metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20⋊4(C4⋊C4), C4⋊Dic5⋊19C4, C10.87(C4×D4), C2.3(C20⋊Q8), C10.29(C4×Q8), (C2×C20).17Q8, (C2×C20).136D4, C10.19(C4⋊Q8), C22.19(Q8×D5), C4⋊1(C10.D4), C2.3(C20⋊2D4), (C2×Dic5).21Q8, (C2×C4).28Dic10, C22.105(D4×D5), C10.88(C4⋊D4), C2.1(D10⋊3Q8), (C2×Dic5).152D4, (C22×C4).331D10, C10.69(C22⋊Q8), C2.3(C4.Dic10), C2.17(D20⋊8C4), C10.16(C42.C2), C22.26(C2×Dic10), C23.287(C22×D5), C2.10(Dic5⋊3Q8), C22.52(D4⋊2D5), (C22×C20).140C22, (C22×C10).337C23, C5⋊5(C23.65C23), C22.21(Q8⋊2D5), C10.10C42.15C2, (C22×Dic5).49C22, (C10×C4⋊C4).9C2, C10.58(C2×C4⋊C4), (C2×C4⋊C4).11D5, (C2×C4).77(C4×D5), (C2×C4×Dic5).3C2, (C2×C10).73(C2×Q8), C22.131(C2×C4×D5), (C2×C20).253(C2×C4), (C2×C10).327(C2×D4), (C2×C4⋊Dic5).32C2, C22.61(C2×C5⋊D4), (C2×C4).183(C5⋊D4), (C2×Dic5).30(C2×C4), C2.10(C2×C10.D4), (C2×C10).186(C4○D4), (C2×C10).214(C22×C4), (C2×C10.D4).13C2, SmallGroup(320,600)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20⋊4(C4⋊C4)
G = < a,b,c | a20=b4=c4=1, bab-1=a-1, cac-1=a11, cbc-1=b-1 >
Subgroups: 510 in 170 conjugacy classes, 83 normal (41 characteristic)
C1, C2, C4, C4, C22, C5, C2×C4, C2×C4, C23, C10, C42, C4⋊C4, C22×C4, C22×C4, C22×C4, Dic5, C20, C20, C2×C10, C2.C42, C2×C42, C2×C4⋊C4, C2×C4⋊C4, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×C10, C23.65C23, C4×Dic5, C10.D4, C4⋊Dic5, C5×C4⋊C4, C22×Dic5, C22×Dic5, C22×C20, C22×C20, C10.10C42, C2×C4×Dic5, C2×C10.D4, C2×C4⋊Dic5, C10×C4⋊C4, C20⋊4(C4⋊C4)
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D5, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, D10, C2×C4⋊C4, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C42.C2, C4⋊Q8, Dic10, C4×D5, C5⋊D4, C22×D5, C23.65C23, C10.D4, C2×Dic10, C2×C4×D5, D4×D5, D4⋊2D5, Q8×D5, Q8⋊2D5, C2×C5⋊D4, Dic5⋊3Q8, C20⋊Q8, C4.Dic10, D20⋊8C4, C2×C10.D4, C20⋊2D4, D10⋊3Q8, C20⋊4(C4⋊C4)
►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)
(1 102 294 77)(2 101 295 76)(3 120 296 75)(4 119 297 74)(5 118 298 73)(6 117 299 72)(7 116 300 71)(8 115 281 70)(9 114 282 69)(10 113 283 68)(11 112 284 67)(12 111 285 66)(13 110 286 65)(14 109 287 64)(15 108 288 63)(16 107 289 62)(17 106 290 61)(18 105 291 80)(19 104 292 79)(20 103 293 78)(21 88 191 255)(22 87 192 254)(23 86 193 253)(24 85 194 252)(25 84 195 251)(26 83 196 250)(27 82 197 249)(28 81 198 248)(29 100 199 247)(30 99 200 246)(31 98 181 245)(32 97 182 244)(33 96 183 243)(34 95 184 242)(35 94 185 241)(36 93 186 260)(37 92 187 259)(38 91 188 258)(39 90 189 257)(40 89 190 256)(41 208 280 169)(42 207 261 168)(43 206 262 167)(44 205 263 166)(45 204 264 165)(46 203 265 164)(47 202 266 163)(48 201 267 162)(49 220 268 161)(50 219 269 180)(51 218 270 179)(52 217 271 178)(53 216 272 177)(54 215 273 176)(55 214 274 175)(56 213 275 174)(57 212 276 173)(58 211 277 172)(59 210 278 171)(60 209 279 170)(121 237 304 157)(122 236 305 156)(123 235 306 155)(124 234 307 154)(125 233 308 153)(126 232 309 152)(127 231 310 151)(128 230 311 150)(129 229 312 149)(130 228 313 148)(131 227 314 147)(132 226 315 146)(133 225 316 145)(134 224 317 144)(135 223 318 143)(136 222 319 142)(137 221 320 141)(138 240 301 160)(139 239 302 159)(140 238 303 158)
