metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C40⋊1Q8, C8⋊1Dic10, C42.13D10, C5⋊1(C8⋊Q8), (C2×C8).52D10, (C2×C20).34D4, (C2×C4).23D20, C8⋊C4.1D5, C10.5(C4⋊Q8), C20.72(C2×Q8), C40⋊6C4.2C2, (C4×C20).1C22, C20⋊2Q8.6C2, C40⋊5C4.10C2, C2.6(C8⋊D10), C10.1(C8⋊C22), (C2×C40).53C22, C2.9(C20⋊2Q8), C4.38(C2×Dic10), C22.95(C2×D20), C4⋊Dic5.7C22, C20.6Q8.2C2, (C2×C20).729C23, C2.6(C8.D10), C10.1(C8.C22), (C5×C8⋊C4).1C2, (C2×C10).112(C2×D4), (C2×C4).673(C22×D5), SmallGroup(320,329)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C8⋊Dic10
G = < a,b,c | a8=b20=1, c2=b10, bab-1=a5, cac-1=a-1, cbc-1=b-1 >
Subgroups: 350 in 90 conjugacy classes, 47 normal (25 characteristic)
C1, C2, C4, C4, C22, C5, C8, C2×C4, C2×C4, Q8, C10, C42, C4⋊C4, C2×C8, C2×Q8, Dic5, C20, C20, C2×C10, C8⋊C4, C4.Q8, C2.D8, C42.C2, C4⋊Q8, C40, Dic10, C2×Dic5, C2×C20, C8⋊Q8, C10.D4, C4⋊Dic5, C4⋊Dic5, C4⋊Dic5, C4×C20, C2×C40, C2×Dic10, C40⋊6C4, C40⋊5C4, C5×C8⋊C4, C20⋊2Q8, C20.6Q8, C8⋊Dic10
Quotients: C1, C2, C22, D4, Q8, C23, D5, C2×D4, C2×Q8, D10, C4⋊Q8, C8⋊C22, C8.C22, Dic10, D20, C22×D5, C8⋊Q8, C2×Dic10, C2×D20, C20⋊2Q8, C8⋊D10, C8.D10, C8⋊Dic10
►Regular action on 320 points
Generators in S320
(1 143 40 215 259 301 47 121)(2 302 21 122 260 144 48 216)(3 145 22 217 241 303 49 123)(4 304 23 124 242 146 50 218)(5 147 24 219 243 305 51 125)(6 306 25 126 244 148 52 220)(7 149 26 201 245 307 53 127)(8 308 27 128 246 150 54 202)(9 151 28 203 247 309 55 129)(10 310 29 130 248 152 56 204)(11 153 30 205 249 311 57 131)(12 312 31 132 250 154 58 206)(13 155 32 207 251 313 59 133)(14 314 33 134 252 156 60 208)(15 157 34 209 253 315 41 135)(16 316 35 136 254 158 42 210)(17 159 36 211 255 317 43 137)(18 318 37 138 256 160 44 212)(19 141 38 213 257 319 45 139)(20 320 39 140 258 142 46 214)(61 185 161 82 104 231 294 267)(62 232 162 268 105 186 295 83)(63 187 163 84 106 233 296 269)(64 234 164 270 107 188 297 85)(65 189 165 86 108 235 298 271)(66 236 166 272 109 190 299 87)(67 191 167 88 110 237 300 273)(68 238 168 274 111 192 281 89)(69 193 169 90 112 239 282 275)(70 240 170 276 113 194 283 91)(71 195 171 92 114 221 284 277)(72 222 172 278 115 196 285 93)(73 197 173 94 116 223 286 279)(74 224 174 280 117 198 287 95)(75 199 175 96 118 225 288 261)(76 226 176 262 119 200 289 97)(77 181 177 98 120 227 290 263)(78 228 178 264 101 182 291 99)(79 183 179 100 102 229 292 265)(80 230 180 266 103 184 293 81)
(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)
(1 276 11 266)(2 275 12 265)(3 274 13 264)(4 273 14 263)(5 272 15 262)(6 271 16 261)(7 270 17 280)(8 269 18 279)(9 268 19 278)(10 267 20 277)(21 239 31 229)(22 238 32 228)(23 237 33 227)(24 236 34 226)(25 235 35 225)(26 234 36 224)(27 233 37 223)(28 232 38 222)(29 231 39 221)(30 230 40 240)(41 200 51 190)(42 199 52 189)(43 198 53 188)(44 197 54 187)(45 196 55 186)(46 195 56 185)(47 194 57 184)(48 193 58 183)(49 192 59 182)(50 191 60 181)(61 214 71 204)(62 213 72 203)(63 212 73 202)(64 211 74 201)(65 210 75 220)(66 209 76 219)(67 208 77 218)(68 207 78 217)(69 206 79 216)(70 205 80 215)(81 259 91 249)(82 258 92 248)(83 257 93 247)(84 256 94 246)(85 255 95 245)(86 254 96 244)(87 253 97 243)(88 252 98 242)(89 251 99 241)(90 250 100 260)(101 123 111 133)(102 122 112 132)(103 121 113 131)(104 140 114 130)(105 139 115 129)(106 138 116 128)(107 137 117 127)(108 136 118 126)(109 135 119 125)(110 134 120 124)(141 172 151 162)(142 171 152 161)(143 170 153 180)(144 169 154 179)(145 168 155 178)(146 167 156 177)(147 166 157 176)(148 165 158 175)(149 164 159 174)(150 163 160 173)(281 313 291 303)(282 312 292 302)(283 311 293 301)(284 310 294 320)(285 309 295 319)(286 308 296 318)(287 307 297 317)(288 306 298 316)(289 305 299 315)(290 304 300 314)
