metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic10⋊1C8, C20.2M4(2), Dic5.11Q16, Dic5.21SD16, C5⋊1(Q8⋊C8), C10.3C4≀C2, C4⋊C4.4F5, C20.2(C2×C8), C4.2(D5⋊C8), C20⋊C8.1C2, C4.2(C4.F5), C10.2(C22⋊C8), C2.1(D4⋊F5), C2.1(Q8⋊F5), (C2×Dic5).96D4, C2.4(D10⋊C8), C10.2(Q8⋊C4), (C2×Dic10).10C4, Dic5⋊3Q8.14C2, C22.32(C22⋊F5), (C4×Dic5).187C22, (C4×C5⋊C8).1C2, (C5×C4⋊C4).4C4, (C2×C4).65(C2×F5), (C2×C20).31(C2×C4), (C2×C10).22(C22⋊C4), SmallGroup(320,210)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic10⋊1C8
G = < a,b,c | a20=c8=1, b2=a10, bab-1=a-1, cac-1=a3, cbc-1=a15b >
Subgroups: 258 in 70 conjugacy classes, 30 normal (28 characteristic)
C1, C2, C4, C4, C22, C5, C8, C2×C4, C2×C4, Q8, C10, C42, C4⋊C4, C4⋊C4, C2×C8, C2×Q8, Dic5, Dic5, C20, C20, C2×C10, C4×C8, C4⋊C8, C4×Q8, C5⋊C8, Dic10, Dic10, C2×Dic5, C2×Dic5, C2×C20, C2×C20, Q8⋊C8, C4×Dic5, C4×Dic5, C10.D4, C5×C4⋊C4, C2×C5⋊C8, C2×Dic10, C4×C5⋊C8, C20⋊C8, Dic5⋊3Q8, Dic10⋊1C8
Quotients: C1, C2, C4, C22, C8, C2×C4, D4, C22⋊C4, C2×C8, M4(2), SD16, Q16, F5, C22⋊C8, Q8⋊C4, C4≀C2, C2×F5, Q8⋊C8, D5⋊C8, C4.F5, C22⋊F5, D10⋊C8, D4⋊F5, Q8⋊F5, Dic10⋊1C8
►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)
(1 241 11 251)(2 260 12 250)(3 259 13 249)(4 258 14 248)(5 257 15 247)(6 256 16 246)(7 255 17 245)(8 254 18 244)(9 253 19 243)(10 252 20 242)(21 83 31 93)(22 82 32 92)(23 81 33 91)(24 100 34 90)(25 99 35 89)(26 98 36 88)(27 97 37 87)(28 96 38 86)(29 95 39 85)(30 94 40 84)(41 236 51 226)(42 235 52 225)(43 234 53 224)(44 233 54 223)(45 232 55 222)(46 231 56 221)(47 230 57 240)(48 229 58 239)(49 228 59 238)(50 227 60 237)(61 184 71 194)(62 183 72 193)(63 182 73 192)(64 181 74 191)(65 200 75 190)(66 199 76 189)(67 198 77 188)(68 197 78 187)(69 196 79 186)(70 195 80 185)(101 176 111 166)(102 175 112 165)(103 174 113 164)(104 173 114 163)(105 172 115 162)(106 171 116 161)(107 170 117 180)(108 169 118 179)(109 168 119 178)(110 167 120 177)(121 142 131 152)(122 141 132 151)(123 160 133 150)(124 159 134 149)(125 158 135 148)(126 157 136 147)(127 156 137 146)(128 155 138 145)(129 154 139 144)(130 153 140 143)(201 308 211 318)(202 307 212 317)(203 306 213 316)(204 305 214 315)(205 304 215 314)(206 303 216 313)(207 302 217 312)(208 301 218 311)(209 320 219 310)(210 319 220 309)(261 298 271 288)(262 297 272 287)(263 296 273 286)(264 295 274 285)(265 294 275 284)(266 293 276 283)(267 292 277 282)(268 291 278 281)(269 290 279 300)(270 289 280 299)
