metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20⋊3Q16, C42.225D10, C4.19(D4×D5), C4⋊Q8.11D5, C20.40(C2×D4), C5⋊2(C4⋊Q16), C4⋊1(C5⋊Q16), C5⋊2C8.30D4, (C2×C20).161D4, (C2×Q8).48D10, C10.44(C2×Q16), C20⋊2Q8.22C2, C2.16(C20⋊D4), C10.25(C4⋊1D4), (C4×C20).139C22, (C2×C20).410C23, (Q8×C10).66C22, (C2×Dic10).119C22, (C5×C4⋊Q8).11C2, (C4×C5⋊2C8).14C2, (C2×C5⋊Q16).7C2, C2.15(C2×C5⋊Q16), (C2×C10).541(C2×D4), (C2×C4).138(C5⋊D4), (C2×C4).507(C22×D5), C22.213(C2×C5⋊D4), (C2×C5⋊2C8).272C22, SmallGroup(320,719)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20⋊3Q16
G = < a,b,c | a20=b8=1, c2=b4, bab-1=a9, cac-1=a11, cbc-1=b-1 >
Subgroups: 414 in 122 conjugacy classes, 51 normal (15 characteristic)
C1, C2, C2, C4, C4, C22, C5, C8, C2×C4, C2×C4, C2×C4, Q8, C10, C10, C42, C4⋊C4, C2×C8, Q16, C2×Q8, C2×Q8, Dic5, C20, C20, C2×C10, C4×C8, C4⋊Q8, C4⋊Q8, C2×Q16, C5⋊2C8, Dic10, C2×Dic5, C2×C20, C2×C20, C2×C20, C5×Q8, C4⋊Q16, C2×C5⋊2C8, C4⋊Dic5, C5⋊Q16, C4×C20, C5×C4⋊C4, C2×Dic10, Q8×C10, C4×C5⋊2C8, C20⋊2Q8, C2×C5⋊Q16, C5×C4⋊Q8, C20⋊3Q16
Quotients: C1, C2, C22, D4, C23, D5, Q16, C2×D4, D10, C4⋊1D4, C2×Q16, C5⋊D4, C22×D5, C4⋊Q16, C5⋊Q16, D4×D5, C2×C5⋊D4, C20⋊D4, C2×C5⋊Q16, C20⋊3Q16
►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)
(1 314 86 131 295 171 118 31)(2 303 87 140 296 180 119 40)(3 312 88 129 297 169 120 29)(4 301 89 138 298 178 101 38)(5 310 90 127 299 167 102 27)(6 319 91 136 300 176 103 36)(7 308 92 125 281 165 104 25)(8 317 93 134 282 174 105 34)(9 306 94 123 283 163 106 23)(10 315 95 132 284 172 107 32)(11 304 96 121 285 161 108 21)(12 313 97 130 286 170 109 30)(13 302 98 139 287 179 110 39)(14 311 99 128 288 168 111 28)(15 320 100 137 289 177 112 37)(16 309 81 126 290 166 113 26)(17 318 82 135 291 175 114 35)(18 307 83 124 292 164 115 24)(19 316 84 133 293 173 116 33)(20 305 85 122 294 162 117 22)(41 217 190 157 263 254 76 239)(42 206 191 146 264 243 77 228)(43 215 192 155 265 252 78 237)(44 204 193 144 266 241 79 226)(45 213 194 153 267 250 80 235)(46 202 195 142 268 259 61 224)(47 211 196 151 269 248 62 233)(48 220 197 160 270 257 63 222)(49 209 198 149 271 246 64 231)(50 218 199 158 272 255 65 240)(51 207 200 147 273 244 66 229)(52 216 181 156 274 253 67 238)(53 205 182 145 275 242 68 227)(54 214 183 154 276 251 69 236)(55 203 184 143 277 260 70 225)(56 212 185 152 278 249 71 234)(57 201 186 141 279 258 72 223)(58 210 187 150 280 247 73 232)(59 219 188 159 261 256 74 221)(60 208 189 148 262 245 75 230)
(1 48 295 270)(2 59 296 261)(3 50 297 272)(4 41 298 263)(5 52 299 274)(6 43 300 265)(7 54 281 276)(8 45 282 267)(9 56 283 278)(10 47 284 269)(11 58 285 280)(12 49 286 271)(13 60 287 262)(14 51 288 273)(15 42 289 264)(16 53 290 275)(17 44 291 266)(18 55 292 277)(19 46 293 268)(20 57 294 279)(21 210 121 247)(22 201 122 258)(23 212 123 249)(24 203 124 260)(25 214 125 251)(26 205 126 242)(27 216 127 253)(28 207 128 244)(29 218 129 255)(30 209 130 246)(31 220 131 257)(32 211 132 248)(33 202 133 259)(34 213 134 250)(35 204 135 241)(36 215 136 252)(37 206 137 243)(38 217 138 254)(39 208 139 245)(40 219 140 256)(61 116 195 84)(62 107 196 95)(63 118 197 86)(64 109 198 97)(65 120 199 88)(66 111 200 99)(67 102 181 90)(68 113 182 81)(69 104 183 92)(70 115 184 83)(71 106 185 94)(72 117 186 85)(73 108 187 96)(74 119 188 87)(75 110 189 98)(76 101 190 89)(77 112 191 100)(78 103 192 91)(79 114 193 82)(80 105 194 93)(141 305 223 162)(142 316 224 173)(143 307 225 164)(144 318 226 175)(145 309 227 166)(146 320 228 177)(147 311 229 168)(148 302 230 179)(149 313 231 170)(150 304 232 161)(151 315 233 172)(152 306 234 163)(153 317 235 174)(154 308 236 165)(155 319 237 176)(156 310 238 167)(157 301 239 178)(158 312 240 169)(159 303 221 180)(160 314 222 171)
