metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20.26Q16, C20.50SD16, C42.195D10, C20.22M4(2), C5⋊5(Q8⋊C8), Q8⋊(C5⋊2C8), (C5×Q8)⋊3C8, C10.27C4≀C2, (C4×Q8).1D5, C20.32(C2×C8), C4⋊C4.4Dic5, (Q8×C20).1C2, (C2×C20).490D4, C4.16(Q8⋊D5), (Q8×C10).17C4, (C2×Q8).4Dic5, C20⋊3C8.11C2, (C4×C20).46C22, C4.14(C5⋊Q16), C4.2(C4.Dic5), C10.31(C22⋊C8), C2.2(Q8⋊Dic5), C10.17(Q8⋊C4), C2.3(D4⋊2Dic5), C2.6(C20.55D4), C22.30(C23.D5), C4.2(C2×C5⋊2C8), (C5×C4⋊C4).19C4, (C4×C5⋊2C8).4C2, (C2×C20).233(C2×C4), (C2×C4).38(C2×Dic5), (C2×C4).162(C5⋊D4), (C2×C10).157(C22⋊C4), SmallGroup(320,93)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20.26Q16
G = < a,b,c | a20=b8=1, c2=a10b4, bab-1=a9, ac=ca, cbc-1=a5b-1 >
Subgroups: 166 in 70 conjugacy classes, 39 normal (35 characteristic)
C1, C2, C4, C4, C22, C5, C8, C2×C4, C2×C4, Q8, Q8, C10, C42, C42, C4⋊C4, C4⋊C4, C2×C8, C2×Q8, C20, C20, C2×C10, C4×C8, C4⋊C8, C4×Q8, C5⋊2C8, C2×C20, C2×C20, C5×Q8, C5×Q8, Q8⋊C8, C2×C5⋊2C8, C4×C20, C4×C20, C5×C4⋊C4, C5×C4⋊C4, Q8×C10, C4×C5⋊2C8, C20⋊3C8, Q8×C20, C20.26Q16
Quotients: C1, C2, C4, C22, C8, C2×C4, D4, D5, C22⋊C4, C2×C8, M4(2), SD16, Q16, Dic5, D10, C22⋊C8, Q8⋊C4, C4≀C2, C5⋊2C8, C2×Dic5, C5⋊D4, Q8⋊C8, C2×C5⋊2C8, C4.Dic5, Q8⋊D5, C5⋊Q16, C23.D5, C20.55D4, Q8⋊Dic5, D4⋊2Dic5, C20.26Q16
►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)
(1 291 57 21 143 177 317 82)(2 300 58 30 144 166 318 91)(3 289 59 39 145 175 319 100)(4 298 60 28 146 164 320 89)(5 287 41 37 147 173 301 98)(6 296 42 26 148 162 302 87)(7 285 43 35 149 171 303 96)(8 294 44 24 150 180 304 85)(9 283 45 33 151 169 305 94)(10 292 46 22 152 178 306 83)(11 281 47 31 153 167 307 92)(12 290 48 40 154 176 308 81)(13 299 49 29 155 165 309 90)(14 288 50 38 156 174 310 99)(15 297 51 27 157 163 311 88)(16 286 52 36 158 172 312 97)(17 295 53 25 159 161 313 86)(18 284 54 34 160 170 314 95)(19 293 55 23 141 179 315 84)(20 282 56 32 142 168 316 93)(61 184 134 276 119 231 213 260)(62 193 135 265 120 240 214 249)(63 182 136 274 101 229 215 258)(64 191 137 263 102 238 216 247)(65 200 138 272 103 227 217 256)(66 189 139 261 104 236 218 245)(67 198 140 270 105 225 219 254)(68 187 121 279 106 234 220 243)(69 196 122 268 107 223 201 252)(70 185 123 277 108 232 202 241)(71 194 124 266 109 221 203 250)(72 183 125 275 110 230 204 259)(73 192 126 264 111 239 205 248)(74 181 127 273 112 228 206 257)(75 190 128 262 113 237 207 246)(76 199 129 271 114 226 208 255)(77 188 130 280 115 235 209 244)(78 197 131 269 116 224 210 253)(79 186 132 278 117 233 211 242)(80 195 133 267 118 222 212 251)
(1 252 153 278)(2 253 154 279)(3 254 155 280)(4 255 156 261)(5 256 157 262)(6 257 158 263)(7 258 159 264)(8 259 160 265)(9 260 141 266)(10 241 142 267)(11 242 143 268)(12 243 144 269)(13 244 145 270)(14 245 146 271)(15 246 147 272)(16 247 148 273)(17 248 149 274)(18 249 150 275)(19 250 151 276)(20 251 152 277)(21 102 92 74)(22 103 93 75)(23 104 94 76)(24 105 95 77)(25 106 96 78)(26 107 97 79)(27 108 98 80)(28 109 99 61)(29 110 100 62)(30 111 81 63)(31 112 82 64)(32 113 83 65)(33 114 84 66)(34 115 85 67)(35 116 86 68)(36 117 87 69)(37 118 88 70)(38 119 89 71)(39 120 90 72)(40 101 91 73)(41 237 311 200)(42 238 312 181)(43 239 313 182)(44 240 314 183)(45 221 315 184)(46 222 316 185)(47 223 317 186)(48 224 318 187)(49 225 319 188)(50 226 320 189)(51 