metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20⋊2Q16, C42.83D10, Dic10.24D4, C4⋊Q8.9D5, C4.57(D4×D5), C4⋊2(C5⋊Q16), C5⋊4(C4⋊2Q16), C20.39(C2×D4), (C2×C20).159D4, (C2×Q8).47D10, C10.42(C2×Q16), C20⋊3C8.21C2, C20.85(C4○D4), C4.6(D4⋊2D5), C2.15(C20⋊2D4), (C2×C20).408C23, (C4×C20).137C22, (C4×Dic10).17C2, Q8⋊Dic5.13C2, (Q8×C10).65C22, C10.106(C4⋊D4), C10.99(C8.C22), C4⋊Dic5.349C22, C2.20(C20.C23), (C2×Dic10).283C22, (C5×C4⋊Q8).9C2, (C2×C5⋊Q16).6C2, C2.13(C2×C5⋊Q16), (C2×C10).539(C2×D4), (C2×C4).190(C5⋊D4), (C2×C4).505(C22×D5), C22.211(C2×C5⋊D4), (C2×C5⋊2C8).140C22, SmallGroup(320,717)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20⋊Q16
G = < a,b,c | a20=b8=1, c2=b4, bab-1=a-1, cac-1=a11, cbc-1=b-1 >
Subgroups: 342 in 108 conjugacy classes, 45 normal (29 characteristic)
C1, C2, C4, C4, C4, C22, C5, C8, C2×C4, C2×C4, Q8, C10, C42, C42, C4⋊C4, C2×C8, Q16, C2×Q8, C2×Q8, Dic5, C20, C20, C20, C2×C10, Q8⋊C4, C4⋊C8, C4×Q8, C4⋊Q8, C2×Q16, C5⋊2C8, Dic10, Dic10, C2×Dic5, C2×C20, C2×C20, C5×Q8, C4⋊2Q16, C2×C5⋊2C8, C4×Dic5, C10.D4, C4⋊Dic5, C5⋊Q16, C4×C20, C5×C4⋊C4, C2×Dic10, Q8×C10, C20⋊3C8, Q8⋊Dic5, C4×Dic10, C2×C5⋊Q16, C5×C4⋊Q8, C20⋊Q16
Quotients: C1, C2, C22, D4, C23, D5, Q16, C2×D4, C4○D4, D10, C4⋊D4, C2×Q16, C8.C22, C5⋊D4, C22×D5, C4⋊2Q16, C5⋊Q16, D4×D5, D4⋊2D5, C2×C5⋊D4, C20⋊2D4, C20.C23, C2×C5⋊Q16, C20⋊Q16
►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)
(1 164 248 284 105 181 310 94)(2 163 249 283 106 200 311 93)(3 162 250 282 107 199 312 92)(4 161 251 281 108 198 313 91)(5 180 252 300 109 197 314 90)(6 179 253 299 110 196 315 89)(7 178 254 298 111 195 316 88)(8 177 255 297 112 194 317 87)(9 176 256 296 113 193 318 86)(10 175 257 295 114 192 319 85)(11 174 258 294 115 191 320 84)(12 173 259 293 116 190 301 83)(13 172 260 292 117 189 302 82)(14 171 241 291 118 188 303 81)(15 170 242 290 119 187 304 100)(16 169 243 289 120 186 305 99)(17 168 244 288 101 185 306 98)(18 167 245 287 102 184 307 97)(19 166 246 286 103 183 308 96)(20 165 247 285 104 182 309 95)(21 60 124 228 266 213 146 71)(22 59 125 227 267 212 147 70)(23 58 126 226 268 211 148 69)(24 57 127 225 269 210 149 68)(25 56 128 224 270 209 150 67)(26 55 129 223 271 208 151 66)(27 54 130 222 272 207 152 65)(28 53 131 221 273 206 153 64)(29 52 132 240 274 205 154 63)(30 51 133 239 275 204 155 62)(31 50 134 238 276 203 156 61)(32 49 135 237 277 202 157 80)(33 48 136 236 278 201 158 79)(34 47 137 235 279 220 159 78)(35 46 138 234 280 219 160 77)(36 45 139 233 261 218 141 76)(37 44 140 232 262 217 142 75)(38 43 121 231 263 216 143 74)(39 42 122 230 264 215 144 73)(40 41 123 229 265 214 145 72)
(1 78 105 235)(2 69 106 226)(3 80 107 237)(4 71 108 228)(5 62 109 239)(6 73 110 230)(7 64 111 221)(8 75 112 232)(9 66 113 223)(10 77 114 234)(11 68 115 225)(12 79 116 236)(13 70 117 227)(14 61 118 238)(15 72 119 229)(16 63 120 240)(17 74 101 231)(18 65 102 222)(19 76 103 233)(20 67 104 224)(21 281 266 91)(22 292 267 82)(23 283 268 93)(24 294 269 84)(25 285 270 95)(26 296 271 86)(27 287 272 97)(28 298 273 88)(29 289 274 99)(30 300 275 90)(31 291 276 81)(32 282 277 92)(33 293 278 83)(34 284 279 94)(35 295 280 85)(36 286 261 96)(37 297 262 87)(38 288 263 98)(39 299 264 89)(40 290 265 100)(41 242 214 304)(42 253 215 315)(43 244 216 306)(44 255 217 317)(45 246 218 308)(46 257 219 319)(47 248 220 310)(48 259 201 301)(49 250 202 312)(50 241 203 303)(51 252 204 314)(52 243 205 305)(53 254 206 316)(54 245 207 307)(55 256 208 318)(56 247 209 309)(57 258 210 320)(58 249 211 311)(59 260 212 302)(60 251 213 313)(121 168 143 185)(122 179 144 196)(123 170 145 187)(124 161 146 198)(125 172 147 189)(126 163 148 200)(127 174 149 191)(128 165 150 182)(129 176 151 193)(130 167 152 184)(131 178 153 195)(132 169 154 186)(133 180 155 197)(134 171 156 188)(135 162 157 199)(136 173 158 190)(137 164 159 181)(138 175 160 192)(139 166 141 183)(140 177 142 194)
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), (1,164,248,284,105,181,310,94)(2,163,249,283,106,200,311,93)(3,162,250,282,107,199,312,92)(4,161,251,281,108,198,313,91)(5,180,252,300,109,197,314,90)(6,179,253,299,110,196,315,89)(7,178,254,298,111,195,316,88)(8,177,255,297,112,194,317,87)(9,176,256,296,113,193,318,86)(10,175,257,295,114,192,319,85)(11,174,258,294,115,191,320,84)(12,173,259,293,116,190,301,83)(13,172,260,292,117,189,302,82)(14,171,241,291,118,188,303,81)(15,170,242,290,119,187,304,100)(16,169,243,289,120,186,305,99)(17,168,244,288,101,185,306,98)(18,167,245,287,102,184,307,97)(19,166,246,286,103,183,308,96)(20,165,247,285,104,182,309,95)(21,60,124,228,266,213,146,71)(22,59,125,227,267,212,147,70)(23,58,126,226,268,211,148,69)(24,57,127,225,269,210,149,68)(25,56,128,224,270,209,150,67)(26,55,129,223,271,208,151,66)(27,54,130,222,272,207,152,65)(28,53,131,221,273,206,153,64)(29,52,132,240,274,205,154,63)(30,51,133,239,275,204,155,62)(31,50,134,238,276,203,156,61)(32,49,135,237,277,202,157,80)(33,48,136,236,278,201,158,79)(34,47,137,235,279,220,159,78)(35,46,138,234,280,219,160,77)(36,45,139,233,261,218,141,76)(37,44,140,232,262,217,142,75)(38,43,121,231,263,216,143,74)(39,42,122,230,264,215,144,73)(40,41,123,229,265,214,145,72), (1,78,105,235)(2,69,106,226)(3,80,107,237)(4,71,108,228)(5,62,109,239)(6,73,110,230)(7,64,111,221)(8,75,112,232)(9,66,113,223)(10,77,114,234)(11,68,115,225)(12,79,116,236)(13,70,117,227)(14,61,118,238)(15,72,119,229)(16,63,120,240)(17,74,101,231)(18,65,102,222)(19,76,103,233)(20,67,104,224)(21,281,266,91)(22,292,267,82)(23,283,268,93)(24,294,269,84)(25,285,270,95)(26,296,271,86)(27,287,272,97)(28,298,273,88)(29,289,274,99)(30,300,275,90)(31,291,276,81)(32,282,277,92)(33,293,278,83)(34,284,279,94)(35,295,280,85)(36,286,261,96)(37,297,262,87)(38,288,263,98)(39,299,264,89)(40,290,265,100)(41,242,214,304)(42,253,215,315)(43,244,216,306)(44,255,217,317)(45,246,218,308)(46,257,219,319)(47,248,220,310)(48,259,201,301)(49,250,202,312)(50,241,203,303)(51,252,204,314)(52,243,205,305)(53,254,206,316)(54,245,207,307)(55,256,208,318)(56,247,209,309)(57,258,210,320)(58,249,211,311)(59,260,212,302)(60,251,213,313)(121,168,143,185)(122,179,144,196)(123,170,145,187)(124,161,146,198)(125,172,147,189)(126,163,148,200)(127,174,149,191)(128,165,150,182)(129,176,151,193)(130,167,152,184)(131,178,153,195)(132,169,154,186)(133,180,155,197)(134,171,156,188)(135,162,157,199)(136,173,158,190)(137,164,159,181)(138,175,160,192)(139,166,141,183)(140,177,142,194)>;