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), (1,314,86,131,295,171,118,31)(2,303,87,140,296,180,119,40)(3,312,88,129,297,169,120,29)(4,301,89,138,298,178,101,38)(5,310,90,127,299,167,102,27)(6,319,91,136,300,176,103,36)(7,308,92,125,281,165,104,25)(8,317,93,134,282,174,105,34)(9,306,94,123,283,163,106,23)(10,315,95,132,284,172,107,32)(11,304,96,121,285,161,108,21)(12,313,97,130,286,170,109,30)(13,302,98,139,287,179,110,39)(14,311,99,128,288,168,111,28)(15,320,100,137,289,177,112,37)(16,309,81,126,290,166,113,26)(17,318,82,135,291,175,114,35)(18,307,83,124,292,164,115,24)(19,316,84,133,293,173,116,33)(20,305,85,122,294,162,117,22)(41,217,190,157,263,254,76,239)(42,206,191,146,264,243,77,228)(43,215,192,155,265,252,78,237)(44,204,193,144,266,241,79,226)(45,213,194,153,267,250,80,235)(46,202,195,142,268,259,61,224)(47,211,196,151,269,248,62,233)(48,220,197,160,270,257,63,222)(49,209,198,149,271,246,64,231)(50,218,199,158,272,255,65,240)(51,207,200,147,273,244,66,229)(52,216,181,156,274,253,67,238)(53,205,182,145,275,242,68,227)(54,214,183,154,276,251,69,236)(55,203,184,143,277,260,70,225)(56,212,185,152,278,249,71,234)(57,201,186,141,279,258,72,223)(58,210,187,150,280,247,73,232)(59,219,188,159,261,256,74,221)(60,208,189,148,262,245,75,230), (1,48,295,270)(2,59,296,261)(3,50,297,272)(4,41,298,263)(5,52,299,274)(6,43,300,265)(7,54,281,276)(8,45,282,267)(9,56,283,278)(10,47,284,269)(11,58,285,280)(12,49,286,271)(13,60,287,262)(14,51,288,273)(15,42,289,264)(16,53,290,275)(17,44,291,266)(18,55,292,277)(19,46,293,268)(20,57,294,279)(21,210,121,247)(22,201,122,258)(23,212,123,249)(24,203,124,260)(25,214,125,251)(26,205,126,242)(27,216,127,253)(28,207,128,244)(29,218,129,255)(30,209,130,246)(31,220,131,257)(32,211,132,248)(33,202,133,259)(34,213,134,250)(35,204,135,241)(36,215,136,252)(37,206,137,243)(38,217,138,254)(39,208,139,245)(40,219,140,256)(61,116,195,84)(62,107,196,95)(63,118,197,86)(64,109,198,97)(65,120,199,88)(66,111,200,99)(67,102,181,90)(68,113,182,81)(69,104,183,92)(70,115,184,83)(71,106,185,94)(72,117,186,85)(73,108,187,96)(74,119,188,87)(75,110,189,98)(76,101,190,89)(77,112,191,100)(78,103,192,91)(79,114,193,82)(80,105,194,93)(141,305,223,162)(142,316,224,173)(143,307,225,164)(144,318,226,175)(145,309,227,166)(146,320,228,177)(147,311,229,168)(148,302,230,179)(149,313,231,170)(150,304,232,161)(151,315,233,172)(152,306,234,163)(153,317,235,174)(154,308,236,165)(155,319,237,176)(156,310,238,167)(157,301,239,178)(158,312,240,169)(159,303,221,180)(160,314,222,171)>;