G:=sub<Sym(320)| (1,143,40,215,259,301,47,121)(2,302,21,122,260,144,48,216)(3,145,22,217,241,303,49,123)(4,304,23,124,242,146,50,218)(5,147,24,219,243,305,51,125)(6,306,25,126,244,148,52,220)(7,149,26,201,245,307,53,127)(8,308,27,128,246,150,54,202)(9,151,28,203,247,309,55,129)(10,310,29,130,248,152,56,204)(11,153,30,205,249,311,57,131)(12,312,31,132,250,154,58,206)(13,155,32,207,251,313,59,133)(14,314,33,134,252,156,60,208)(15,157,34,209,253,315,41,135)(16,316,35,136,254,158,42,210)(17,159,36,211,255,317,43,137)(18,318,37,138,256,160,44,212)(19,141,38,213,257,319,45,139)(20,320,39,140,258,142,46,214)(61,185,161,82,104,231,294,267)(62,232,162,268,105,186,295,83)(63,187,163,84,106,233,296,269)(64,234,164,270,107,188,297,85)(65,189,165,86,108,235,298,271)(66,236,166,272,109,190,299,87)(67,191,167,88,110,237,300,273)(68,238,168,274,111,192,281,89)(69,193,169,90,112,239,282,275)(70,240,170,276,113,194,283,91)(71,195,171,92,114,221,284,277)(72,222,172,278,115,196,285,93)(73,197,173,94,116,223,286,279)(74,224,174,280,117,198,287,95)(75,199,175,96,118,225,288,261)(76,226,176,262,119,200,289,97)(77,181,177,98,120,227,290,263)(78,228,178,264,101,182,291,99)(79,183,179,100,102,229,292,265)(80,230,180,266,103,184,293,81), (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), (1,276,11,266)(2,275,12,265)(3,274,13,264)(4,273,14,263)(5,272,15,262)(6,271,16,261)(7,270,17,280)(8,269,18,279)(9,268,19,278)(10,267,20,277)(21,239,31,229)(22,238,32,228)(23,237,33,227)(24,236,34,226)(25,235,35,225)(26,234,36,224)(27,233,37,223)(28,232,38,222)(29,231,39,221)(30,230,40,240)(41,200,51,190)(42,199,52,189)(43,198,53,188)(44,197,54,187)(45,196,55,186)(46,195,56,185)(47,194,57,184)(48,193,58,183)(49,192,59,182)(50,191,60,181)(61,214,71,204)(62,213,72,203)(63,212,73,202)(64,211,74,201)(65,210,75,220)(66,209,76,219)(67,208,77,218)(68,207,78,217)(69,206,79,216)(70,205,80,215)(81,259,91,249)(82,258,92,248)(83,257,93,247)(84,256,94,246)(85,255,95,245)(86,254,96,244)(87,253,97,243)(88,252,98,242)(89,251,99,241)(90,250,100,260)(101,123,111,133)(102,122,112,132)(103,121,113,131)(104,140,114,130)(105,139,115,129)(106,138,116,128)(107,137,117,127)(108,136,118,126)(109,135,119,125)(110,134,120,124)(141,172,151,162)(142,171,152,161)(143,170,153,180)(144,169,154,179)(145,168,155,178)(146,167,156,177)(147,166,157,176)(148,165,158,175)(149,164,159,174)(150,163,160,173)(281,313,291,303)(282,312,292,302)(283,311,293,301)(284,310,294,320)(285,309,295,319)(286,308,296,318)(287,307,297,317)(288,306,298,316)(289,305,299,315)(290,304,300,314)>;