227 301 190)(52 228 302 191)(53 229 303 192)(54 230 304 193)(55 231 305 194)(56 232 306 195)(57 233 307 196)(58 234 308 197)(59 235 309 198)(60 236 310 199)(121 295 210 171)(122 296 211 172)(123 297 212 173)(124 298 213 174)(125 299 214 175)(126 300 215 176)(127 281 216 177)(128 282 217 178)(129 283 218 179)(130 284 219 180)(131 285 220 161)(132 286 201 162)(133 287 202 163)(134 288 203 164)(135 289 204 165)(136 290 205 166)(137 291 206 167)(138 292 207 168)(139 293 208 169)(140 294 209 170)
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), (1,291,57,21,143,177,317,82)(2,300,58,30,144,166,318,91)(3,289,59,39,145,175,319,100)(4,298,60,28,146,164,320,89)(5,287,41,37,147,173,301,98)(6,296,42,26,148,162,302,87)(7,285,43,35,149,171,303,96)(8,294,44,24,150,180,304,85)(9,283,45,33,151,169,305,94)(10,292,46,22,152,178,306,83)(11,281,47,31,153,167,307,92)(12,290,48,40,154,176,308,81)(13,299,49,29,155,165,309,90)(14,288,50,38,156,174,310,99)(15,297,51,27,157,163,311,88)(16,286,52,36,158,172,312,97)(17,295,53,25,159,161,313,86)(18,284,54,34,160,170,314,95)(19,293,55,23,141,179,315,84)(20,282,56,32,142,168,316,93)(61,184,134,276,119,231,213,260)(62,193,135,265,120,240,214,249)(63,182,136,274,101,229,215,258)(64,191,137,263,102,238,216,247)(65,200,138,272,103,227,217,256)(66,189,139,261,104,236,218,245)(67,198,140,270,105,225,219,254)(68,187,121,279,106,234,220,243)(69,196,122,268,107,223,201,252)(70,185,123,277,108,232,202,241)(71,194,124,266,109,221,203,250)(72,183,125,275,110,230,204,259)(73,192,126,264,111,239,205,248)(74,181,127,273,112,228,206,257)(75,190,128,262,113,237,207,246)(76,199,129,271,114,226,208,255)(77,188,130,280,115,235,209,244)(78,197,131,269,116,224,210,253)(79,186,132,278,117,233,211,242)(80,195,133,267,118,222,212,251), (1,252,153,278)(2,253,154,279)(3,254,155,280)(4,255,156,261)(5,256,157,262)(6,257,158,263)(7,258,159,264)(8,259,160,265)(9,260,141,266)(10,241,142,267)(11,242,143,268)(12,243,144,269)(13,244,145,270)(14,245,146,271)(15,246,147,272)(16,247,148,273)(17,248,149,274)(18,249,150,275)(19,250,151,276)(20,251,152,277)(21,102,92,74)(22,103,93,75)(23,104,94,76)(24,105,95,77)(25,106,96,78)(26,107,97,79)(27,108,98,80)(28,109,99,61)(29,110,100,62)(30,111,81,63)(31,112,82,64)(32,113,83,65)(33,114,84,66)(34,115,85,67)(35,116,86,68)(36,117,87,69)(37,118,88,70)(38,119,89,71)(39,120,90,72)(40,101,91,73)(41,237,311,200)(42,238,312,181)(43,239,313,182)(44,240,314,183)(45,221,315,184)(46,222,316,185)(47,223,317,186)(48,224,318,187)(49,225,319,188)(50,226,320,189)(51,227,301,190)(52,228,302,191)(53,229,303,192)(54,230,304,193)(55,231,305,194)(56,232,306,195)(57,233,307,196)(58,234,308,197)(59,235,309,198)(60,236,310,199)(121,295,210,171)(122,296,211,172)(123,297,212,173)(124,298,213,174)(125,299,214,175)(126,300,215,176)(127,281,216,177)(128,282,217,178)(129,283,218,179)(130,284,219,180)(131,285,220,161)(132,286,201,162)(133,287,202,163)(134,288,203,164)(135,289,204,165)(136,290,205,166)(137,291,206,167)(138,292,207,168)(139,293,208,169)(140,294,209,170)>;
