metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20.10D8, C20.6Q16, C20.10SD16, C42.11D10, C4⋊Q8.2D5, C4.9(Q8⋊D5), C4⋊C4.2Dic5, C4.13(D4⋊D5), (C2×C20).108D4, C5⋊4(C4.10D8), C4.7(D4.D5), C20⋊3C8.13C2, C4.7(C5⋊Q16), (C4×C20).49C22, C2.5(Q8⋊Dic5), C2.5(D4⋊Dic5), C10.40(D4⋊C4), C10.20(Q8⋊C4), C2.4(C20.10D4), C10.14(C4.10D4), C22.43(C23.D5), (C5×C4⋊Q8).2C2, (C5×C4⋊C4).15C4, (C2×C20).346(C2×C4), (C2×C4).13(C2×Dic5), (C2×C4).178(C5⋊D4), (C2×C10).169(C22⋊C4), SmallGroup(320,105)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20.10D8
G = < a,b,c | a20=b8=1, c2=a5, bab-1=a-1, cac-1=a9, cbc-1=a15b-1 >
Subgroups: 174 in 64 conjugacy classes, 35 normal (31 characteristic)
C1, C2, C4, C4, C22, C5, C8, C2×C4, C2×C4, Q8, C10, C42, C4⋊C4, C4⋊C4, C2×C8, C2×Q8, C20, C20, C2×C10, C4⋊C8, C4⋊Q8, C5⋊2C8, C2×C20, C2×C20, C5×Q8, C4.10D8, C2×C5⋊2C8, C4×C20, C5×C4⋊C4, C5×C4⋊C4, Q8×C10, C20⋊3C8, C5×C4⋊Q8, C20.10D8
Quotients: C1, C2, C4, C22, C2×C4, D4, D5, C22⋊C4, D8, SD16, Q16, Dic5, D10, C4.10D4, D4⋊C4, Q8⋊C4, C2×Dic5, C5⋊D4, C4.10D8, D4⋊D5, D4.D5, Q8⋊D5, C5⋊Q16, C23.D5, D4⋊Dic5, Q8⋊Dic5, C20.10D4, C20.10D8
►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 98 242 234 133 280 107 150)(2 97 243 233 134 279 108 149)(3 96 244 232 135 278 109 148)(4 95 245 231 136 277 110 147)(5 94 246 230 137 276 111 146)(6 93 247 229 138 275 112 145)(7 92 248 228 139 274 113 144)(8 91 249 227 140 273 114 143)(9 90 250 226 121 272 115 142)(10 89 251 225 122 271 116 141)(11 88 252 224 123 270 117 160)(12 87 253 223 124 269 118 159)(13 86 254 222 125 268 119 158)(14 85 255 221 126 267 120 157)(15 84 256 240 127 266 101 156)(16 83 257 239 128 265 102 155)(17 82 258 238 129 264 103 154)(18 81 259 237 130 263 104 153)(19 100 260 236 131 262 105 152)(20 99 241 235 132 261 106 151)(21 72 281 173 44 301 198 218)(22 71 282 172 45 320 199 217)(23 70 283 171 46 319 200 216)(24 69 284 170 47 318 181 215)(25 68 285 169 48 317 182 214)(26 67 286 168 49 316 183 213)(27 66 287 167 50 315 184 212)(28 65 288 166 51 314 185 211)(29 64 289 165 52 313 186 210)(30 63 290 164 53 312 187 209)(31 62 291 163 54 311 188 208)(32 61 292 162 55 310 189 207)(33 80 293 161 56 309 190 206)(34 79 294 180 57 308 191 205)(35 78 295 179 58 307 192 204)(36 77 296 178 59 306 193 203)(37 76 297 177 60 305 194 202)(38 75 298 176 41 304 195 201)(39 74 299 175 42 303 196 220)(40 73 300 174 43 302 197 219)
(1 282 6 287 11 292 16 297)(2 291 7 296 12 281 17 286)(3 300 8 285 13 290 18 295)(4 289 9 294 14 299 19 284)(5 298 10 283 15 288 20 293)(21 258 26 243 31 248 36 253)(22 247 27 252 32 257 37 242)(23 256 28 241 33 246 38 251)(24 245 29 250 34 255 39 260)(25 254 30 259 35 244 40 249)(41 116 46 101 51 106 56 111)(42 105 47 110 52 115 57 120)(43 114 48 119 53 104 58 109)(44 103 49 108 54 113 59 118)(45 112 50 117 55 102 60 107)(61 98 66 83 71 88 76 93)(62 87 67 92 72 97 77 82)(63 96 68 81 73 86 78 91)(64 85 69 90 74 95 79 100)(65 94 70 99 75 84 80 89)(121 191 126 196 131 181 136 186)(122 200 127 185 132 190 137 195)(123 189 128 194 133 199 138 184)(124 198 129 183 134 188 139 193)(125 187 130 192 135 197 140 182)(141 166 146 171 151 176 156 161)(142 175 147 180 152 165 157 170)(143 164 148 169 153 174 158 179)(144 173 149 178 154 163 159 168)(145 162 150 167 155 172 160 177)(201 240 206 225 211 230 216 235)(202 229 207 234 212 239 217 224)(203 238 208 223 213 228 218 233)(204 227 209 232 214 237 219 222)(205 236 210 221 215 226 220 231)(261 304 266 309 271 314 276 319)(262 313 267 318 272 303 277 308)(263 302 268 307 273 312 278 317)(264 311 269 316 274 301 279 306)(265 320 270 305 275 310 280 315)