G:=Group( (1,143,40,215,259,301,47,121)(2,302,21,122,260,144,48,216)(3,145,22,217,241,303,49,123)(4,304,23,124,242,146,50,218)(5,147,24,219,243,305,51,125)(6,306,25,126,244,148,52,220)(7,149,26,201,245,307,53,127)(8,308,27,128,246,150,54,202)(9,151,28,203,247,309,55,129)(10,310,29,130,248,152,56,204)(11,153,30,205,249,311,57,131)(12,312,31,132,250,154,58,206)(13,155,32,207,251,313,59,133)(14,314,33,134,252,156,60,208)(15,157,34,209,253,315,41,135)(16,316,35,136,254,158,42,210)(17,159,36,211,255,317,43,137)(18,318,37,138,256,160,44,212)(19,141,38,213,257,319,45,139)(20,320,39,140,258,142,46,214)(61,185,161,82,104,231,294,267)(62,232,162,268,105,186,295,83)(63,187,163,84,106,233,296,269)(64,234,164,270,107,188,297,85)(65,189,165,86,108,235,298,271)(66,236,166,272,109,190,299,87)(67,191,167,88,110,237,300,273)(68,238,168,274,111,192,281,89)(69,193,169,90,112,239,282,275)(70,240,170,276,113,194,283,91)(71,195,171,92,114,221,284,277)(72,222,172,278,115,196,285,93)(73,197,173,94,116,223,286,279)(74,224,174,280,117,198,287,95)(75,199,175,96,118,225,288,261)(76,226,176,262,119,200,289,97)(77,181,177,98,120,227,290,263)(78,228,178,264,101,182,291,99)(79,183,179,100,102,229,292,265)(80,230,180,266,103,184,293,81), (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), (1,276,11,266)(2,275,12,265)(3,274,13,264)(4,273,14,263)(5,272,15,262)(6,271,16,261)(7,270,17,280)(8,269,18,279)(9,268,19,278)(10,267,20,277)(21,239,31,229)(22,238,32,228)(23,237,33,227)(24,236,34,226)(25,235,35,225)(26,234,36,224)(27,233,37,223)(28,232,38,222)(29,231,39,221)(30,230,40,240)(41,200,51,190)(42,199,52,189)(43,198,53,188)(44,197,54,187)(45,196,55,186)(46,195,56,185)(47,194,57,184)(48,193,58,183)(49,192,59,182)(50,191,60,181)(61,214,71,204)(62,213,72,203)(63,212,73,202)(64,211,74,201)(65,210,75,220)(66,209,76,219)(67,208,77,218)(68,207,78,217)(69,206,79,216)(70,205,80,215)(81,259,91,249)(82,258,92,248)(83,257,93,247)(84,256,94,246)(85,255,95,245)(86,254,96,244)(87,253,97,243)(88,252,98,242)(89,251,99,241)(90,250,100,260)(101,123,111,133)(102,122,112,132)(103,121,113,131)(104,140,114,130)(105,139,115,129)(106,138,116,128)(107,137,117,127)(108,136,118,126)(109,135,119,125)(110,134,120,124)(141,172,151,162)(142,171,152,161)(143,170,153,180)(144,169,154,179)(145,168,155,178)(146,167,156,177)(147,166,157,176)(148,165,158,175)(149,164,159,174)(150,163,160,173)(281,313,291,303)(282,312,292,302)(283,311,293,301)(284,310,294,320)(285,309,295,319)(286,308,296,318)(287,307,297,317)(288,306,298,316)(289,305,299,315)(290,304,300,314) );
G=PermutationGroup([[(1,143,40,215,259,301,47,121),(2,302,21,122,260,144,48,216),(3,145,22,217,241,303,49,123),(4,304,23,124,242,146,50,218),(5,147,24,219,243,305,51,125),(6,306,25,126,244,148,52,220),(7,149,26,201,245,307,53,127),(8,308,27,128,246,150,54,202),(9,151,28,203,247,309,55,129),(10,310,29,130,248,152,56,204),(11,153,30,205,249,311,57,131),(12,312,31,132,250,154,58,206),(13,155,32,207,251,313,59,133),(14,314,33,134,252,156,60,208),(15,157,34,209,253,315,41,135),(16,316,35,136,254,158,42,210),(17,159,36,211,255,317,43,137),(18,318,37,138,256,160,44,212),(19,141,38,213,257,319,45,139),(20,320,39,140,258,142,46,214),(61,185,161,82,104,231,294,267),(62,232,162,268,105,186,295,83),(63,187,163,84,106,233,296,269),(64,234,164,270,107,188,297,85),(65,189,165,86,108,235,298,271),(66,236,166,272,109,190,299,87),(67,191,167,88,110,237,300,273),(68,238,168,274,111,192,281,89),(69,193,169,90,112,239,282,275),(70,240,170,276,113,194,283,91),(71,195,171,92,114,221,284,277),(72,222,172,278,115,196,285,93),(73,197,173,94,116,223,286,279),(74,224,174,280,117,198,287,95),(75,199,175,96,118,225,288,261),(76,226,176,262,119,200,289,97),(77,181,177,98,120,227,290,263),(78,228,178,264,101,182,291,99),(79,183,179,100,102,229,292,265),(80,230,180,266,103,184,293,81