(1 181 158 54)(2 192 159 45)(3 183 160 56)(4 194 141 47)(5 185 142 58)(6 196 143 49)(7 187 144 60)(8 198 145 51)(9 189 146 42)(10 200 147 53)(11 191 148 44)(12 182 149 55)(13 193 150 46)(14 184 151 57)(15 195 152 48)(16 186 153 59)(17 197 154 50)(18 188 155 41)(19 199 156 52)(20 190 157 43)(21 228 263 284)(22 239 264 295)(23 230 265 286)(24 221 266 297)(25 232 267 288)(26 223 268 299)(27 234 269 290)(28 225 270 281)(29 236 271 292)(30 227 272 283)(31 238 273 294)(32 229 274 285)(33 240 275 296)(34 231 276 287)(35 222 277 298)(36 233 278 289)(37 224 279 300)(38 235 280 291)(39 226 261 282)(40 237 262 293)(61 249 307 219)(62 260 308 210)(63 251 309 201)(64 242 310 212)(65 253 311 203)(66 244 312 214)(67 255 313 205)(68 246 314 216)(69 257 315 207)(70 248 316 218)(71 259 317 209)(72 250 318 220)(73 241 319 211)(74 252 320 202)(75 243 301 213)(76 254 302 204)(77 245 303 215)(78 256 304 206)(79 247 305 217)(80 258 306 208)(81 133 179 115)(82 124 180 106)(83 135 161 117)(84 126 162 108)(85 137 163 119)(86 128 164 110)(87 139 165 101)(88 130 166 112)(89 121 167 103)(90 132 168 114)(91 123 169 105)(92 134 170 116)(93 125 171 107)(94 136 172 118)(95 127 173 109)(96 138 174 120)(97 129 175 111)(98 140 176 102)(99 131 177 113)(100 122 178 104)
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), (1,102,294,77)(2,101,295,76)(3,120,296,75)(4,119,297,74)(5,118,298,73)(6,117,299,72)(7,116,300,71)(8,115,281,70)(9,114,282,69)(10,113,283,68)(11,112,284,67)(12,111,285,66)(13,110,286,65)(14,109,287,64)(15,108,288,63)(16,107,289,62)(17,106,290,61)(18,105,291,80)(19,104,292,79)(20,103,293,78)(21,88,191,255)(22,87,192,254)(23,86,193,253)(24,85,194,252)(25,84,195,251)(26,83,196,250)(27,82,197,249)(28,81,198,248)(29,100,199,247)(30,99,200,246)(31,98,181,245)(32,97,182,244)(33,96,183,243)(34,95,184,242)(35,94,185,241)(36,93,186,260)(37,92,187,259)(38,91,188,258)(39,90,189,257)(40,89,190,256)(41,208,280,169)(42,207,261,168)(43,206,262,167)(44,205,263,166)(45,204,264,165)(46,203,265,164)(47,202,266,163)(48,201,267,162)(49,220,268,161)(50,219,269,180)(51,218,270,179)(52,217,271,178)(53,216,272,177)(54,215,273,176)(55,214,274,175)(56,213,275,174)(57,212,276,173)(58,211,277,172)(59,210,278,171)(60,209,279,170)(121,237,304,157)(122,236,305,156)(123,235,306,155)(124,234,307,154)(125,233,308,153)(126,232,309,152)(127,231,310,151)(128,230,311,150)(129,229,312,149)(130,228,313,148)(131,227,314,147)(132,226,315,146)(133,225,316,145)(134,224,317,144)(135,223,318,143)(136,222,319,142)(137,221,320,141)(138,240,301,160)(139,239,302,159)(140,238,303,158), (1,181,158,54)(2,192,159,45)(3,183,160,56)(4,194,141,47)(5,185,142,58)(6,196,143,49)(7,187,144,60)(8,198,145,51)(9,189,146,42)(10,200,147,53)(11,191,148,44)(12,182,149,55)(13,193,150,46)(14,184,151,57)(15,195,152,48)(16,186,153,59)(17,197,154,50)(18,188,155,41)(19,199,156,52)(20,190,157,43)(21,228,263,284)(22,239,264,295)(23,230,265,286)(24,221,266,297)(25,232,267,288)(26,223,268,299)(27,234,269,290)(28,225,270,281)(29,236,271,292)(30,227,272,283)(31,238,273,294)(32,229,274,285)(33,240,275,296)(34,231,276,287)(35,222,277,298)(36,233,278,289)(37,224,279,300)(38,235,280,291)(39,226,261,282)(40,237,262,293)(61,249,307,219)(62,260,308,210)(63,251,309,201)(64,242,310,212)(65,253,311,203)(66,244,312,214)(67,255,313,205)(68,246,314,216)(69,257,315,207)(70,248,316,218)(71,259,317,209)(72,250,318,220)(73,241,319,211)(74,252,320,202)(75,243,301,213)(76,254,302,204)(77,245,303,215)(78,256,304,206)(79,247,305,217)(80,258,306,208)(81,133,179,115)(82,124,180,106)(83,135,161,117)(84,126,162,108)(85,137,163,119)(86,128,164,110)(87,139,165,101)(88,130,166,112)(89,121,167,103)(90,132,168,114)(91,123,169,105)(92,134,170,116)(93,125,171,107)(94,136,172,118)(95,127,173,109)(96,138,174,120)(97,129,175,111)(98,140,176,102)(99,131,177,113)(100,122,178,104)>;
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), (1,102,294,77)(2,101,295,76)(3,120,296,75)(4,119,297,74)(5,118,298,73)(6,117,299,72)(7,116,300,71)(8,115,281,70)(9,114,282,69)(10,113,283,68)(11,112,284,67)(12,111,285,66)(13,110,286,65)(14,109,287,64)(15,108,288,63)(16,107,289,62)(17,106,290,61)(18,105,291,80)(19,104,292,79)(20,103,293,78)(21,88,191,255)(22,87,192,254)(23,86,193,253)(24,85,194,252)(25,84,195,251)(26,83,196,250)(27,82,197,249)(28,81,198,248)(29,100,199,247)(30,99,200,246)(31,98,181,245)(32,97,182,244)(33,96,183,243)(34,95,184,242)(35,94,185,241)(36,93,186,260)(37,92,187,259)(38,91,188,258)(39,90,189,257)(40,89,190,256)(41,208,280,169)(42,207,261,168)(43,206,262,167)(44,205,263,166)(45,204,264,165)(46,203,265,164)(47,202,266,163)(48,201,267,162)(49,220,268,161)(50,219,269,180)(51,218,270,179)(52,217,271,178)(53,216,272,177)(54,215,273,176)(55,214,274,175)(56,213,275,174)(57,212,276,173)(58,211,277,172)(59,210,278,171)(60,209,279,170)(121,237,304,157)(122,236,305,156)(123,235,306,155)(124,234,307,154)(125,233,308,153)(126,232,309,152)(127,231,310,151)(128,230,311,150)(129,229,312,149)(130,228,313,148)(131,227,314,147)(132,226,315,146)(133,225,316,145)(134,224,317,144)(135,223,318,143)(136,222,319,142)(137,221,320,141)(138,240,301,160)(139,239,302,159)(140,238,303,158), (1,181,158,54)(2,192,159,45)(3,183,160,56)(4,194,141,47)(5,185,142,58)(6,196,143,49)(7,187,144,60)(8,198,145,51)(9,189,146,42)(10,200,147,53)(11,191,148,44)(12,182,149,55)(13,193,150,46)(14,184,151,57)(15,195,152,48)(16,186,153,59)(17,197,154,50)(18,188,155,41