metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20.16SD16, C42.221D10, C5⋊2C8⋊8Q8, C4⋊Q8.5D5, C5⋊3(C8⋊3Q8), C4.35(Q8×D5), C4⋊C4.80D10, C4.3(Q8⋊D5), C20.36(C2×Q8), (C2×C20).152D4, C10.31(C4⋊Q8), C4.4(D4.D5), C20⋊2Q8.20C2, C10.60(C2×SD16), (C4×C20).126C22, (C2×C20).397C23, C20.Q8.16C2, C4⋊Dic5.157C22, C2.11(Dic5⋊Q8), (C5×C4⋊Q8).5C2, C2.11(C2×Q8⋊D5), (C4×C5⋊2C8).12C2, C2.14(C2×D4.D5), (C2×C10).528(C2×D4), (C2×C4).134(C5⋊D4), (C5×C4⋊C4).127C22, (C2×C4).494(C22×D5), C22.200(C2×C5⋊D4), (C2×C5⋊2C8).268C22, SmallGroup(320,706)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20.SD16
G = < a,b,c | a20=b8=1, c2=a10, bab-1=a9, cac-1=a11, cbc-1=b3 >
Subgroups: 318 in 98 conjugacy classes, 51 normal (23 characteristic)
C1, C2, C4, C4, C22, C5, C8, C2×C4, C2×C4, Q8, C10, C42, C4⋊C4, C4⋊C4, C2×C8, C2×Q8, Dic5, C20, C20, C2×C10, C4×C8, C4.Q8, C4⋊Q8, C4⋊Q8, C5⋊2C8, Dic10, C2×Dic5, C2×C20, C2×C20, C5×Q8, C8⋊3Q8, C2×C5⋊2C8, C4⋊Dic5, C4⋊Dic5, C4×C20, C5×C4⋊C4, C5×C4⋊C4, C2×Dic10, Q8×C10, C4×C5⋊2C8, C20.Q8, C20⋊2Q8, C5×C4⋊Q8, C20.SD16
Quotients: C1, C2, C22, D4, Q8, C23, D5, SD16, C2×D4, C2×Q8, D10, C4⋊Q8, C2×SD16, C5⋊D4, C22×D5, C8⋊3Q8, D4.D5, Q8⋊D5, Q8×D5, C2×C5⋊D4, C2×D4.D5, C2×Q8⋊D5, Dic5⋊Q8, C20.SD16
►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 25 56 85 63 290 115 217)(2 34 57 94 64 299 116 206)(3 23 58 83 65 288 117 215)(4 32 59 92 66 297 118 204)(5 21 60 81 67 286 119 213)(6 30 41 90 68 295 120 202)(7 39 42 99 69 284 101 211)(8 28 43 88 70 293 102 220)(9 37 44 97 71 282 103 209)(10 26 45 86 72 291 104 218)(11 35 46 95 73 300 105 207)(12 24 47 84 74 289 106 216)(13 33 48 93 75 298 107 205)(14 22 49 82 76 287 108 214)(15 31 50 91 77 296 109 203)(16 40 51 100 78 285 110 212)(17 29 52 89 79 294 111 201)(18 38 53 98 80 283 112 210)(19 27 54 87 61 292 113 219)(20 36 55 96 62 281 114 208)(121 223 145 308 169 254 265 184)(122 232 146 317 170 243 266 193)(123 221 147 306 171 252 267 182)(124 230 148 315 172 241 268 191)(125 239 149 304 173 250 269 200)(126 228 150 313 174 259 270 189)(127 237 151 302 175 248 271 198)(128 226 152 311 176 257 272 187)(129 235 153 320 177 246 273 196)(130 224 154 309 178 255 274 185)(131 233 155 318 179 244 275 194)(132 222 156 307 180 253 276 183)(133 231 157 316 161 242 277 192)(134 240 158 305 162 251 278 181)(135 229 159 314 163 260 279 190)(136 238 160 303 164 249 280 199)(137 227 141 312 165 258 261 188)(138 236 142 301 166 247 262 197)(139 225 143 310 167 256 263 186)(140 234 144 319 168 245 264 195)
(1 278 11 268)(2 269 12 279)(3 280 13 270)(4 271 14 261)(5 262 15 272)(6 273 16 263)(7 264 17 274)(8 275 18 265)(9 266 19 276)(10 277 20 267)(21 236 31 226)(22 227 32 237)(23 238 33 228)(24 229 34 239)(25 240 35 230)(26 231 36 221)(27 222 37 232)(28 233 38 223)(29 224 39 234)(30 235 40 225)(41 177 51 167)(42 168 52 178)(43 179 53 169)(44 170 54 180)(45 161 55 171)(46 172 56 162)(47 163 57 173)(48 174 58 164)(49 165 59 175)(50 176 60 166)(61 156 71 146)(62 147 72 157)(63 158 73 148)(64 149 74 159)(65 160 75 150)(66 151 76 141)(67 142 77 152)(68 153 78 143)(69 144 79 154)(70 155 80 145)(81 197 91 187)(82 188 92 198)(83 199 93 189)(84 190 94 200)(85 181 95 191)(86 192 96 182)(87 183 97 193)(88 194 98 184)(89 185 99 195)(90 196 100 186)(101 140 111 130)(102 131 112 121)(103 122 113 132)(104 133 114 123)(105 124 115 134)(106 135 116 125)(107 126 117 136)(108 137 118 127)(109 128 119 138)(110 139 120 129)(201 309 211 319)(202 320 212 310)(203 311 213 301)(204 302 214 312)(205 313 215 303)(206 304 216 314)(207 315 217 305)(208 306 218 316)(209 317 219 307)(210 308 220 318)(241 290 251 300)(242 281 252 291)(243 292 253 282)(244 283 254 293)(245 294 255 284)(246 285 256 295)(247 296 257 286)(248 287 258 297)(249 298 259 288)(250 289 260 299)