)], [(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)], [(1,276,11,266),(2,275,12,265),(3,274,13,264),(4,273,14,263),(5,272,15,262),(6,271,16,261),(7,270,17,280),(8,269,18,279),(9,268,19,278),(10,267,20,277),(21,239,31,229),(22,238,32,228),(23,237,33,227),(24,236,34,226),(25,235,35,225),(26,234,36,224),(27,233,37,223),(28,232,38,222),(29,231,39,221),(30,230,40,240),(41,200,51,190),(42,199,52,189),(43,198,53,188),(44,197,54,187),(45,196,55,186),(46,195,56,185),(47,194,57,184),(48,193,58,183),(49,192,59,182),(50,191,60,181),(61,214,71,204),(62,213,72,203),(63,212,73,202),(64,211,74,201),(65,210,75,220),(66,209,76,219),(67,208,77,218),(68,207,78,217),(69,206,79,216),(70,205,80,215),(81,259,91,249),(82,258,92,248),(83,257,93,247),(84,256,94,246),(85,255,95,245),(86,254,96,244),(87,253,97,243),(88,252,98,242),(89,251,99,241),(90,250,100,260),(101,123,111,133),(102,122,112,132),(103,121,113,131),(104,140,114,130),(105,139,115,129),(106,138,116,128),(107,137,117,127),(108,136,118,126),(109,135,119,125),(110,134,120,124),(141,172,151,162),(142,171,152,161),(143,170,153,180),(144,169,154,179),(145,168,155,178),(146,167,156,177),(147,166,157,176),(148,165,158,175),(149,164,159,174),(150,163,160,173),(281,313,291,303),(282,312,292,302),(283,311,293,301),(284,310,294,320),(285,309,295,319),(286,308,296,318),(287,307,297,317),(288,306,298,316),(289,305,299,315),(290,304,300,314)]])
56 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5A | 5B | 8A | 8B | 8C | 8D | 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 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 40 | 40 | 40 | 40 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
56 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | + | + | + | - | + | + | - | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | Q8 | D4 | D5 | D10 | D10 | Dic10 | D20 | C8⋊C22 | C8.C22 | C8⋊D10 | C8.D10 |
| kernel | C8⋊Dic10 | C40⋊6C4 | C40⋊5C4 | C5×C8⋊C4 | C20⋊2Q8 | C20.6Q8 | C40 | C2×C20 | C8⋊C4 | C42 | C2×C8 | C8 | C2×C4 | C10 | C10 | C2 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 4 | 2 | 2 | 2 | 4 | 16 | 8 | 1 | 1 | 4 | 4 |
Matrix representation of C8⋊Dic10 ►in GL6(𝔽41)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 37 | 20 | 22 |
| 0 | 0 | 4 | 35 | 16 | 20 |
| 0 | 0 | 32 | 15 | 6 | 4 |
| 0 | 0 | 39 | 32 | 37 | 23 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 23 | 15 | 40 |
| 0 | 0 | 18 | 18 | 9 | 15 |
| 0 | 0 | 5 | 6 | 23 | 18 |
| 0 | 0 | 5 | 5 | 23 | 38 |
| 3 | 20 | 0 | 0 | 0 | 0 |
| 20 | 38 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 28 | 2 | 37 |
| 0 | 0 | 24 | 28 | 37 | 15 |
| 0 | 0 | 35 | 23 | 5 | 11 |
| 0 | 0 | 23 | 32 | 22 | 36 |
G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,18,4,32,39,0,0,37,35,15,32,0,0,20,16,6,37,0,0,22,20,4,23],[0,40,0,0,0,0,1,0,0,0,0,0,0,0,3,18,5,5,0,0,23,18,6,5,0,0,15,9,23,23,0,0,40,15,18,38],[3,20,0,0,0,0,20,38,0,0,0,0,0,0,13,24,35,23,0,0,28,28,23,32,0,0,2,37,5,22,0,0,37,15,11,36] >;
C8⋊Dic10 in GAP, Magma, Sage, TeX
C_8\rtimes {\rm Dic}_{10} % in TeX
G:=Group("C8:Dic10"); // GroupNames label
G:=SmallGroup(320,329);
// by ID
G=gap.SmallGroup(320,329);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,253,120,254,387,58,1123,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^8=b^20=1,c^2=b^10,b*a*b^-1=a^5,c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations