4, C4.15(D4.D5), (C4×C20).42C22, (C4×Dic10).6C2, C4.13(C5⋊Q16), C2.2(D20⋊7C4), C2.8(D10⋊1C8), C10.21(C22⋊C8), C10.9(Q8⋊C4), (C2×Dic10).24C4, C2.1(C10.Q16), C22.35(D10⋊C4), (C5×C4⋊C8).5C2, (C4×C5⋊2C8).3C2, (C2×C4).66(C4×D5), (C2×C20).222(C2×C4), (C2×C4).266(C5⋊D4), (C2×C10).110(C22⋊C4), SmallGroup(320,42)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic10⋊4C8
G = < a,b,c | a20=c8=1, b2=a10, bab-1=a-1, cac-1=a11, cbc-1=a5b >
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, C4×C5⋊2C8, C5×C4⋊C8, C4×Dic10, Dic10⋊4C8
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, D10⋊C4, D4.D5, C5⋊Q16, C10.Q16, D10⋊1C8, D20⋊7C4, Dic10⋊4C8
►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)
(1 144 11 154)(2 143 12 153)(3 142 13 152)(4 141 14 151)(5 160 15 150)(6 159 16 149)(7 158 17 148)(8 157 18 147)(9 156 19 146)(10 155 20 145)(21 181 31 191)(22 200 32 190)(23 199 33 189)(24 198 34 188)(25 197 35 187)(26 196 36 186)(27 195 37 185)(28 194 38 184)(29 193 39 183)(30 192 40 182)(41 130 51 140)(42 129 52 139)(43 128 53 138)(44 127 54 137)(45 126 55 136)(46 125 56 135)(47 124 57 134)(48 123 58 133)(49 122 59 132)(50 121 60 131)(61 202 71 212)(62 201 72 211)(63 220 73 210)(64 219 74 209)(65 218 75 208)(66 217 76 207)(67 216 77 206)(68 215 78 205)(69 214 79 204)(70 213 80 203)(81 256 91 246)(82 255 92 245)(83 254 93 244)(84 253 94 243)(85 252 95 242)(86 251 96 241)(87 250 97 260)(88 249 98 259)(89 248 99 258)(90 247 100 257)(101 281 111 291)(102 300 112 290)(103 299 113 289)(104 298 114 288)(105 297 115 287)(106 296 116 286)(107 295 117 285)(108 294 118 284)(109 293 119 283)(110 292 120 282)(161 261 171 271)(162 280 172 270)(163 279 173 269)(164 278 174 268)(165 277 175 267)(166 276 176 266)(167 275 177 265)(168 274 178 264)(169 273 179 263)(170 272 180 262)(221 319 231 309)(222 318 232 308)(223 317 233 307)(224 316 234 306)(225 315 235 305)(226 314 236 304)(227 313 237 303)(228 312 238 302)(229 311 239 301)(230 310 240 320)
(1 109 272 63 36 224 89 49)(2 120 273 74 37 235 90 60)(3 111 274 65 38 226 91 51)(4 102 275 76 39 237 92 42)(5 113 276 67 40 228 93 53)(6 104 277 78 21 239 94 44)(7 115 278 69 22 230 95 55)(8 106 279 80 23 221 96 46)(9 117 280 71 24 232 97 57)(10 108 261 62 25 223 98 48)(11 119 262 73 26 234 99 59)(12 110 263 64 27 225 100 50)(13 101 264 75 28 236 81 41)(14 112 265 66 29 227 82 52)(15 103 266 77 30 238 83 43)(16 114 267 68 31 229 84 54)(17 105 268 79 32 240 85 45)(18 116 269 70 33 231 86 56)(19 107 270 61 34 222 87 47)(20 118 271 72 35 233 88 58)(121 148 292 164 219 190 315 252)(122 159 293 175 220 181 316 243)(123 150 294 166 201 192 317 254)(124 141 295 177 202 183 318 245)(125 152 296 168 203 194 319 256)(126 143 297 179 204 185 320 247)(127 154 298 170 205 196 301 258)(128 145 299 161 206 187 302 249)(129 156 300 172 207 198 303 260)(130 147 281 163 208 189 304 251)(131 158 282 174 209 200 305 242)(132 149 283 165 210 191 306 253)(133 160 284 176 211 182 307 244)(134 151 285 167 212 193 308 255)(135 142 286 178 213 184 309 246)(136 153 287 169 214 195 310 257)(137 144 288 180 215 186 311 248)(138 155 289 171 216 197 312 259)(139 146 290 162 217 188 313 250)(140 157 291 173 218 199 314 241)
