metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic10⋊2C8, C5⋊C8⋊4Q8, C5⋊1(C8×Q8), C2.1(Q8×F5), C20.7(C2×C8), C4⋊C4.13F5, C10.1(C4×Q8), C4.4(D5⋊C8), C20⋊C8.3C2, C10.9(C8○D4), C10.7(C22×C8), Dic5.1(C2×C8), C2.4(D4.F5), Dic5.28(C2×Q8), C10.D4.9C4, Dic5⋊C8.4C2, (C2×Dic10).11C4, Dic5.67(C4○D4), Dic5⋊3Q8.15C2, C22.38(C22×F5), (C4×Dic5).191C22, (C2×Dic5).330C23, (C4×C5⋊C8).8C2, (C5×C4⋊C4).7C4, C2.9(C2×D5⋊C8), (C2×C4).61(C2×F5), (C2×C20).93(C2×C4), (C2×C5⋊C8).27C22, (C2×C10).41(C22×C4), (C2×Dic5).56(C2×C4), SmallGroup(320,1041)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic10⋊C8
G = < a,b,c | a20=c8=1, b2=a10, bab-1=a-1, cac-1=a13, bc=cb >
Subgroups: 282 in 102 conjugacy classes, 56 normal (26 characteristic)
C1, C2, C4, C4, C22, C5, C8, C2×C4, C2×C4, C2×C4, Q8, C10, C42, C4⋊C4, C4⋊C4, C2×C8, C2×Q8, Dic5, Dic5, Dic5, C20, C20, C2×C10, C4×C8, C4⋊C8, C4×Q8, C5⋊C8, C5⋊C8, Dic10, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C8×Q8, C4×Dic5, C4×Dic5, C10.D4, C5×C4⋊C4, C2×C5⋊C8, C2×C5⋊C8, C2×Dic10, C4×C5⋊C8, C4×C5⋊C8, C20⋊C8, Dic5⋊C8, Dic5⋊3Q8, Dic10⋊C8
Quotients: C1, C2, C4, C22, C8, C2×C4, Q8, C23, C2×C8, C22×C4, C2×Q8, C4○D4, F5, C4×Q8, C22×C8, C8○D4, C2×F5, C8×Q8, D5⋊C8, C22×F5, C2×D5⋊C8, D4.F5, Q8×F5, Dic10⋊C8
►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)
(1 287 11 297)(2 286 12 296)(3 285 13 295)(4 284 14 294)(5 283 15 293)(6 282 16 292)(7 281 17 291)(8 300 18 290)(9 299 19 289)(10 298 20 288)(21 85 31 95)(22 84 32 94)(23 83 33 93)(24 82 34 92)(25 81 35 91)(26 100 36 90)(27 99 37 89)(28 98 38 88)(29 97 39 87)(30 96 40 86)(41 186 51 196)(42 185 52 195)(43 184 53 194)(44 183 54 193)(45 182 55 192)(46 181 56 191)(47 200 57 190)(48 199 58 189)(49 198 59 188)(50 197 60 187)(61 303 71 313)(62 302 72 312)(63 301 73 311)(64 320 74 310)(65 319 75 309)(66 318 76 308)(67 317 77 307)(68 316 78 306)(69 315 79 305)(70 314 80 304)(101 179 111 169)(102 178 112 168)(103 177 113 167)(104 176 114 166)(105 175 115 165)(106 174 116 164)(107 173 117 163)(108 172 118 162)(109 171 119 161)(110 170 120 180)(121 253 131 243)(122 252 132 242)(123 251 133 241)(124 250 134 260)(125 249 135 259)(126 248 136 258)(127 247 137 257)(128 246 138 256)(129 245 139 255)(130 244 140 254)(141 266 151 276)(142 265 152 275)(143 264 153 274)(144 263 154 273)(145 262 155 272)(146 261 156 271)(147 280 157 270)(148 279 158 269)(149 278 159 268)(150 277 160 267)(201 234 211 224)(202 233 212 223)(203 232 213 222)(204 231 214 221)(205 230 215 240)(206 229 216 239)(207 228 217 238)(208 227 218 237)(209 226 219 236)(210 225 220 235)