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), (1,314,86,131,295,171,118,31)(2,303,87,140,296,180,119,40)(3,312,88,129,297,169,120,29)(4,301,89,138,298,178,101,38)(5,310,90,127,299,167,102,27)(6,319,91,136,300,176,103,36)(7,308,92,125,281,165,104,25)(8,317,93,134,282,174,105,34)(9,306,94,123,283,163,106,23)(10,315,95,132,284,172,107,32)(11,304,96,121,285,161,108,21)(12,313,97,130,286,170,109,30)(13,302,98,139,287,179,110,39)(14,311,99,128,288,168,111,28)(15,320,100,137,289,177,112,37)(16,309,81,126,290,166,113,26)(17,318,82,135,291,175,114,35)(18,307,83,124,292,164,115,24)(19,316,84,133,293,173,116,33)(20,305,85,122,294,162,117,22)(41,217,190,157,263,254,76,239)(42,206,191,146,264,243,77,228)(43,215,192,155,265,252,78,237)(44,204,193,144,266,241,79,226)(45,213,194,153,267,250,80,235)(46,202,195,142,268,259,61,224)(47,211,196,151,269,248,62,233)(48,220,197,160,270,257,63,222)(49,209,198,149,271,246,64,231)(50,218,199,158,272,255,65,240)(51,207,200,147,273,244,66,229)(52,216,181,156,274,253,67,238)(53,205,182,145,275,242,68,227)(54,214,183,154,276,251,69,236)(55,203,184,143,277,260,70,225)(56,212,185,152,278,249,71,234)(57,201,186,141,279,258,72,223)(58,210,187,150,280,247,73,232)(59,219,188,159,261,256,74,221)(60,208,189,148,262,245,75,230), (1,48,295,270)(2,59,296,261)(3,50,297,272)(4,41,298,263)(5,52,299,274)(6,43,300,265)(7,54,281,276)(8,45,282,267)(9,56,283,278)(10,47,284,269)(11,58,285,280)(12,49,286,271)(13,60,287,262)(14,51,288,273)(15,42,289,264)(16,53,290,275)(17,44,291,266)(18,55,292,277)(19,46,293,268)(20,57,294,279)(21,210,121,247)(22,201,122,258)(23,212,123,249)(24,203,124,260)(25,214,125,251)(26,205,126,242)(27,216,127,253)(28,207,128,244)(29,218,129,255)(30,209,130,246)(31,220,131,257)(32,211,132,248)(33,202,133,259)(34,213,134,250)(35,204,135,241)(36,215,136,252)(37,206,137,243)(38,217,138,254)(39,208,139,245)(40,219,140,256)(61,116,195,84)(62,107,196,95)(63,118,197,86)(64,109,198,97)(65,120,199,88)(66,111,200,99)(67,102,181,90)(68,113,182,81)(69,104,183,92)(70,115,184,83)(71,106,185,94)(72,117,186,85)(73,108,187,96)(74,119,188,87)(75,110,189,98)(76,101,190,89)(77,112,191,100)(78,103,192,91)(79,114,193,82)(80,105,194,93)(141,305,223,162)(142,316,224,173)(143,307,225,164)(144,318,226,175)(145,309,227,166)(146,320,228,177)(147,311,229,168)(148,302,230,179)(149,313,231,170)(150,304,232,161)(151,315,233,172)(152,306,234,163)(153,317,235,174)(154,308,236,165)(155,319,237,176)(156,310,238,167)(157,301,239,178)(158,312,240,169)(159,303,221,180)(160,314,222,171) );
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)], [(1,314,86,131,295,171,118,31),(2,303,87,140,296,180,119,40),(3,312,88,129,297,169,120,29),(4,301,89,138,298,178,101,38),(5,310,90,127,299,167,102,27),(6,319,91,136,300,176,103,36),(7,308,92,125,281,165,104,25),(8,317,93,134,282,174,105,34),(9,306,94,123,283,163,106,23),(10,315,95,132,284,172,107,32),(11,304,96,121,285,161,108,21),(12,313,97,130,286,170,109,30),(13,302,98,139,287,179,110,39),(14,311,99,128,288,168,111,28),(15,320,100,137,289,177,112,37),(16,309,81,126,290,166,113,26),(17,318,82,135,291,175,114,35),(18,307,83,124,292,164,115,24),(19,316,84,133,293,173,116,33),(20,305,85,122,294,162,117,22),(41,217,190,157,263,254,76,239),(42,206,191,146,264,243,77,228),(43,215,192,155,265,252,78,237),(44,204,193,144,266,241,79,226),(45,213,194,153,267,250,80,235),(46,202,195,142,268,259,61,224),(47,211,196,151,269,248,62,233),(48,220,197,160,270,257,63,222),(49,209,198,149,271,246,64,231),(50,218,199,158,272,255,65,240),(51,207,200,147,273,244,66,229),(52,216,181,156,274,253,67,238),(53,205,182,145,275,242,68,227),(54,214,