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), (1,144,11,154)(2,143,12,153)(3,142,13,152)(4,141,14,151)(5,160,15,150)(6,159,16,149)(7,158,17,148)(8,157,18,147)(9,156,19,146)(10,155,20,145)(21,181,31,191)(22,200,32,190)(23,199,33,189)(24,198,34,188)(25,197,35,187)(26,196,36,186)(27,195,37,185)(28,194,38,184)(29,193,39,183)(30,192,40,182)(41,130,51,140)(42,129,52,139)(43,128,53,138)(44,127,54,137)(45,126,55,136)(46,125,56,135)(47,124,57,134)(48,123,58,133)(49,122,59,132)(50,121,60,131)(61,202,71,212)(62,201,72,211)(63,220,73,210)(64,219,74,209)(65,218,75,208)(66,217,76,207)(67,216,77,206)(68,215,78,205)(69,214,79,204)(70,213,80,203)(81,256,91,246)(82,255,92,245)(83,254,93,244)(84,253,94,243)(85,252,95,242)(86,251,96,241)(87,250,97,260)(88,249,98,259)(89,248,99,258)(90,247,100,257)(101,281,111,291)(102,300,112,290)(103,299,113,289)(104,298,114,288)(105,297,115,287)(106,296,116,286)(107,295,117,285)(108,294,118,284)(109,293,119,283)(110,292,120,282)(161,261,171,271)(162,280,172,270)(163,279,173,269)(164,278,174,268)(165,277,175,267)(166,276,176,266)(167,275,177,265)(168,274,178,264)(169,273,179,263)(170,272,180,262)(221,319,231,309)(222,318,232,308)(223,317,233,307)(224,316,234,306)(225,315,235,305)(226,314,236,304)(227,313,237,303)(228,312,238,302)(229,311,239,301)(230,310,240,320), (1,109,272,63,36,224,89,49)(2,120,273,74,37,235,90,60)(3,111,274,65,38,226,91,51)(4,102,275,76,39,237,92,42)(5,113,276,67,40,228,93,53)(6,104,277,78,21,239,94,44)(7,115,278,69,22,230,95,55)(8,106,279,80,23,221,96,46)(9,117,280,71,24,232,97,57)(10,108,261,62,25,223,98,48)(11,119,262,73,26,234,99,59)(12,110,263,64,27,225,100,50)(13,101,264,75,28,236,81,41)(14,112,265,66,29,227,82,52)(15,103,266,77,30,238,83,43)(16,114,267,68,31,229,84,54)(17,105,268,79,32,240,85,45)(18,116,269,70,33,231,86,56)(19,107,270,61,34,222,87,47)(20,118,271,72,35,233,88,58)(121,148,292,164,219,190,315,252)(122,159,293,175,220,181,316,243)(123,150,294,166,201,192,317,254)(124,141,295,177,202,183,318,245)(125,152,296,168,203,194,319,256)(126,143,297,179,204,185,320,247)(127,154,298,170,205,196,301,258)(128,145,299,161,206,187,302,249)(129,156,300,172,207,198,303,260)(130,147,281,163,208,189,304,251)(131,158,282,174,209,200,305,242)(132,149,283,165,210,191,306,253)(133,160,284,176,211,182,307,244)(134,151,285,167,212,193,308,255)(135,142,286,178,213,184,309,246)(136,153,287,169,214,195,310,257)(137,144,288,180,215,186,311,248)(138,155,289,171,216,197,312,259)(139,146,290,162,217,188,313,250)(140,157,291,173,218,199,314,241)>;
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), (1,144,11,154)(2,143,12,153)(3,142,13,152)(4,141,14,151)(5,160,15,150)(6,159,16,149)(7,158,17,148)(8,157,18,147)(9,156,19,146)(10,155,20,145)(21,181,31,191)(22,200,32,190)(23,199,33,189)(24,198,34,188)(25,197,35,187)(26,196,36,186)(27,195,37,185)(28,194,38,184)(29,193,39,183)(30,192,40,182)(41,130,51,140)(42,129,52,139)(43,128,53,138)(44,127,54,137)(45,126,55,136)(46,125,56,135)(47,124,57,134)(48,123,58,133)(49,122,59,132)(50