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), (1,98,242,234,133,280,107,150)(2,97,243,233,134,279,108,149)(3,96,244,232,135,278,109,148)(4,95,245,231,136,277,110,147)(5,94,246,230,137,276,111,146)(6,93,247,229,138,275,112,145)(7,92,248,228,139,274,113,144)(8,91,249,227,140,273,114,143)(9,90,250,226,121,272,115,142)(10,89,251,225,122,271,116,141)(11,88,252,224,123,270,117,160)(12,87,253,223,124,269,118,159)(13,86,254,222,125,268,119,158)(14,85,255,221,126,267,120,157)(15,84,256,240,127,266,101,156)(16,83,257,239,128,265,102,155)(17,82,258,238,129,264,103,154)(18,81,259,237,130,263,104,153)(19,100,260,236,131,262,105,152)(20,99,241,235,132,261,106,151)(21,72,281,173,44,301,198,218)(22,71,282,172,45,320,199,217)(23,70,283,171,46,319,200,216)(24,69,284,170,47,318,181,215)(25,68,285,169,48,317,182,214)(26,67,286,168,49,316,183,213)(27,66,287,167,50,315,184,212)(28,65,288,166,51,314,185,211)(29,64,289,165,52,313,186,210)(30,63,290,164,53,312,187,209)(31,62,291,163,54,311,188,208)(32,61,292,162,55,310,189,207)(33,80,293,161,56,309,190,206)(34,79,294,180,57,308,191,205)(35,78,295,179,58,307,192,204)(36,77,296,178,59,306,193,203)(37,76,297,177,60,305,194,202)(38,75,298,176,41,304,195,201)(39,74,299,175,42,303,196,220)(40,73,300,174,43,302,197,219), (1,282,6,287,11,292,16,297)(2,291,7,296,12,281,17,286)(3,300,8,285,13,290,18,295)(4,289,9,294,14,299,19,284)(5,298,10,283,15,288,20,293)(21,258,26,243,31,248,36,253)(22,247,27,252,32,257,37,242)(23,256,28,241,33,246,38,251)(24,245,29,250,34,255,39,260)(25,254,30,259,35,244,40,249)(41,116,46,101,51,106,56,111)(42,105,47,110,52,115,57,120)(43,114,48,119,53,104,58,109)(44,103,49,108,54,113,59,118)(45,112,50,117,55,102,60,107)(61,98,66,83,71,88,76,93)(62,87,67,92,72,97,77,82)(63,96,68,81,73,86,78,91)(64,85,69,90,74,95,79,100)(65,94,70,99,75,84,80,89)(121,191,126,196,131,181,136,186)(122,200,127,185,132,190,137,195)(123,189,128,194,133,199,138,184)(124,198,129,183,134,188,139,193)(125,187,130,192,135,197,140,182)(141,166,146,171,151,176,156,161)(142,175,147,180,152,165,157,170)(143,164,148,169,153,174,158,179)(144,173,149,178,154,163,159,168)(145,162,150,167,155,172,160,177)(201,240,206,225,211,230,216,235)(202,229,207,234,212,239,217,224)(203,238,208,223,213,228,218,233)(204,227,209,232,214,237,219,222)(205,236,210,221,215,226,220,231)(261,304,266,309,271,314,276,319)(262,313,267,318,272,303,277,308)(263,302,268,307,273,312,278,317)(264,311,269,316,274,301,279,306)(265,320,270,305,275,310,280,315)>;