(1 270 191 231 177 79 83 256)(2 267 200 224 178 76 92 249)(3 264 189 237 179 73 81 242)(4 261 198 230 180 70 90 255)(5 278 187 223 161 67 99 248)(6 275 196 236 162 64 88 241)(7 272 185 229 163 61 97 254)(8 269 194 222 164 78 86 247)(9 266 183 235 165 75 95 260)(10 263 192 228 166 72 84 253)(11 280 181 221 167 69 93 246)(12 277 190 234 168 66 82 259)(13 274 199 227 169 63 91 252)(14 271 188 240 170 80 100 245)(15 268 197 233 171 77 89 258)(16 265 186 226 172 74 98 251)(17 262 195 239 173 71 87 244)(18 279 184 232 174 68 96 257)(19 276 193 225 175 65 85 250)(20 273 182 238 176 62 94 243)(21 124 299 151 54 210 105 309)(22 121 288 144 55 207 114 302)(23 138 297 157 56 204 103 315)(24 135 286 150 57 201 112 308)(25 132 295 143 58 218 101 301)(26 129 284 156 59 215 110 314)(27 126 293 149 60 212 119 307)(28 123 282 142 41 209 108 320)(29 140 291 155 42 206 117 313)(30 137 300 148 43 203 106 306)(31 134 289 141 44 220 115 319)(32 131 298 154 45 217 104 312)(33 128 287 147 46 214 113 305)(34 125 296 160 47 211 102 318)(35 122 285 153 48 208 111 311)(36 139 294 146 49 205 120 304)(37 136 283 159 50 202 109 317)(38 133 292 152 51 219 118 310)(39 130 281 145 52 216 107 303)(40 127 290 158 53 213 116 316)
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), (1,287,11,297)(2,286,12,296)(3,285,13,295)(4,284,14,294)(5,283,15,293)(6,282,16,292)(7,281,17,291)(8,300,18,290)(9,299,19,289)(10,298,20,288)(21,85,31,95)(22,84,32,94)(23,83,33,93)(24,82,34,92)(25,81,35,91)(26,100,36,90)(27,99,37,89)(28,98,38,88)(29,97,39,87)(30,96,40,86)(41,186,51,196)(42,185,52,195)(43,184,53,194)(44,183,54,193)(45,182,55,192)(46,181,56,191)(47,200,57,190)(48,199,58,189)(49,198,59,188)(50,197,60,187)(61,303,71,313)(62,302,72,312)(63,301,73,311)(64,320,74,310)(65,319,75,309)(66,318,76,308)(67,317,77,307)(68,316,78,306)(69,315,79,305)(70,314,80,304)(101,179,111,169)(102,178,112,168)(103,177,113,167)(104,176,114,166)(105,175,115,165)(106,174,116,164)(107,173,117,163)(108,172,118,162)(109,171,119,161)(110,170,120,180)(121,253,131,243)(122,252,132,242)(123,251,133,241)(124,250,134,260)(125,249,135,259)(126,248,136,258)(127,247,137,257)(128,246,138,256)(129,245,139,255)(130,244,140,254)(141,266,151,276)(142,265,152,275)(143,264,153,274)(144,263,154,273)(145,262,155,272)(146,261,156,271)(147,280,157,270)(148,279,158,269)(149,278,159,268)(150,277,160,267)(201,234,211,224)(202,233,212,223)(203,232,213,222)(204,231,214,221)(205,230,215,240)(206,229,216,239)(207,228,217,238)(208,227,218,237)(209,226,219,236)(210,225,220,235), (1,270,191,231,177,79,83,256)(2,267,200,224,178,76,92,249)(3,264,189,237,179,73,81,242)(4,261,198,230,180,70,90,255)(5,278,187,223,161,67,99,248)(6,275,196,236,162,64,88,241)(7,272,185,229,163,61,97,254)(8,269,194,222,164,78,86,247)(9,266,183,235,165,75,95,260)(10,263,192,228,166,72,84,253)(11,280,181,221,167,69,93,246)(12,277,190,234,168,66,82,259)(13,274,199,227,169,63,91,252)(14,271,188,240,170,80,100,245)(15,268,197,233,171,77,89,258)(16,265,186,226,172,74,98