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), (1,164,248,284,105,181,310,94)(2,163,249,283,106,200,311,93)(3,162,250,282,107,199,312,92)(4,161,251,281,108,198,313,91)(5,180,252,300,109,197,314,90)(6,179,253,299,110,196,315,89)(7,178,254,298,111,195,316,88)(8,177,255,297,112,194,317,87)(9,176,256,296,113,193,318,86)(10,175,257,295,114,192,319,85)(11,174,258,294,115,191,320,84)(12,173,259,293,116,190,301,83)(13,172,260,292,117,189,302,82)(14,171,241,291,118,188,303,81)(15,170,242,290,119,187,304,100)(16,169,243,289,120,186,305,99)(17,168,244,288,101,185,306,98)(18,167,245,287,102,184,307,97)(19,166,246,286,103,183,308,96)(20,165,247,285,104,182,309,95)(21,60,124,228,266,213,146,71)(22,59,125,227,267,212,147,70)(23,58,126,226,268,211,148,69)(24,57,127,225,269,210,149,68)(25,56,128,224,270,209,150,67)(26,55,129,223,271,208,151,66)(27,54,130,222,272,207,152,65)(28,53,131,221,273,206,153,64)(29,52,132,240,274,205,154,63)(30,51,133,239,275,204,155,62)(31,50,134,238,276,203,156,61)(32,49,135,237,277,202,157,80)(33,48,136,236,278,201,158,79)(34,47,137,235,279,220,159,78)(35,46,138,234,280,219,160,77)(36,45,139,233,261,218,141,76)(37,44,140,232,262,217,142,75)(38,43,121,231,263,216,143,74)(39,42,122,230,264,215,144,73)(40,41,123,229,265,214,145,72), (1,78,105,235)(2,69,106,226)(3,80,107,237)(4,71,108,228)(5,62,109,239)(6,73,110,230)(7,64,111,221)(8,75,112,232)(9,66,113,223)(10,77,114,234)(11,68,115,225)(12,79,116,236)(13,70,117,227)(14,61,118,238)(15,72,119,229)(16,63,120,240)(17,74,101,231)(18,65,102,222)(19,76,103,233)(20,67,104,224)(21,281,266,91)(22,292,267,82)(23,283,268,93)(24,294,269,84)(25,285,270,95)(26,296,271,86)(27,287,272,97)(28,298,273,88)(29,289,274,99)(30,300,275,90)(31,291,276,81)(32,282,277,92)(33,293,278,83)(34,284,279,94)(35,295,280,85)(36,286,261,96)(37,297,262,87)(38,288,263,98)(39,299,264,89)(40,290,265,100)(41,242,214,304)(42,253,215,315)(43,244,216,306)(44,255,217,317)(45,246,218,308)(46,257,219,319)(47,248,220,310)(48,259,201,301)(49,250,202,312)(50,241,203,303)(51,252,204,314)(52,243,205,305)(53,254,206,316)(54,245,207,307)(55,256,208,318)(56,247,209,309)(57,258,210,320)(58,249,211,311)(59,260,212,302)(60,251,213,313)(121,168,143,185)(122,179,144,196)(123,170,145,187)(124,161,146,198)(125,172,147,189)(126,163,148,200)(127,174,149,191)(128,165,150,182)(129,176,151,193)(130,167,152,184)(131,178,153,195)(132,169,154,186)(133,180,155,197)(134,171,156,188)(135,162,157,199)(136,173,158,190)(137,164,159,181)(138,175,160,192)(139,166,141,183)(140,177,142,194) );
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)], [(1,164,248,284,105,181,310,94),(2,163,249,283,106,200,311,93),(3,162,250,282,107,199,312,92),(4,161,251,281,108,198,313,91),(5,180,252,300,109,197,314,90),(6,179,253,299,110,196,315,89),(7,178,254,298,111,195,316,88),(8,177,255,297,112,194,317,87),(9,176,256,296,113,193,318,86),(10,175,257,295,114,192,319,85),(11,174,258,294,115,191,320,84),(12,173,259,293,116,190,301,83),(13,172,260,292,117,189,302,82),(14,171,241,291,118,188,303,81),(15,170,242,290,119,187,304,100),(16,169,243,289,120,186,305,99),(17,168,244,288,101,185,306,98),(18,167,245,287,102,184,307,97),(19,166,246,286,103,183,308,96),(20,165,247,285,104,182,309,95),(21,60,124,228,266,213,146,71),(22,59,125,227,267,212,147,70),(23,58,126,226,268,211,148,69),(24,57,127,225,269,210,149,68),(25,56,128,224,270,209,150,67),(26,55,129,223,271,208,151,66),(27,54,130,222,272,207,152,65),(28,53,131,221,273,206,153,64),(29,52,132,240,274,205,154,63),(30,51,133,239,275,204,155,62),(31,50,134,238,276,203,156,61),(32,49,135,237,277,202,157,80),(33,48,136,236,278,201,158,79),(34,47,137,235,279,220,159,78),(35,46,138,234,280,219,160,77),(36,45,139,233,261,218,141,76),(37,44,140