(1 264 134 50 78 40 118 212)(2 271 123 53 79 27 107 215)(3 278 132 56 80 34 116 218)(4 265 121 59 61 21 105 201)(5 272 130 42 62 28 114 204)(6 279 139 45 63 35 103 207)(7 266 128 48 64 22 112 210)(8 273 137 51 65 29 101 213)(9 280 126 54 66 36 110 216)(10 267 135 57 67 23 119 219)(11 274 124 60 68 30 108 202)(12 261 133 43 69 37 117 205)(13 268 122 46 70 24 106 208)(14 275 131 49 71 31 115 211)(15 262 140 52 72 38 104 214)(16 269 129 55 73 25 113 217)(17 276 138 58 74 32 102 220)(18 263 127 41 75 39 111 203)(19 270 136 44 76 26 120 206)(20 277 125 47 77 33 109 209)(81 163 310 257 292 153 240 183)(82 170 319 260 293 160 229 186)(83 177 308 243 294 147 238 189)(84 164 317 246 295 154 227 192)(85 171 306 249 296 141 236 195)(86 178 315 252 297 148 225 198)(87 165 304 255 298 155 234 181)(88 172 313 258 299 142 223 184)(89 179 302 241 300 149 232 187)(90 166 311 244 281 156 221 190)(91 173 320 247 282 143 230 193)(92 180 309 250 283 150 239 196)(93 167 318 253 284 157 228 199)(94 174 307 256 285 144 237 182)(95 161 316 259 286 151 226 185)(96 168 305 242 287 158 235 188)(97 175 314 245 288 145 224 191)(98 162 303 248 289 152 233 194)(99 169 312 251 290 159 222 197)(100 176 301 254 291 146 231 200)
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), (1,241,11,251)(2,260,12,250)(3,259,13,249)(4,258,14,248)(5,257,15,247)(6,256,16,246)(7,255,17,245)(8,254,18,244)(9,253,19,243)(10,252,20,242)(21,83,31,93)(22,82,32,92)(23,81,33,91)(24,100,34,90)(25,99,35,89)(26,98,36,88)(27,97,37,87)(28,96,38,86)(29,95,39,85)(30,94,40,84)(41,236,51,226)(42,235,52,225)(43,234,53,224)(44,233,54,223)(45,232,55,222)(46,231,56,221)(47,230,57,240)(48,229,58,239)(49,228,59,238)(50,227,60,237)(61,184,71,194)(62,183,72,193)(63,182,73,192)(64,181,74,191)(65,200,75,190)(66,199,76,189)(67,198,77,188)(68,197,78,187)(69,196,79,186)(70,195,80,185)(101,176,111,166)(102,175,112,165)(103,174,113,164)(104,173,114,163)(105,172,115,162)(106,171,116,161)(107,170,117,180)(108,169,118,179)(109,168,119,178)(110,167,120,177)(121,142,131,152)(122,141,132,151)(123,160,133,150)(124,159,134,149)(125,158,135,148)(126,157,136,147)(127,156,137,146)(128,155,138,145)(129,154,139,144)(130,153,140,143)(201,308,211,318)(202,307,212,317)(203,306,213,316)(204,305,214,315)(205,304,215,314)(206,303,216,313)(207,302,217,312)(208,301,218,311)(209,320,219,310)(210,319,220,309)(261,298,271,288)(262,297,272,287)(263,296,273,286)(264,295,274,285)(265,294,275,284)(266,293,276,283)(267,292,277,282)(268,291,278,281)(269,290,279,300)(270,289,280,299), (1,264,134,50,78,40,118,212)(2,271,123,53,79,27,107,215)(3,278,132,56,80,34,116,218)(4,265,121,59,61,21,105,201)(5,272,130,42,62,28,114,204)(6,279,139,45,63,35,103,207)(7,266,128,48,64,22,112,210)(8,273,137,51,65,29,101,213)(9,280,126,54,66,36,110,216)(10,267,135,57,67,23,119,219)(11,274,124,60,68,30,108,202)(12,261,133,43,69,37,117,205)(13,268,122,46,70,24,106,208)(14,275,131,49,71,31,115,211)(15,262,140,52,72,38,104,214)(16,269,129,55,73,25,113,217)(17,276,138,58,74,32,102,220)(18,263,127,41,75,39,111,203)(19,270,136,44,76,26,120,206)(20,277,125,47,77,33,109,209)(81,163,310,257