,251)(17,262,195,239,173,71,87,244)(18,279,184,232,174,68,96,257)(19,276,193,225,175,65,85,250)(20,273,182,238,176,62,94,243)(21,124,299,151,54,210,105,309)(22,121,288,144,55,207,114,302)(23,138,297,157,56,204,103,315)(24,135,286,150,57,201,112,308)(25,132,295,143,58,218,101,301)(26,129,284,156,59,215,110,314)(27,126,293,149,60,212,119,307)(28,123,282,142,41,209,108,320)(29,140,291,155,42,206,117,313)(30,137,300,148,43,203,106,306)(31,134,289,141,44,220,115,319)(32,131,298,154,45,217,104,312)(33,128,287,147,46,214,113,305)(34,125,296,160,47,211,102,318)(35,122,285,153,48,208,111,311)(36,139,294,146,49,205,120,304)(37,136,283,159,50,202,109,317)(38,133,292,152,51,219,118,310)(39,130,281,145,52,216,107,303)(40,127,290,158,53,213,116,316)>;
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), (1,287,11,297)(2,286,12,296)(3,285,13,295)(4,284,14,294)(5,283,15,293)(6,282,16,292)(7,281,17,291)(8,300,18,290)(9,299,19,289)(10,298,20,288)(21,85,31,95)(22,84,32,94)(23,83,33,93)(24,82,34,92)(25,81,35,91)(26,100,36,90)(27,99,37,89)(28,98,38,88)(29,97,39,87)(30,96,40,86)(41,186,51,196)(42,185,52,195)(43,184,53,194)(44,183,54,193)(45,182,55,192)(46,181,56,191)(47,200,57,190)(48,199,58,189)(49,198,59,188)(50,197,60,187)(61,303,71,313)(62,302,72,312)(63,301,73,311)(64,320,74,310)(65,319,75,309)(66,318,76,308)(67,317,77,307)(68,316,78,306)(69,315,79,305)(70,314,80,304)(101,179,111,169)(102,178,112,168)(103,177,113,167)(104,176,114,166)(105,175,115,165)(106,174,116,164)(107,173,117,163)(108,172,118,162)(109,171,119,161)(110,170,120,180)(121,253,131,243)(122,252,132,242)(123,251,133,241)(124,250,134,260)(125,249,135,259)(126,248,136,258)(127,247,137,257)(128,246,138,256)(129,245,139,255)(130,244,140,254)(141,266,151,276)(142,265,152,275)(143,264,153,274)(144,263,154,273)(145,262,155,272)(146,261,156,271)(147,280,157,270)(148,279,158,269)(149,278,159,268)(150,277,160,267)(201,234,211,224)(202,233,212,223)(203,232,213,222)(204,231,214,221)(205,230,215,240)(206,229,216,239)(207,228,217,238)(208,227,218,237)(209,226,219,236)(210,225,220,235), (1,270,191,231,177,79,83,256)(2,267,200,224,178,76,92,249)(3,264,189,237,179,73,81,242)(4,261,198,230,180,70,90,255)(5,278,187,223,161,67,99,248)(6,275,196,236,162,64,88,241)(7,272,185,229,163,61,97,254)(8,269,194,222,164,78,86,247)(9,266,183,235,165,75,95,260)(10,263,192,228,166,72,84,253)(11,280,181,221,167,69,93,246)(12,277,190,234,168,66,82,259)(13,274,199,227,169,63,91,252)(14,271,188,240,170,80,100,245)(15,268,197,233,171,77,89,258)(16,265,186,226,172,74,98,251)(17,262,195,239,173,71,87,244)(18,279,184,232,174,68,96,257)(19,276,193,225,175,65,85,250)(20,273,182,238,176,62,94,243)(21,124,299,151,54,210,105,309)(22,121,288,144,55,207,114,302)(23,138,297,157,56,204,103,315)(24,135,286,150,57,201,112