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), (1,98,242,234,133,280,107,150)(2,97,243,233,134,279,108,149)(3,96,244,232,135,278,109,148)(4,95,245,231,136,277,110,147)(5,94,246,230,137,276,111,146)(6,93,247,229,138,275,112,145)(7,92,248,228,139,274,113,144)(8,91,249,227,140,273,114,143)(9,90,250,226,121,272,115,142)(10,89,251,225,122,271,116,141)(11,88,252,224,123,270,117,160)(12,87,253,223,124,269,118,159)(13,86,254,222,125,268,119,158)(14,85,255,221,126,267,120,157)(15,84,256,240,127,266,101,156)(16,83,257,239,128,265,102,155)(17,82,258,238,129,264,103,154)(18,81,259,237,130,263,104,153)(19,100,260,236,131,262,105,152)(20,99,241,235,132,261,106,151)(21,72,281,173,44,301,198,218)(22,71,282,172,45,320,199,217)(23,70,283,171,46,319,200,216)(24,69,284,170,47,318,181,215)(25,68,285,169,48,317,182,214)(26,67,286,168,49,316,183,213)(27,66,287,167,50,315,184,212)(28,65,288,166,51,314,185,211)(29,64,289,165,52,313,186,210)(30,63,290,164,53,312,187,209)(31,62,291,163,54,311,188,208)(32,61,292,162,55,310,189,207)(33,80,293,161,56,309,190,206)(34,79,294,180,57,308,191,205)(35,78,295,179,58,307,192,204)(36,77,296,178,59,306,193,203)(37,76,297,177,60,305,194,202)(38,75,298,176,41,304,195,201)(39,74,299,175,42,303,196,220)(40,73,300,174,43,302,197,219), (1,282,6,287,11,292,16,297)(2,291,7,296,12,281,17,286)(3,300,8,285,13,290,18,295)(4,289,9,294,14,299,19,284)(5,298,10,283,15,288,20,293)(21,258,26,243,31,248,36,253)(22,247,27,252,32,257,37,242)(23,256,28,241,33,246,38,251)(24,245,29,250,34,255,39,260)(25,254,30,259,35,244,40,249)(41,116,46,101,51,106,56,111)(42,105,47,110,52,115,57,120)(43,114,48,119,53,104,58,109)(44,103,49,108,54,113,59,118)(45,112,50,117,55,102,60,107)(61,98,66,83,71,88,76,93)(62,87,67,92,72,97,77,82)(63,96,68,81,73,86,78,91)(64,85,69,90,74,95,79,100)(65,94,70,99,75,84,80,89)(121,191,126,196,131,181,136,186)(122,200,127,185,132,190,137,195)(123,189,128,194,133,199,138,184)(124,198,129,183,134,188,139,193)(125,187,130,192,135,197,140,182)(141,166,146,171,151,176,156,161)(142,175,147,180,152,165,157,170)(143,164,148,169,153,174,158,179)(144,173,149,178,154,163,159,168)(145,162,150,167,155,172,160,177)(201,240,206,225,211,230,216,235)(202,229,207,234,212,239,217,224)(203,238,208,223,213,228,218,233)(204,227,209,232,214,237,219,222)(205,236,210,221,215,226,220,231)(261,304,266,309,271,314,276,319)(262,313,267,318,272,303,277,308)(263,302,268,307,273,312,278,317)(264,311,269,316,274,301,279,306)(265,320,270,305,275,310,280,315) );
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)], [(1,98,242,234,133,280,107,150),(2,97,243,233,134,279,108,149),(3,96,244,232,135,278,109,148),(4,95,245,231,136,277,110,147),(5,94,246,230,137,276,111,146),(6,93,247,229,138,275,112,145),(7,92,248,228,139,274,113,144),(8,91,249,227,140,273,114,143),(9,90,250,226,121,272,115,142),(10,89,251,225,122,271,116,141),(11,88,252,224,123,270,117,160),(12,87,253,223,124,269,118,159),(13,86,254,222,125,268,119,158),(14,85,255,221,126,267,120,157),(15,84,256,240,127,266,101,156),(16,83,257,239,128,265,102,155),(17,82,258,238,129,264,103,154),(18,81,259,237,130,263,104,153),(19,100,260,236,131,262,105,152),(20,99,241,235,132,261,106,151),(21,72,281,173,44,301,198,218),(22,71,282,172,45,320,199,217),(23,70,283,171,46,319,200,216),(24,69,284,170,47,318,181,215),(25,68,285,169,48,317,182,214),(26,67,286,168,49,316,183,213),(27,66,287,167,50,315,184,212),(28,65,288,166,51,314,185,211),(29,64,289,165,52,313,186,210),(30,63,290,164,53,312,187,209),(31,62,291,163,54,311,188,208),(32,61,292,162,55,310,189,207),(33,80,293,161,56,309,190,206),(34,79,294,180,57,308,191,205),(35,78,295,179,58,307,192,204),(36,77,296,178,59,306,193,203),(37,76,297,177,60,305,194,202),(38,75,298,176,41,304,195,201),(39,74,299,175,42