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), (1,25,56,85,63,290,115,217)(2,34,57,94,64,299,116,206)(3,23,58,83,65,288,117,215)(4,32,59,92,66,297,118,204)(5,21,60,81,67,286,119,213)(6,30,41,90,68,295,120,202)(7,39,42,99,69,284,101,211)(8,28,43,88,70,293,102,220)(9,37,44,97,71,282,103,209)(10,26,45,86,72,291,104,218)(11,35,46,95,73,300,105,207)(12,24,47,84,74,289,106,216)(13,33,48,93,75,298,107,205)(14,22,49,82,76,287,108,214)(15,31,50,91,77,296,109,203)(16,40,51,100,78,285,110,212)(17,29,52,89,79,294,111,201)(18,38,53,98,80,283,112,210)(19,27,54,87,61,292,113,219)(20,36,55,96,62,281,114,208)(121,223,145,308,169,254,265,184)(122,232,146,317,170,243,266,193)(123,221,147,306,171,252,267,182)(124,230,148,315,172,241,268,191)(125,239,149,304,173,250,269,200)(126,228,150,313,174,259,270,189)(127,237,151,302,175,248,271,198)(128,226,152,311,176,257,272,187)(129,235,153,320,177,246,273,196)(130,224,154,309,178,255,274,185)(131,233,155,318,179,244,275,194)(132,222,156,307,180,253,276,183)(133,231,157,316,161,242,277,192)(134,240,158,305,162,251,278,181)(135,229,159,314,163,260,279,190)(136,238,160,303,164,249,280,199)(137,227,141,312,165,258,261,188)(138,236,142,301,166,247,262,197)(139,225,143,310,167,256,263,186)(140,234,144,319,168,245,264,195), (1,278,11,268)(2,269,12,279)(3,280,13,270)(4,271,14,261)(5,262,15,272)(6,273,16,263)(7,264,17,274)(8,275,18,265)(9,266,19,276)(10,277,20,267)(21,236,31,226)(22,227,32,237)(23,238,33,228)(24,229,34,239)(25,240,35,230)(26,231,36,221)(27,222,37,232)(28,233,38,223)(29,224,39,234)(30,235,40,225)(41,177,51,167)(42,168,52,178)(43,179,53,169)(44,170,54,180)(45,161,55,171)(46,172,56,162)(47,163,57,173)(48,174,58,164)(49,165,59,175)(50,176,60,166)(61,156,71,146)(62,147,72,157)(63,158,73,148)(64,149,74,159)(65,160,75,150)(66,151,76,141)(67,142,77,152)(68,153,78,143)(69,144,79,154)(70,155,80,145)(81,197,91,187)(82,188,92,198)(83,199,93,189)(84,190,94,200)(85,181,95,191)(86,192,96,182)(87,183,97,193)(88,194,98,184)(89,185,99,195)(90,196,100,186)(101,140,111,130)(102,131,112,121)(103,122,113,132)(104,133,114,123)(105,124,115,134)(106,135,116,125)(107,126,117,136)(108,137,118,127)(109,128,119,138)(110,139,120,129)(201,309,211,319)(202,320,212,310)(203,311,213,301)(204,302,214,312)(205,313,215,303)(206,304,216,314)(207,315,217,305)(208,306,218,316)(209,317,219,307)(210,308,220,318)(241,290,251,300)(242,281,252,291)(243,292,253,282)(244,283,254,293)(245,294,255,284)(246,285,256,295)(247,296,257,286)(248,287,258,297)(249,298,259,288)(250,289,260,299)>;