183,154,276,251,69,236),(55,203,184,143,277,260,70,225),(56,212,185,152,278,249,71,234),(57,201,186,141,279,258,72,223),(58,210,187,150,280,247,73,232),(59,219,188,159,261,256,74,221),(60,208,189,148,262,245,75,230)], [(1,48,295,270),(2,59,296,261),(3,50,297,272),(4,41,298,263),(5,52,299,274),(6,43,300,265),(7,54,281,276),(8,45,282,267),(9,56,283,278),(10,47,284,269),(11,58,285,280),(12,49,286,271),(13,60,287,262),(14,51,288,273),(15,42,289,264),(16,53,290,275),(17,44,291,266),(18,55,292,277),(19,46,293,268),(20,57,294,279),(21,210,121,247),(22,201,122,258),(23,212,123,249),(24,203,124,260),(25,214,125,251),(26,205,126,242),(27,216,127,253),(28,207,128,244),(29,218,129,255),(30,209,130,246),(31,220,131,257),(32,211,132,248),(33,202,133,259),(34,213,134,250),(35,204,135,241),(36,215,136,252),(37,206,137,243),(38,217,138,254),(39,208,139,245),(40,219,140,256),(61,116,195,84),(62,107,196,95),(63,118,197,86),(64,109,198,97),(65,120,199,88),(66,111,200,99),(67,102,181,90),(68,113,182,81),(69,104,183,92),(70,115,184,83),(71,106,185,94),(72,117,186,85),(73,108,187,96),(74,119,188,87),(75,110,189,98),(76,101,190,89),(77,112,191,100),(78,103,192,91),(79,114,193,82),(80,105,194,93),(141,305,223,162),(142,316,224,173),(143,307,225,164),(144,318,226,175),(145,309,227,166),(146,320,228,177),(147,311,229,168),(148,302,230,179),(149,313,231,170),(150,304,232,161),(151,315,233,172),(152,306,234,163),(153,317,235,174),(154,308,236,165),(155,319,237,176),(156,310,238,167),(157,301,239,178),(158,312,240,169),(159,303,221,180),(160,314,222,171)]])
50 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 8A | ··· | 8H | 10A | ··· | 10F | 20A | ··· | 20L | 20M | ··· | 20T |
| order | 1 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 8 | 8 | 40 | 40 | 2 | 2 | 10 | ··· | 10 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
50 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | - | + | |
| image | C1 | C2 | C2 | C2 | C2 | D4 | D4 | D5 | Q16 | D10 | D10 | C5⋊D4 | C5⋊Q16 | D4×D5 |
| kernel | C20⋊3Q16 | C4×C5⋊2C8 | C20⋊2Q8 | C2×C5⋊Q16 | C5×C4⋊Q8 | C5⋊2C8 | C2×C20 | C4⋊Q8 | C20 | C42 | C2×Q8 | C2×C4 | C4 | C4 |
| # reps | 1 | 1 | 1 | 4 | 1 | 4 | 2 | 2 | 8 | 2 | 4 | 8 | 8 | 4 |
Matrix representation of C20⋊3Q16 ►in GL6(𝔽41)
| 30 | 9 | 0 | 0 | 0 | 0 |
| 32 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 1 | 0 | 0 |
| 0 | 0 | 33 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 3 | 0 | 0 |
| 0 | 0 | 40 | 39 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 29 |
| 0 | 0 | 0 | 0 | 12 | 12 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 20 |
| 0 | 0 | 0 | 0 | 20 | 38 |
G:=sub<GL(6,GF(41))| [30,32,0,0,0,0,9,11,0,0,0,0,0,0,34,33,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,40,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,2,40,0,0,0,0,3,39,0,0,0,0,0,0,12,12,0,0,0,0,29,12],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,3,20,0,0,0,0,20,38] >;
C20⋊3Q16 in GAP, Magma, Sage, TeX
C_{20}\rtimes_3Q_{16} % in TeX
G:=Group("C20:3Q16"); // GroupNames label
G:=SmallGroup(320,719);
// by ID
G=gap.SmallGroup(320,719);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,253,120,254,219,184,1123,297,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=b^4,b*a*b^-1=a^9,c*a*c^-1=a^11,c*b*c^-1=b^-1>;
// generators/relations