)(19,199,156,52)(20,190,157,43)(21,228,263,284)(22,239,264,295)(23,230,265,286)(24,221,266,297)(25,232,267,288)(26,223,268,299)(27,234,269,290)(28,225,270,281)(29,236,271,292)(30,227,272,283)(31,238,273,294)(32,229,274,285)(33,240,275,296)(34,231,276,287)(35,222,277,298)(36,233,278,289)(37,224,279,300)(38,235,280,291)(39,226,261,282)(40,237,262,293)(61,249,307,219)(62,260,308,210)(63,251,309,201)(64,242,310,212)(65,253,311,203)(66,244,312,214)(67,255,313,205)(68,246,314,216)(69,257,315,207)(70,248,316,218)(71,259,317,209)(72,250,318,220)(73,241,319,211)(74,252,320,202)(75,243,301,213)(76,254,302,204)(77,245,303,215)(78,256,304,206)(79,247,305,217)(80,258,306,208)(81,133,179,115)(82,124,180,106)(83,135,161,117)(84,126,162,108)(85,137,163,119)(86,128,164,110)(87,139,165,101)(88,130,166,112)(89,121,167,103)(90,132,168,114)(91,123,169,105)(92,134,170,116)(93,125,171,107)(94,136,172,118)(95,127,173,109)(96,138,174,120)(97,129,175,111)(98,140,176,102)(99,131,177,113)(100,122,178,104) );
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)], [(1,102,294,77),(2,101,295,76),(3,120,296,75),(4,119,297,74),(5,118,298,73),(6,117,299,72),(7,116,300,71),(8,115,281,70),(9,114,282,69),(10,113,283,68),(11,112,284,67),(12,111,285,66),(13,110,286,65),(14,109,287,64),(15,108,288,63),(16,107,289,62),(17,106,290,61),(18,105,291,80),(19,104,292,79),(20,103,293,78),(21,88,191,255),(22,87,192,254),(23,86,193,253),(24,85,194,252),(25,84,195,251),(26,83,196,250),(27,82,197,249),(28,81,198,248),(29,100,199,247),(30,99,200,246),(31,98,181,245),(32,97,182,244),(33,96,183,243),(34,95,184,242),(35,94,185,241),(36,93,186,260),(37,92,187,259),(38,91,188,258),(39,90,189,257),(40,89,190,256),(41,208,280,169),(42,207,261,168),(43,206,262,167),(44,205,263,166),(45,204,264,165),(46,203,265,164),(47,202,266,163),(48,201,267,162),(49,220,268,161),(50,219,269,180),(51,218,270,179),(52,217,271,178),(53,216,272,177),(54,215,273,176),(55,214,274,175),(56,213,275,174),(57,212,276,173),(58,211,277,172),(59,210,278,171),(60,209,279,170),(121,237,304,157),(122,236,305,156),(123,235,306,155),(124,234,307,154),(125,233,308,153),(126,232,309,152),(127,231,310,151),(128,230,311,150),(129,229,312,149),(130,228,313,148),(131,227,314,147),(132,226,315,146),(133,225,316,145),(134,224,317,144),(135,223,318,143),(136,222,319,142),(137,221,320,141),(138,240,301,160),(139,239,302,159),(140,238,303,158)], [(1,181,158,54),(2,192,159,45),(3,183,160,56),(4,194,141,47),(5,185,142,58),(6,196,143,49),(7,187,144,60),(8,198,145,51),(9,189,146,42),(10,200,147,53),(11,191,148,44),(12,182,149,55),(13,193,150,46),(14,184,151,57),(15,195,152,48),(16,186,153,59),(17,197,154,50),(18,188,155,41),(19,199,156,52),(20,190,157,43),(21,228,263,284),(22,239,264,295),(23,230,265,286),(24,221,266,297),(25,232,267,288),(26,223,268,299),(27,234,269,290),(28,225,270,281),(29,236,271