,121,60,131)(61,202,71,212)(62,201,72,211)(63,220,73,210)(64,219,74,209)(65,218,75,208)(66,217,76,207)(67,216,77,206)(68,215,78,205)(69,214,79,204)(70,213,80,203)(81,256,91,246)(82,255,92,245)(83,254,93,244)(84,253,94,243)(85,252,95,242)(86,251,96,241)(87,250,97,260)(88,249,98,259)(89,248,99,258)(90,247,100,257)(101,281,111,291)(102,300,112,290)(103,299,113,289)(104,298,114,288)(105,297,115,287)(106,296,116,286)(107,295,117,285)(108,294,118,284)(109,293,119,283)(110,292,120,282)(161,261,171,271)(162,280,172,270)(163,279,173,269)(164,278,174,268)(165,277,175,267)(166,276,176,266)(167,275,177,265)(168,274,178,264)(169,273,179,263)(170,272,180,262)(221,319,231,309)(222,318,232,308)(223,317,233,307)(224,316,234,306)(225,315,235,305)(226,314,236,304)(227,313,237,303)(228,312,238,302)(229,311,239,301)(230,310,240,320), (1,109,272,63,36,224,89,49)(2,120,273,74,37,235,90,60)(3,111,274,65,38,226,91,51)(4,102,275,76,39,237,92,42)(5,113,276,67,40,228,93,53)(6,104,277,78,21,239,94,44)(7,115,278,69,22,230,95,55)(8,106,279,80,23,221,96,46)(9,117,280,71,24,232,97,57)(10,108,261,62,25,223,98,48)(11,119,262,73,26,234,99,59)(12,110,263,64,27,225,100,50)(13,101,264,75,28,236,81,41)(14,112,265,66,29,227,82,52)(15,103,266,77,30,238,83,43)(16,114,267,68,31,229,84,54)(17,105,268,79,32,240,85,45)(18,116,269,70,33,231,86,56)(19,107,270,61,34,222,87,47)(20,118,271,72,35,233,88,58)(121,148,292,164,219,190,315,252)(122,159,293,175,220,181,316,243)(123,150,294,166,201,192,317,254)(124,141,295,177,202,183,318,245)(125,152,296,168,203,194,319,256)(126,143,297,179,204,185,320,247)(127,154,298,170,205,196,301,258)(128,145,299,161,206,187,302,249)(129,156,300,172,207,198,303,260)(130,147,281,163,208,189,304,251)(131,158,282,174,209,200,305,242)(132,149,283,165,210,191,306,253)(133,160,284,176,211,182,307,244)(134,151,285,167,212,193,308,255)(135,142,286,178,213,184,309,246)(136,153,287,169,214,195,310,257)(137,144,288,180,215,186,311,248)(138,155,289,171,216,197,312,259)(139,146,290,162,217,188,313,250)(140,157,291,173,218,199,314,241) );
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)], [(1,144,11,154),(2,143,12,153),(3,142,13,152),(4,141,14,151),(5,160,15,150),(6,159,16,149),(7,158,17,148),(8,157,18,147),(9,156,19,146),(10,155,20,145),(21,181,31,191),(22,200,32,190),(23,199,33,189),(24,198,34,188),(25,197,35,187),(26,196,36,186),(27,195,37,185),(28,194,38,184),(29,193,39,183),(30,192,40,182),(41,130,51,140),(42,129,52,139),(43,128,53,138),(44,127,54,137),(45,126,55,136),(46,125,56,135),(47,124,57,134),(48,123,58,133),(49,122,59,132),(50,121,60,131),(61,202,71,212),(62,201,72,211),(63,220,73,210),(64,219,74,209),(65,218,75,208),(66,217,76,207),(67,216,77,206),(68,215,78,205),(69,214,79,204),(70,213,80,203),(81,256,91,246),(82,255,92,245),(83,254,93,244),(84,253,94,243),(85,252,95,242),(86,251,96,241),(87,250,97,260),(88,249,98,259),(89,248,99,258),(90,247,100,257),(101,281,111,291),(102,300,112,290),(103,299,113,289),(104,298,114,288),(105,297,115,287),(106,296,116,286),(107,295,117,285),(108,294,118,284),(109,293,119,283),(110,292,120,282),(161,261,171,271),