,232,262,217,142,75),(38,43,121,231,263,216,143,74),(39,42,122,230,264,215,144,73),(40,41,123,229,265,214,145,72)], [(1,78,105,235),(2,69,106,226),(3,80,107,237),(4,71,108,228),(5,62,109,239),(6,73,110,230),(7,64,111,221),(8,75,112,232),(9,66,113,223),(10,77,114,234),(11,68,115,225),(12,79,116,236),(13,70,117,227),(14,61,118,238),(15,72,119,229),(16,63,120,240),(17,74,101,231),(18,65,102,222),(19,76,103,233),(20,67,104,224),(21,281,266,91),(22,292,267,82),(23,283,268,93),(24,294,269,84),(25,285,270,95),(26,296,271,86),(27,287,272,97),(28,298,273,88),(29,289,274,99),(30,300,275,90),(31,291,276,81),(32,282,277,92),(33,293,278,83),(34,284,279,94),(35,295,280,85),(36,286,261,96),(37,297,262,87),(38,288,263,98),(39,299,264,89),(40,290,265,100),(41,242,214,304),(42,253,215,315),(43,244,216,306),(44,255,217,317),(45,246,218,308),(46,257,219,319),(47,248,220,310),(48,259,201,301),(49,250,202,312),(50,241,203,303),(51,252,204,314),(52,243,205,305),(53,254,206,316),(54,245,207,307),(55,256,208,318),(56,247,209,309),(57,258,210,320),(58,249,211,311),(59,260,212,302),(60,251,213,313),(121,168,143,185),(122,179,144,196),(123,170,145,187),(124,161,146,198),(125,172,147,189),(126,163,148,200),(127,174,149,191),(128,165,150,182),(129,176,151,193),(130,167,152,184),(131,178,153,195),(132,169,154,186),(133,180,155,197),(134,171,156,188),(135,162,157,199),(136,173,158,190),(137,164,159,181),(138,175,160,192),(139,166,141,183),(140,177,142,194)]])
47 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 5A | 5B | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 20A | ··· | 20L | 20M | ··· | 20T |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 8 | 8 | 20 | 20 | 20 | 20 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
47 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | + | - | - | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D5 | Q16 | C4○D4 | D10 | D10 | C5⋊D4 | C8.C22 | C5⋊Q16 | D4×D5 | D4⋊2D5 | C20.C23 |
| kernel | C20⋊Q16 | C20⋊3C8 | Q8⋊Dic5 | C4×Dic10 | C2×C5⋊Q16 | C5×C4⋊Q8 | Dic10 | C2×C20 | C4⋊Q8 | C20 | C20 | C42 | C2×Q8 | C2×C4 | C10 | C4 | C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 2 | 2 | 4 | 8 | 1 | 4 | 2 | 2 | 4 |
Matrix representation of C20⋊Q16 ►in GL6(𝔽41)
| 6 | 40 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 37 | 0 | 0 |
| 0 | 0 | 21 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 2 | 15 | 0 | 0 | 0 | 0 |
| 27 | 39 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 4 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 0 | 0 | 0 | 0 | 12 | 17 |
| 23 | 6 | 0 | 0 | 0 | 0 |
| 35 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 4 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 29 |
| 0 | 0 | 0 | 0 | 2 | 33 |
G:=sub<GL(6,GF(41))| [6,1,0,0,0,0,40,0,0,0,0,0,0,0,40,21,0,0,0,0,37,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[2,27,0,0,0,0,15,39,0,0,0,0,0,0,1,0,0,0,0,0,4,40,0,0,0,0,0,0,0,12,0,0,0,0,17,17],[23,35,0,0,0,0,6,18,0,0,0,0,0,0,1,0,0,0,0,0,4,40,0,0,0,0,0,0,8,2,0,0,0,0,29,33] >;
C20⋊Q16 in GAP, Magma, Sage, TeX
C_{20}\rtimes Q_{16} % in TeX
G:=Group("C20:Q16"); // GroupNames label
G:=SmallGroup(320,717);
// by ID
G=gap.SmallGroup(320,717);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,120,254,219,184,1123,297,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=b^4,b*a*b^-1=a^-1,c*a*c^-1=a^11,c*b*c^-1=b^-1>;
// generators/relations