,292,153,240,183)(82,170,319,260,293,160,229,186)(83,177,308,243,294,147,238,189)(84,164,317,246,295,154,227,192)(85,171,306,249,296,141,236,195)(86,178,315,252,297,148,225,198)(87,165,304,255,298,155,234,181)(88,172,313,258,299,142,223,184)(89,179,302,241,300,149,232,187)(90,166,311,244,281,156,221,190)(91,173,320,247,282,143,230,193)(92,180,309,250,283,150,239,196)(93,167,318,253,284,157,228,199)(94,174,307,256,285,144,237,182)(95,161,316,259,286,151,226,185)(96,168,305,242,287,158,235,188)(97,175,314,245,288,145,224,191)(98,162,303,248,289,152,233,194)(99,169,312,251,290,159,222,197)(100,176,301,254,291,146,231,200)>;
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), (1,241,11,251)(2,260,12,250)(3,259,13,249)(4,258,14,248)(5,257,15,247)(6,256,16,246)(7,255,17,245)(8,254,18,244)(9,253,19,243)(10,252,20,242)(21,83,31,93)(22,82,32,92)(23,81,33,91)(24,100,34,90)(25,99,35,89)(26,98,36,88)(27,97,37,87)(28,96,38,86)(29,95,39,85)(30,94,40,84)(41,236,51,226)(42,235,52,225)(43,234,53,224)(44,233,54,223)(45,232,55,222)(46,231,56,221)(47,230,57,240)(48,229,58,239)(49,228,59,238)(50,227,60,237)(61,184,71,194)(62,183,72,193)(63,182,73,192)(64,181,74,191)(65,200,75,190)(66,199,76,189)(67,198,77,188)(68,197,78,187)(69,196,79,186)(70,195,80,185)(101,176,111,166)(102,175,112,165)(103,174,113,164)(104,173,114,163)(105,172,115,162)(106,171,116,161)(107,170,117,180)(108,169,118,179)(109,168,119,178)(110,167,120,177)(121,142,131,152)(122,141,132,151)(123,160,133,150)(124,159,134,149)(125,158,135,148)(126,157,136,147)(127,156,137,146)(128,155,138,145)(129,154,139,144)(130,153,140,143)(201,308,211,318)(202,307,212,317)(203,306,213,316)(204,305,214,315)(205,304,215,314)(206,303,216,313)(207,302,217,312)(208,301,218,311)(209,320,219,310)(210,319,220,309)(261,298,271,288)(262,297,272,287)(263,296,273,286)(264,295,274,285)(265,294,275,284)(266,293,276,283)(267,292,277,282)(268,291,278,281)(269,290,279,300)(270,289,280,299), (1,264,134,50,78,40,118,212)(2,271,123,53,79,27,107,215)(3,278,132,56,80,34,116,218)(4,265,121,59,61,21,105,201)(5,272,130,42,62,28,114,204)(6,279,139,45,63,35,103,207)(7,266,128,48,64,22,112,210)(8,273,137,51,65,29,101,213)(9,280,126,54,66,36,110,216)(10,267,135,57,67,23,119,219)(11,274,124,60,68,30,108,202)(12,261,133,43,69,37,117,205)(13,268,122,46,70,24,106,208)(14,275,131,49,71,31,115,211)(15,262,140,52,72,38,104,214)(16,269,129,55,73,25,113,217)(17,276,138,58,74,32,102,220)(18,263,127,41,75,39,111,203)(19,270,136,44,76,26,120,206)(20,277,125,47,77,33,109,209)(81,163,310,257,292,153,240,183)(82,170,319,260,293,160,229,186)(83,177,308,243,294,147,238,189)(84,164,317,246,295,154,227,192)(85,171,306,249,296,141,236,195)(86,178,315,252,297,148,225,198)(87,165,304,255,298,155,234,181)(88,172,313,258,299,142,223,184)(89,179,302,241,300,149,232,187)(90,166,311,244,281,156,221,190)(91,173,320,247,282,143,230,193)(92,180,309,250,283,150,239,196)(93,167,318,253,284,157,228,199)(94,174,307,256,285,144,237,182)(95,161,316,259,286,151,226,185)(96,168,305,242,287,158,235,188)(97,175,314,245,288,145,224,191)(98,162,303,248,289,152,233,194)(99,169,312,251,290,159,222,197)(100,176,301,254,291,146,231,200) );