,308)(25,132,295,143,58,218,101,301)(26,129,284,156,59,215,110,314)(27,126,293,149,60,212,119,307)(28,123,282,142,41,209,108,320)(29,140,291,155,42,206,117,313)(30,137,300,148,43,203,106,306)(31,134,289,141,44,220,115,319)(32,131,298,154,45,217,104,312)(33,128,287,147,46,214,113,305)(34,125,296,160,47,211,102,318)(35,122,285,153,48,208,111,311)(36,139,294,146,49,205,120,304)(37,136,283,159,50,202,109,317)(38,133,292,152,51,219,118,310)(39,130,281,145,52,216,107,303)(40,127,290,158,53,213,116,316) );
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)], [(1,287,11,297),(2,286,12,296),(3,285,13,295),(4,284,14,294),(5,283,15,293),(6,282,16,292),(7,281,17,291),(8,300,18,290),(9,299,19,289),(10,298,20,288),(21,85,31,95),(22,84,32,94),(23,83,33,93),(24,82,34,92),(25,81,35,91),(26,100,36,90),(27,99,37,89),(28,98,38,88),(29,97,39,87),(30,96,40,86),(41,186,51,196),(42,185,52,195),(43,184,53,194),(44,183,54,193),(45,182,55,192),(46,181,56,191),(47,200,57,190),(48,199,58,189),(49,198,59,188),(50,197,60,187),(61,303,71,313),(62,302,72,312),(63,301,73,311),(64,320,74,310),(65,319,75,309),(66,318,76,308),(67,317,77,307),(68,316,78,306),(69,315,79,305),(70,314,80,304),(101,179,111,169),(102,178,112,168),(103,177,113,167),(104,176,114,166),(105,175,115,165),(106,174,116,164),(107,173,117,163),(108,172,118,162),(109,171,119,161),(110,170,120,180),(121,253,131,243),(122,252,132,242),(123,251,133,241),(124,250,134,260),(125,249,135,259),(126,248,136,258),(127,247,137,257),(128,246,138,256),(129,245,139,255),(130,244,140,254),(141,266,151,276),(142,265,152,275),(143,264,153,274),(144,263,154,273),(145,262,155,272),(146,261,156,271),(147,280,157,270),(148,279,158,269),(149,278,159,268),(150,277,160,267),(201,234,211,224),(202,233,212,223),(203,232,213,222),(204,231,214,221),(205,230,215,240),(206,229,216,239),(207,228,217,238),(208,227,218,237),(209,226,219,236),(210,225,220,235)], [(1,270,191,231,177,79,83,256),(2,267,200,224,178,76,92,249),(3,264,189,237,179,73,81,242),(4,261,198,230,180,70,90,255),(5,278,187,223,161,67,99,248),(6,275,196,236,162,64,88,241),(7,272,185,229,163,61,97,254),(8,269,194,222,164,78,86,247),(9,266,183,235,165,75,95,260),(10,263,192,228,166,72,84,253),(11,280,181,221,167,69,93,246),(12,277,190,234,168,66,82,259),(13,274,199,227,169,63,91,252),(14,271,188,240,170,80,100,245),(15,268,197,233,171,77,89,258),(16,265,186,226,172,74,98,251),(17,262,195,239,173,71,87,244),(18,279,184,232,174,68,96,257),(19,276,193,225,175,65,85,250),(20,273,182,238,176,62,94,243),(21,124,299,151,54,210,105,309),(22,121,288,144,55,207,114,302),(23,138,297,157,56,204,103,315),(24,135,286,150,57,201,112,308),(25,132,295,143,58,218,101,301),(26,129,284,156,59,215,110,314),(27,126,293,149,60,212,119,307),(28,123,282,142,41,209,108,320),(29,140,291,155,42,206,117,313),(30,137,300,148,43,203,106,306),(31,134,289,141,44,220,115,319),(32,131,298,154,45,217,104,312),(33,128,287,147,46,214,113,305),(34,125,296,160,47,211,102,318),(35,122,285,153,48,208,111,311),(36,139,294,146,49,205,120,304),(37,136,283,159,50,202,109,317),(38,133,292,152,51,219,118,310),(39,130,281,145,52,216,107,303),(40,127,290,158,53,213,116,316)]])