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), (1,291,57,21,143,177,317,82)(2,300,58,30,144,166,318,91)(3,289,59,39,145,175,319,100)(4,298,60,28,146,164,320,89)(5,287,41,37,147,173,301,98)(6,296,42,26,148,162,302,87)(7,285,43,35,149,171,303,96)(8,294,44,24,150,180,304,85)(9,283,45,33,151,169,305,94)(10,292,46,22,152,178,306,83)(11,281,47,31,153,167,307,92)(12,290,48,40,154,176,308,81)(13,299,49,29,155,165,309,90)(14,288,50,38,156,174,310,99)(15,297,51,27,157,163,311,88)(16,286,52,36,158,172,312,97)(17,295,53,25,159,161,313,86)(18,284,54,34,160,170,314,95)(19,293,55,23,141,179,315,84)(20,282,56,32,142,168,316,93)(61,184,134,276,119,231,213,260)(62,193,135,265,120,240,214,249)(63,182,136,274,101,229,215,258)(64,191,137,263,102,238,216,247)(65,200,138,272,103,227,217,256)(66,189,139,261,104,236,218,245)(67,198,140,270,105,225,219,254)(68,187,121,279,106,234,220,243)(69,196,122,268,107,223,201,252)(70,185,123,277,108,232,202,241)(71,194,124,266,109,221,203,250)(72,183,125,275,110,230,204,259)(73,192,126,264,111,239,205,248)(74,181,127,273,112,228,206,257)(75,190,128,262,113,237,207,246)(76,199,129,271,114,226,208,255)(77,188,130,280,115,235,209,244)(78,197,131,269,116,224,210,253)(79,186,132,278,117,233,211,242)(80,195,133,267,118,222,212,251), (1,252,153,278)(2,253,154,279)(3,254,155,280)(4,255,156,261)(5,256,157,262)(6,257,158,263)(7,258,159,264)(8,259,160,265)(9,260,141,266)(10,241,142,267)(11,242,143,268)(12,243,144,269)(13,244,145,270)(14,245,146,271)(15,246,147,272)(16,247,148,273)(17,248,149,274)(18,249,150,275)(19,250,151,276)(20,251,152,277)(21,102,92,74)(22,103,93,75)(23,104,94,76)(24,105,95,77)(25,106,96,78)(26,107,97,79)(27,108,98,80)(28,109,99,61)(29,110,100,62)(30,111,81,63)(31,112,82,64)(32,113,83,65)(33,114,84,66)(34,115,85,67)(35,116,86,68)(36,117,87,69)(37,118,88,70)(38,119,89,71)(39,120,90,72)(40,101,91,73)(41,237,311,200)(42,238,312,181)(43,239,313,182)(44,240,314,183)(45,221,315,184)(46,222,316,185)(47,223,317,186)(48,224,318,187)(49,225,319,188)(50,226,320,189)(51,227,301,190)(52,228,302,191)(53,229,303,192)(54,230,304,193)(55,231,305,194)(56,232,306,195)(57,233,307,196)(58,234,308,197)(59,235,309,198)(60,236,310,199)(121,295,210,171)(122,296,211,172)(123,297,212,173)(124,298,213,174)(125,299,214,175)(126,300,215,176)(127,281,216,177)(128,282,217,178)(129,283,218,179)(130,284,219,180)(131,285,220,161)(132,286,201,162)(133,287,202,163)(134,288,203,164)(135,289,204,165)(136,290,205,166)(137,291,206,167)(138,292,207,168)(139,293,208,169)(140,294,209,170) );
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)], [(1,291,57,21,143,177,317,82),(2,300,58,30,144,166,318,91),(3,289,59,39,145,175,319,100),(4,298,60,28,146,164,320,89),(5,287,41,37,147,173,301,98),(6,296,42,26,148,162,302,87),(7,285,43,35,149,171,303,96),(8,294,44,24,150,180,304,85),(9,283,45,33,151,169,305,94),(10,292,46,22,152,178,306,83),(11,281,47,31,153,167,307,92),(12,290,48,40,154,176,308,81),(13,299,49,29,155,165,309,90),(14,288,50,38,156,174,310,99),(15,297,51,27,157,163,311,88),(16,286,52,36,158,172,312,97),(17,295,53,25,159,161,313,86),(18,284,54,34,160,170,314,95),(19,293,55,23,141,179,315,84),(20,282,56,32,142,168,316,93),(61,184,134,276,119,231,213,260),(62,193,135,265,120,240,214,249),(63,182,136,274,101,229,215,258),(64,191,137,263,102,238,216,247),(65,200,138,272,103,227,217,256),(66,189,139,261,104,236,218,245),(67,198,140,270,105,225,219,254),(68,187,121,279,106,234,220,243),(69,196,122,268,107,223,201,252),(70,185,123,277,108,232,202,241),(71,194,124,266,109,221,203,250),(72,183,125,275,110,230