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)], [(1,241,11,251),(2,260,12,250),(3,259,13,249),(4,258,14,248),(5,257,15,247),(6,256,16,246),(7,255,17,245),(8,254,18,244),(9,253,19,243),(10,252,20,242),(21,83,31,93),(22,82,32,92),(23,81,33,91),(24,100,34,90),(25,99,35,89),(26,98,36,88),(27,97,37,87),(28,96,38,86),(29,95,39,85),(30,94,40,84),(41,236,51,226),(42,235,52,225),(43,234,53,224),(44,233,54,223),(45,232,55,222),(46,231,56,221),(47,230,57,240),(48,229,58,239),(49,228,59,238),(50,227,60,237),(61,184,71,194),(62,183,72,193),(63,182,73,192),(64,181,74,191),(65,200,75,190),(66,199,76,189),(67,198,77,188),(68,197,78,187),(69,196,79,186),(70,195,80,185),(101,176,111,166),(102,175,112,165),(103,174,113,164),(104,173,114,163),(105,172,115,162),(106,171,116,161),(107,170,117,180),(108,169,118,179),(109,168,119,178),(110,167,120,177),(121,142,131,152),(122,141,132,151),(123,160,133,150),(124,159,134,149),(125,158,135,148),(126,157,136,147),(127,156,137,146),(128,155,138,145),(129,154,139,144),(130,153,140,143),(201,308,211,318),(202,307,212,317),(203,306,213,316),(204,305,214,315),(205,304,215,314),(206,303,216,313),(207,302,217,312),(208,301,218,311),(209,320,219,310),(210,319,220,309),(261,298,271,288),(262,297,272,287),(263,296,273,286),(264,295,274,285),(265,294,275,284),(266,293,276,283),(267,292,277,282),(268,291,278,281),(269,290,279,300),(270,289,280,299)], [(1,264,134,50,78,40,118,212),(2,271,123,53,79,27,107,215),(3,278,132,56,80,34,116,218),(4,265,121,59,61,21,105,201),(5,272,130,42,62,28,114,204),(6,279,139,45,63,35,103,207),(7,266,128,48,64,22,112,210),(8,273,137,51,65,29,101,213),(9,280,126,54,66,36,110,216),(10,267,135,57,67,23,119,219),(11,274,124,60,68,30,108,202),(12,261,133,43,69,37,117,205),(13,268,122,46,70,24,106,208),(14,275,131,49,71,31,115,211),(15,262,140,52,72,38,104,214),(16,269,129,55,73,25,113,217),(17,276,138,58,74,32,102,220),(18,263,127,41,75,39,111,203),(19,270,136,44,76,26,120,206),(20,277,125,47,77,33,109,209),(81,163,310,257,292,153,240,183),(82,170,319,260,293,160,229,186),(83,177,308,243,294,147,238,189),(84,164,317,246,295,154,227,192),(85,171,306,249,296,141,236,195),(86,178,315,252,297,148,225,198),(87,165,304,255,298,155,234,181),(88,172,313,258,299,142,223,184),(89,179,302,241,300,149,232,187),(90,166,311,244,281,156,221,190),(91,173,320,247,282,143,230,193),(92,180,309,250,283,150,239,196),(93,167,318,253,284,157,228,199),(94,174,307,256,285,144,237,182),(95,161,316,259,286,151,226,185),(96,168,305,242,287,158,235,188),(97,175,314,245,288,145,224,191),(98,162,303,248,289,152,233,194),(99,169,312,251,290,159,222,197),(100,176,301,254,291,146,231,200)]])