50 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | ··· | 4P | 5 | 8A | ··· | 8H | 8I | ··· | 8T | 10A | 10B | 10C | 20A | ··· | 20F |
| order | 1 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 8 | ··· | 8 | 8 | ··· | 8 | 10 | 10 | 10 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 5 | 5 | 5 | 5 | 10 | ··· | 10 | 4 | 5 | ··· | 5 | 10 | ··· | 10 | 4 | 4 | 4 | 8 | ··· | 8 |
50 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 8 | 8 |
| type | + | + | + | + | + | - | + | + | - | - | |||||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | C4 | C4 | C8 | Q8 | C4○D4 | C8○D4 | F5 | C2×F5 | D5⋊C8 | D4.F5 | Q8×F5 |
| kernel | Dic10⋊C8 | C4×C5⋊C8 | C20⋊C8 | Dic5⋊C8 | Dic5⋊3Q8 | C10.D4 | C5×C4⋊C4 | C2×Dic10 | Dic10 | C5⋊C8 | Dic5 | C10 | C4⋊C4 | C2×C4 | C4 | C2 | C2 |
| # reps | 1 | 3 | 1 | 2 | 1 | 4 | 2 | 2 | 16 | 2 | 2 | 4 | 1 | 3 | 4 | 1 | 1 |
Matrix representation of Dic10⋊C8 ►in GL8(𝔽41)
| 22 | 2 | 0 | 0 | 0 | 0 | 0 | 0 |
| 24 | 19 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 30 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 40 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 32 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 34 | 9 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 30 | 17 | 16 |
| 0 | 0 | 0 | 0 | 8 | 6 | 33 | 16 |
| 0 | 0 | 0 | 0 | 25 | 22 | 33 | 35 |
| 0 | 0 | 0 | 0 | 0 | 22 | 11 | 24 |
| 14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 14 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 14 | 13 | 33 |
| 0 | 0 | 0 | 0 | 26 | 6 | 22 | 5 |
| 0 | 0 | 0 | 0 | 35 | 19 | 36 | 18 |
| 0 | 0 | 0 | 0 | 8 | 32 | 28 | 27 |
G:=sub<GL(8,GF(41))| [22,24,0,0,0,0,0,0,2,19,0,0,0,0,0,0,0,0,30,1,0,0,0,0,0,0,1,11,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0],[32,34,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,19,8,25,0,0,0,0,0,30,6,22,22,0,0,0,0,17,33,33,11,0,0,0,0,16,16,35,24],[14,0,0,0,0,0,0,0,0,14,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,13,26,35,8,0,0,0,0,14,6,19,32,0,0,0,0,13,22,36,28,0,0,0,0,33,5,18,27] >;
Dic10⋊C8 in GAP, Magma, Sage, TeX
{\rm Dic}_{10}\rtimes C_8 % in TeX
G:=Group("Dic10:C8"); // GroupNames label
G:=SmallGroup(320,1041);
// by ID
G=gap.SmallGroup(320,1041);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,120,219,268,136,6278,1595]);
// 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^13,b*c=c*b>;
// generators/relations