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), (1,25,56,85,63,290,115,217)(2,34,57,94,64,299,116,206)(3,23,58,83,65,288,117,215)(4,32,59,92,66,297,118,204)(5,21,60,81,67,286,119,213)(6,30,41,90,68,295,120,202)(7,39,42,99,69,284,101,211)(8,28,43,88,70,293,102,220)(9,37,44,97,71,282,103,209)(10,26,45,86,72,291,104,218)(11,35,46,95,73,300,105,207)(12,24,47,84,74,289,106,216)(13,33,48,93,75,298,107,205)(14,22,49,82,76,287,108,214)(15,31,50,91,77,296,109,203)(16,40,51,100,78,285,110,212)(17,29,52,89,79,294,111,201)(18,38,53,98,80,283,112,210)(19,27,54,87,61,292,113,219)(20,36,55,96,62,281,114,208)(121,223,145,308,169,254,265,184)(122,232,146,317,170,243,266,193)(123,221,147,306,171,252,267,182)(124,230,148,315,172,241,268,191)(125,239,149,304,173,250,269,200)(126,228,150,313,174,259,270,189)(127,237,151,302,175,248,271,198)(128,226,152,311,176,257,272,187)(129,235,153,320,177,246,273,196)(130,224,154,309,178,255,274,185)(131,233,155,318,179,244,275,194)(132,222,156,307,180,253,276,183)(133,231,157,316,161,242,277,192)(134,240,158,305,162,251,278,181)(135,229,159,314,163,260,279,190)(136,238,160,303,164,249,280,199)(137,227,141,312,165,258,261,188)(138,236,142,301,166,247,262,197)(139,225,143,310,167,256,263,186)(140,234,144,319,168,245,264,195), (1,278,11,268)(2,269,12,279)(3,280,13,270)(4,271,14,261)(5,262,15,272)(6,273,16,263)(7,264,17,274)(8,275,18,265)(9,266,19,276)(10,277,20,267)(21,236,31,226)(22,227,32,237)(23,238,33,228)(24,229,34,239)(25,240,35,230)(26,231,36,221)(27,222,37,232)(28,233,38,223)(29,224,39,234)(30,235,40,225)(41,177,51,167)(42,168,52,178)(43,179,53,169)(44,170,54,180)(45,161,55,171)(46,172,56,162)(47,163,57,173)(48,174,58,164)(49,165,59,175)(50,176,60,166)(61,156,71,146)(62,147,72,157)(63,158,73,148)(64,149,74,159)(65,160,75,150)(66,151,76,141)(67,142,77,152)(68,153,78,143)(69,144,79,154)(70,155,80,145)(81,197,91,187)(82,188,92,198)(83,199,93,189)(84,190,94,200)(85,181,95,191)(86,192,96,182)(87,183,97,193)(88,194,98,184)(89,185,99,195)(90,196,100,186)(101,140,111,130)(102,131,112,121)(103,122,113,132)(104,133,114,123)(105,124,115,134)(106,135,116,125)(107,126,117,136)(108,137,118,127)(109,128,119,138)(110,139,120,129)(201,309,211,319)(202,320,212,310)(203,311,213,301)(204,302,214,312)(205,313,215,303)(206,304,216,314)(207,315,217,305)(208,306,218,316)(209,317,219,307)(210,308,220,318)(241,290,251,300)(242,281,252,291)(243,292,253,282)(244,283,254,293)(245,294,255,284)(246,285,256,295)(247,296,257,286)(248,287,258,297)(249,298,259,288)(250,289,260,299) );
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)], [(1,25,56,85,63,290,115,217),(2,34,57,94,64,299,116,206),(3,23,58,83,65,288,117,215),(4,32,59,92,66,297,118,204),(5,21,60,81,67,286,119,213),(6,30,41,90,68,295,120,202),(7,39,42,99,69,284,101,211),(8,28,43,88,70,293,102,220),(9,37,44,97,71,282,103,209),(10,26,45,86,72,291,104,218),(11,35,46,95,73,300,105,207),(12,24,47,84,74,289,106,216),(13,33,48,93,75,298,107,205),(14,22,49,82,76,287,108,214),(15,31,50,91,77,296,109,203),(16,40,51,100,78,285,110,212),(17,29,52,89,79,294,111,201),(18,38,53,98,80,283,112,210),(19,27,54,87,61,292,113,219),(20,36,55,96,62,281,114,208),(121,223,145,308,169,254,265,184),(122,232,146,317,170,243,266,193),(123,221,147,306,171,252,267,182),(124,230,148,315,172,241,268,191),(125,239,149,304,173,250,269,200),(126,228,150,313,174,259,270,189),(127,237,151,302,175,248,271,198),(128,226,152,311,176,257,272,187),(129,235,153,320,177,246,273,196),(130,224,154,309,178,255,274,185),(131,233,155,318,179,244,275,194),(132,222,156,307,180,253,276,183