38 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 5 | 8A | ··· | 8H | 8I | 8J | 8K | 8L | 10A | 10B | 10C | 20A | ··· | 20F |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 8 | ··· | 8 | 8 | 8 | 8 | 8 | 10 | 10 | 10 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 5 | 5 | 5 | 5 | 10 | 10 | 20 | 20 | 4 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 4 | 4 | 4 | 8 | ··· | 8 |
38 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 8 | 8 |
| type | + | + | + | + | + | - | + | + | + | - | - | ||||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | C8 | D4 | SD16 | Q16 | M4(2) | C4≀C2 | F5 | C2×F5 | D5⋊C8 | C4.F5 | C22⋊F5 | D4⋊F5 | Q8⋊F5 |
| kernel | Dic10⋊1C8 | C4×C5⋊C8 | C20⋊C8 | Dic5⋊3Q8 | C5×C4⋊C4 | C2×Dic10 | Dic10 | C2×Dic5 | Dic5 | Dic5 | C20 | C10 | C4⋊C4 | C2×C4 | C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 2 | 8 | 2 | 2 | 2 | 2 | 4 | 1 | 1 | 2 | 2 | 2 | 1 | 1 |
Matrix representation of Dic10⋊1C8 ►in GL8(𝔽41)
| 1 | 39 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 40 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 40 | 0 | 0 | 0 |
| 9 | 23 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 23 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 6 | 13 | 25 |
| 0 | 0 | 0 | 0 | 27 | 19 | 38 | 1 |
| 0 | 0 | 0 | 0 | 40 | 3 | 14 | 22 |
| 0 | 0 | 0 | 0 | 24 | 20 | 35 | 28 |
| 11 | 30 | 0 | 0 | 0 | 0 | 0 | 0 |
| 26 | 30 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 26 | 23 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 23 | 17 | 28 |
| 0 | 0 | 0 | 0 | 23 | 10 | 25 | 34 |
| 0 | 0 | 0 | 0 | 31 | 16 | 7 | 10 |
| 0 | 0 | 0 | 0 | 13 | 33 | 35 | 18 |
G:=sub<GL(8,GF(41))| [1,1,0,0,0,0,0,0,39,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,40,40,40,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0],[9,0,0,0,0,0,0,0,23,32,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,23,40,0,0,0,0,0,0,0,0,21,27,40,24,0,0,0,0,6,19,3,20,0,0,0,0,13,38,14,35,0,0,0,0,25,1,22,28],[11,26,0,0,0,0,0,0,30,30,0,0,0,0,0,0,0,0,26,12,0,0,0,0,0,0,23,15,0,0,0,0,0,0,0,0,6,23,31,13,0,0,0,0,23,10,16,33,0,0,0,0,17,25,7,35,0,0,0,0,28,34,10,18] >;
Dic10⋊1C8 in GAP, Magma, Sage, TeX
{\rm Dic}_{10}\rtimes_1C_8 % in TeX
G:=Group("Dic10:1C8"); // GroupNames label
G:=SmallGroup(320,210);
// by ID
G=gap.SmallGroup(320,210);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,141,120,268,1123,570,136,6278,3156]);
// 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^3,c*b*c^-1=a^15*b>;
// generators/relations