,204,259),(73,192,126,264,111,239,205,248),(74,181,127,273,112,228,206,257),(75,190,128,262,113,237,207,246),(76,199,129,271,114,226,208,255),(77,188,130,280,115,235,209,244),(78,197,131,269,116,224,210,253),(79,186,132,278,117,233,211,242),(80,195,133,267,118,222,212,251)], [(1,252,153,278),(2,253,154,279),(3,254,155,280),(4,255,156,261),(5,256,157,262),(6,257,158,263),(7,258,159,264),(8,259,160,265),(9,260,141,266),(10,241,142,267),(11,242,143,268),(12,243,144,269),(13,244,145,270),(14,245,146,271),(15,246,147,272),(16,247,148,273),(17,248,149,274),(18,249,150,275),(19,250,151,276),(20,251,152,277),(21,102,92,74),(22,103,93,75),(23,104,94,76),(24,105,95,77),(25,106,96,78),(26,107,97,79),(27,108,98,80),(28,109,99,61),(29,110,100,62),(30,111,81,63),(31,112,82,64),(32,113,83,65),(33,114,84,66),(34,115,85,67),(35,116,86,68),(36,117,87,69),(37,118,88,70),(38,119,89,71),(39,120,90,72),(40,101,91,73),(41,237,311,200),(42,238,312,181),(43,239,313,182),(44,240,314,183),(45,221,315,184),(46,222,316,185),(47,223,317,186),(48,224,318,187),(49,225,319,188),(50,226,320,189),(51,227,301,190),(52,228,302,191),(53,229,303,192),(54,230,304,193),(55,231,305,194),(56,232,306,195),(57,233,307,196),(58,234,308,197),(59,235,309,198),(60,236,310,199),(121,295,210,171),(122,296,211,172),(123,297,212,173),(124,298,213,174),(125,299,214,175),(126,300,215,176),(127,281,216,177),(128,282,217,178),(129,283,218,179),(130,284,219,180),(131,285,220,161),(132,286,201,162),(133,287,202,163),(134,288,203,164),(135,289,204,165),(136,290,205,166),(137,291,206,167),(138,292,207,168),(139,293,208,169),(140,294,209,170)]])
68 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 5A | 5B | 8A | ··· | 8H | 8I | 8J | 8K | 8L | 10A | ··· | 10F | 20A | ··· | 20H | 20I | ··· | 20AF |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | ··· | 8 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | 2 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
68 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | - | - | + | - | ||||||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | C8 | D4 | D5 | M4(2) | SD16 | Q16 | D10 | Dic5 | Dic5 | C4≀C2 | C5⋊D4 | C5⋊2C8 | C4.Dic5 | Q8⋊D5 | C5⋊Q16 | D4⋊2Dic5 |
| kernel | C20.26Q16 | C4×C5⋊2C8 | C20⋊3C8 | Q8×C20 | C5×C4⋊C4 | Q8×C10 | C5×Q8 | C2×C20 | C4×Q8 | C20 | C20 | C20 | C42 | C4⋊C4 | C2×Q8 | C10 | C2×C4 | Q8 | C4 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 2 | 8 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 8 | 8 | 8 | 2 | 2 | 4 |
Matrix representation of C20.26Q16 ►in GL4(𝔽41) generated by
| 9 | 9 | 0 | 0 |
| 4 | 13 | 0 | 0 |
| 0 | 0 | 9 | 0 |
| 0 | 0 | 0 | 9 |
| 28 | 31 | 0 | 0 |
| 26 | 13 | 0 | 0 |
| 0 | 0 | 0 | 39 |
| 0 | 0 | 25 | 31 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 20 | 11 |
| 0 | 0 | 12 | 21 |
G:=sub<GL(4,GF(41))| [9,4,0,0,9,13,0,0,0,0,9,0,0,0,0,9],[28,26,0,0,31,13,0,0,0,0,0,25,0,0,39,31],[1,0,0,0,0,1,0,0,0,0,20,12,0,0,11,21] >;
C20.26Q16 in GAP, Magma, Sage, TeX
C_{20}._{26}Q_{16} % in TeX
G:=Group("C20.26Q16"); // GroupNames label
G:=SmallGroup(320,93);
// by ID
G=gap.SmallGroup(320,93);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,141,232,100,1123,570,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=a^10*b^4,b*a*b^-1=a^9,a*c=c*a,c*b*c^-1=a^5*b^-1>;
// generators/relations