(162,280,172,270),(163,279,173,269),(164,278,174,268),(165,277,175,267),(166,276,176,266),(167,275,177,265),(168,274,178,264),(169,273,179,263),(170,272,180,262),(221,319,231,309),(222,318,232,308),(223,317,233,307),(224,316,234,306),(225,315,235,305),(226,314,236,304),(227,313,237,303),(228,312,238,302),(229,311,239,301),(230,310,240,320)], [(1,109,272,63,36,224,89,49),(2,120,273,74,37,235,90,60),(3,111,274,65,38,226,91,51),(4,102,275,76,39,237,92,42),(5,113,276,67,40,228,93,53),(6,104,277,78,21,239,94,44),(7,115,278,69,22,230,95,55),(8,106,279,80,23,221,96,46),(9,117,280,71,24,232,97,57),(10,108,261,62,25,223,98,48),(11,119,262,73,26,234,99,59),(12,110,263,64,27,225,100,50),(13,101,264,75,28,236,81,41),(14,112,265,66,29,227,82,52),(15,103,266,77,30,238,83,43),(16,114,267,68,31,229,84,54),(17,105,268,79,32,240,85,45),(18,116,269,70,33,231,86,56),(19,107,270,61,34,222,87,47),(20,118,271,72,35,233,88,58),(121,148,292,164,219,190,315,252),(122,159,293,175,220,181,316,243),(123,150,294,166,201,192,317,254),(124,141,295,177,202,183,318,245),(125,152,296,168,203,194,319,256),(126,143,297,179,204,185,320,247),(127,154,298,170,205,196,301,258),(128,145,299,161,206,187,302,249),(129,156,300,172,207,198,303,260),(130,147,281,163,208,189,304,251),(131,158,282,174,209,200,305,242),(132,149,283,165,210,191,306,253),(133,160,284,176,211,182,307,244),(134,151,285,167,212,193,308,255),(135,142,286,178,213,184,309,246),(136,153,287,169,214,195,310,257),(137,144,288,180,215,186,311,248),(138,155,289,171,216,197,312,259),(139,146,290,162,217,188,313,250),(140,157,291,173,218,199,314,241)]])
68 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 5A | 5B | 8A | 8B | 8C | 8D | 8E | ··· | 8L | 10A | ··· | 10F | 20A | ··· | 20H | 20I | ··· | 20P | 40A | ··· | 40P |
| 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 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | 2 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
68 irreducible representations
| dim | 1 | 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 | C4 | C8 | D4 | D5 | M4(2) | SD16 | Q16 | D10 | C4≀C2 | C4×D5 | D20 | C5⋊D4 | C8×D5 | C8⋊D5 | D4.D5 | C5⋊Q16 | D20⋊7C4 |
| kernel | Dic10⋊4C8 | C4×C5⋊2C8 | C5×C4⋊C8 | 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 | 2 | 2 | 4 |
Matrix representation of Dic10⋊4C8 ►in GL4(𝔽41) generated by
| 0 | 1 | 0 | 0 |
| 40 | 0 | 0 | 0 |
| 0 | 0 | 1 | 40 |
| 0 | 0 | 8 | 34 |
| 40 | 11 | 0 | 0 |
| 11 | 1 | 0 | 0 |
| 0 | 0 | 7 | 40 |
| 0 | 0 | 7 | 34 |
| 20 | 38 | 0 | 0 |
| 38 | 21 | 0 | 0 |
| 0 | 0 | 33 | 2 |
| 0 | 0 | 25 | 8 |
G:=sub<GL(4,GF(41))| [0,40,0,0,1,0,0,0,0,0,1,8,0,0,40,34],[40,11,0,0,11,1,0,0,0,0,7,7,0,0,40,34],[20,38,0,0,38,21,0,0,0,0,33,25,0,0,2,8] >;
Dic10⋊4C8 in GAP, Magma, Sage, TeX
{\rm Dic}_{10}\rtimes_4C_8 % in TeX
G:=Group("Dic10:4C8"); // GroupNames label
G:=SmallGroup(320,42);
// by ID
G=gap.SmallGroup(320,42);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,141,36,100,1123,570,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=c^8=1,b^2=a^10,b*a*b^-1=a^-1,c*a*c^-1=a^11,c*b*c^-1=a^5*b>;
// generators/relations