,303,196,220),(40,73,300,174,43,302,197,219)], [(1,282,6,287,11,292,16,297),(2,291,7,296,12,281,17,286),(3,300,8,285,13,290,18,295),(4,289,9,294,14,299,19,284),(5,298,10,283,15,288,20,293),(21,258,26,243,31,248,36,253),(22,247,27,252,32,257,37,242),(23,256,28,241,33,246,38,251),(24,245,29,250,34,255,39,260),(25,254,30,259,35,244,40,249),(41,116,46,101,51,106,56,111),(42,105,47,110,52,115,57,120),(43,114,48,119,53,104,58,109),(44,103,49,108,54,113,59,118),(45,112,50,117,55,102,60,107),(61,98,66,83,71,88,76,93),(62,87,67,92,72,97,77,82),(63,96,68,81,73,86,78,91),(64,85,69,90,74,95,79,100),(65,94,70,99,75,84,80,89),(121,191,126,196,131,181,136,186),(122,200,127,185,132,190,137,195),(123,189,128,194,133,199,138,184),(124,198,129,183,134,188,139,193),(125,187,130,192,135,197,140,182),(141,166,146,171,151,176,156,161),(142,175,147,180,152,165,157,170),(143,164,148,169,153,174,158,179),(144,173,149,178,154,163,159,168),(145,162,150,167,155,172,160,177),(201,240,206,225,211,230,216,235),(202,229,207,234,212,239,217,224),(203,238,208,223,213,228,218,233),(204,227,209,232,214,237,219,222),(205,236,210,221,215,226,220,231),(261,304,266,309,271,314,276,319),(262,313,267,318,272,303,277,308),(263,302,268,307,273,312,278,317),(264,311,269,316,274,301,279,306),(265,320,270,305,275,310,280,315)]])
47 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 5A | 5B | 8A | ··· | 8H | 10A | ··· | 10F | 20A | ··· | 20L | 20M | ··· | 20T |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 8 | 8 | 2 | 2 | 20 | ··· | 20 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
47 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | - | - | + | - | + | - | ||||
| image | C1 | C2 | C2 | C4 | D4 | D5 | D8 | SD16 | Q16 | D10 | Dic5 | C5⋊D4 | C4.10D4 | D4⋊D5 | D4.D5 | Q8⋊D5 | C5⋊Q16 | C20.10D4 |
| kernel | C20.10D8 | C20⋊3C8 | C5×C4⋊Q8 | C5×C4⋊C4 | C2×C20 | C4⋊Q8 | C20 | C20 | C20 | C42 | C4⋊C4 | C2×C4 | C10 | C4 | C4 | C4 | C4 | C2 |
| # reps | 1 | 2 | 1 | 4 | 2 | 2 | 2 | 4 | 2 | 2 | 4 | 8 | 1 | 2 | 2 | 2 | 2 | 4 |
Matrix representation of C20.10D8 ►in GL6(𝔽41)
| 16 | 9 | 0 | 0 | 0 | 0 |
| 17 | 25 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 40 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 11 | 17 | 0 | 0 | 0 | 0 |
| 29 | 30 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 25 | 0 | 0 |
| 0 | 0 | 28 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 31 | 7 |
| 0 | 0 | 0 | 0 | 25 | 40 |
| 40 | 26 | 0 | 0 | 0 | 0 |
| 40 | 25 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 3 | 0 | 0 |
| 0 | 0 | 2 | 35 | 0 | 0 |
| 0 | 0 | 0 | 0 | 30 | 29 |
| 0 | 0 | 0 | 0 | 17 | 11 |
G:=sub<GL(6,GF(41))| [16,17,0,0,0,0,9,25,0,0,0,0,0,0,34,1,0,0,0,0,40,0,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[11,29,0,0,0,0,17,30,0,0,0,0,0,0,23,28,0,0,0,0,25,18,0,0,0,0,0,0,31,25,0,0,0,0,7,40],[40,40,0,0,0,0,26,25,0,0,0,0,0,0,6,2,0,0,0,0,3,35,0,0,0,0,0,0,30,17,0,0,0,0,29,11] >;
C20.10D8 in GAP, Magma, Sage, TeX
C_{20}._{10}D_8 % in TeX
G:=Group("C20.10D8"); // GroupNames label
G:=SmallGroup(320,105);
// by ID
G=gap.SmallGroup(320,105);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,141,120,219,100,1571,570,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=a^5,b*a*b^-1=a^-1,c*a*c^-1=a^9,c*b*c^-1=a^15*b^-1>;
// generators/relations