),(133,231,157,316,161,242,277,192),(134,240,158,305,162,251,278,181),(135,229,159,314,163,260,279,190),(136,238,160,303,164,249,280,199),(137,227,141,312,165,258,261,188),(138,236,142,301,166,247,262,197),(139,225,143,310,167,256,263,186),(140,234,144,319,168,245,264,195)], [(1,278,11,268),(2,269,12,279),(3,280,13,270),(4,271,14,261),(5,262,15,272),(6,273,16,263),(7,264,17,274),(8,275,18,265),(9,266,19,276),(10,277,20,267),(21,236,31,226),(22,227,32,237),(23,238,33,228),(24,229,34,239),(25,240,35,230),(26,231,36,221),(27,222,37,232),(28,233,38,223),(29,224,39,234),(30,235,40,225),(41,177,51,167),(42,168,52,178),(43,179,53,169),(44,170,54,180),(45,161,55,171),(46,172,56,162),(47,163,57,173),(48,174,58,164),(49,165,59,175),(50,176,60,166),(61,156,71,146),(62,147,72,157),(63,158,73,148),(64,149,74,159),(65,160,75,150),(66,151,76,141),(67,142,77,152),(68,153,78,143),(69,144,79,154),(70,155,80,145),(81,197,91,187),(82,188,92,198),(83,199,93,189),(84,190,94,200),(85,181,95,191),(86,192,96,182),(87,183,97,193),(88,194,98,184),(89,185,99,195),(90,196,100,186),(101,140,111,130),(102,131,112,121),(103,122,113,132),(104,133,114,123),(105,124,115,134),(106,135,116,125),(107,126,117,136),(108,137,118,127),(109,128,119,138),(110,139,120,129),(201,309,211,319),(202,320,212,310),(203,311,213,301),(204,302,214,312),(205,313,215,303),(206,304,216,314),(207,315,217,305),(208,306,218,316),(209,317,219,307),(210,308,220,318),(241,290,251,300),(242,281,252,291),(243,292,253,282),(244,283,254,293),(245,294,255,284),(246,285,256,295),(247,296,257,286),(248,287,258,297),(249,298,259,288),(250,289,260,299)]])
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 | 4 |
| type | + | + | + | + | + | - | + | + | + | + | - | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | Q8 | D4 | D5 | SD16 | D10 | D10 | C5⋊D4 | D4.D5 | Q8⋊D5 | Q8×D5 |
| kernel | C20.SD16 | C4×C5⋊2C8 | C20.Q8 | C20⋊2Q8 | C5×C4⋊Q8 | C5⋊2C8 | C2×C20 | C4⋊Q8 | C20 | C42 | C4⋊C4 | C2×C4 | C4 | C4 | C4 |
| # reps | 1 | 1 | 4 | 1 | 1 | 4 | 2 | 2 | 8 | 2 | 4 | 8 | 4 | 4 | 4 |
Matrix representation of C20.SD16 ►in GL6(𝔽41)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 40 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 26 | 26 | 0 | 0 | 0 | 0 |
| 15 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 19 | 0 | 0 |
| 0 | 0 | 9 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 26 | 15 |
| 0 | 0 | 0 | 0 | 26 | 26 |
| 18 | 28 | 0 | 0 | 0 | 0 |
| 28 | 23 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 40 | 0 | 0 |
| 0 | 0 | 1 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 34 |
| 0 | 0 | 0 | 0 | 34 | 14 |
G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,34,1,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,40,0],[26,15,0,0,0,0,26,26,0,0,0,0,0,0,19,9,0,0,0,0,19,22,0,0,0,0,0,0,26,26,0,0,0,0,15,26],[18,28,0,0,0,0,28,23,0,0,0,0,0,0,17,1,0,0,0,0,40,24,0,0,0,0,0,0,27,34,0,0,0,0,34,14] >;
C20.SD16 in GAP, Magma, Sage, TeX
C_{20}.{\rm SD}_{16} % in TeX
G:=Group("C20.SD16"); // GroupNames label
G:=SmallGroup(320,706);
// by ID
G=gap.SmallGroup(320,706);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,64,1094,135,58,438,102,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=a^10,b*a*b^-1=a^9,c*a*c^-1=a^11,c*b*c^-1=b^3>;
// generators/relations