,292),(30,227,272,283),(31,238,273,294),(32,229,274,285),(33,240,275,296),(34,231,276,287),(35,222,277,298),(36,233,278,289),(37,224,279,300),(38,235,280,291),(39,226,261,282),(40,237,262,293),(61,249,307,219),(62,260,308,210),(63,251,309,201),(64,242,310,212),(65,253,311,203),(66,244,312,214),(67,255,313,205),(68,246,314,216),(69,257,315,207),(70,248,316,218),(71,259,317,209),(72,250,318,220),(73,241,319,211),(74,252,320,202),(75,243,301,213),(76,254,302,204),(77,245,303,215),(78,256,304,206),(79,247,305,217),(80,258,306,208),(81,133,179,115),(82,124,180,106),(83,135,161,117),(84,126,162,108),(85,137,163,119),(86,128,164,110),(87,139,165,101),(88,130,166,112),(89,121,167,103),(90,132,168,114),(91,123,169,105),(92,134,170,116),(93,125,171,107),(94,136,172,118),(95,127,173,109),(96,138,174,120),(97,129,175,111),(98,140,176,102),(99,131,177,113),(100,122,178,104)]])
68 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 4Q | 4R | 4S | 4T | 5A | 5B | 10A | ··· | 10N | 20A | ··· | 20X |
| order | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 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 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | - | + | + | - | + | - | - | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | Q8 | D4 | Q8 | D5 | C4○D4 | D10 | Dic10 | C4×D5 | C5⋊D4 | D4×D5 | D4⋊2D5 | Q8×D5 | Q8⋊2D5 |
| kernel | C20⋊4(C4⋊C4) | C10.10C42 | C2×C4×Dic5 | C2×C10.D4 | C2×C4⋊Dic5 | C10×C4⋊C4 | C4⋊Dic5 | C2×Dic5 | C2×Dic5 | C2×C20 | C2×C20 | C2×C4⋊C4 | C2×C10 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C22 | C22 | C22 | C22 |
| # reps | 1 | 2 | 1 | 2 | 1 | 1 | 8 | 2 | 2 | 2 | 2 | 2 | 4 | 6 | 8 | 8 | 8 | 2 | 2 | 2 | 2 |
Matrix representation of C20⋊4(C4⋊C4) ►in GL6(𝔽41)
| 39 | 1 | 0 | 0 | 0 | 0 |
| 36 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 | 0 |
| 0 | 0 | 0 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 1 |
| 0 | 0 | 0 | 0 | 5 | 1 |
| 18 | 11 | 0 | 0 | 0 | 0 |
| 4 | 23 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 9 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 19 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 9 | 1 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 9 |
| 0 | 0 | 0 | 0 | 4 | 39 |
G:=sub<GL(6,GF(41))| [39,36,0,0,0,0,1,2,0,0,0,0,0,0,32,0,0,0,0,0,0,9,0,0,0,0,0,0,6,5,0,0,0,0,1,1],[18,4,0,0,0,0,11,23,0,0,0,0,0,0,0,32,0,0,0,0,9,0,0,0,0,0,0,0,0,28,0,0,0,0,19,0],[9,0,0,0,0,0,1,32,0,0,0,0,0,0,0,40,0,0,0,0,1,0,0,0,0,0,0,0,2,4,0,0,0,0,9,39] >;
C20⋊4(C4⋊C4) in GAP, Magma, Sage, TeX
C_{20}\rtimes_4(C_4\rtimes C_4) % in TeX
G:=Group("C20:4(C4:C4)"); // GroupNames label
G:=SmallGroup(320,600);
// by ID
G=gap.SmallGroup(320,600);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,120,254,219,184,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^4=c^4=1,b*a*b^-1=a^-1,c*a*c^-1=a^11,c*b*c^-1=b^-1>;
// generators/relations