metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20⋊5(C4⋊C4), C2.4(C20⋊Q8), (C2×C20).18Q8, Dic5⋊4(C4⋊C4), C5⋊3(C42⋊9C4), (C4×Dic5)⋊11C4, (C2×C20).138D4, C10.20(C4⋊Q8), C22.22(Q8×D5), C2.2(C20⋊D4), C4⋊2(C10.D4), (C2×Dic5).22Q8, (C2×C4).29Dic10, C22.107(D4×D5), (C22×C4).38D10, C10.14(C4⋊1D4), (C2×Dic5).153D4, C2.3(Dic5⋊Q8), (C22×C20).28C22, C22.27(C2×Dic10), C23.290(C22×D5), (C22×C10).340C23, (C22×Dic5).211C22, C2.20(D5×C4⋊C4), C10.59(C2×C4⋊C4), (C2×C4⋊C4).13D5, (C10×C4⋊C4).12C2, (C2×C4×Dic5).6C2, (C2×C4).152(C4×D5), (C2×C10).76(C2×Q8), C22.133(C2×C4×D5), (C2×C20).256(C2×C4), (C2×C10).329(C2×D4), (C2×C4⋊Dic5).34C2, C22.63(C2×C5⋊D4), (C2×C4).127(C5⋊D4), C2.11(C2×C10.D4), (C2×C10).217(C22×C4), (C2×Dic5).149(C2×C4), (C2×C10.D4).14C2, SmallGroup(320,603)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20⋊5(C4⋊C4)
G = < a,b,c | a20=b4=c4=1, bab-1=a9, cac-1=a11, cbc-1=b-1 >
Subgroups: 558 in 186 conjugacy classes, 95 normal (23 characteristic)
C1, C2, C2, C4, C4, C22, C22, C5, C2×C4, C2×C4, C23, C10, C10, C42, C4⋊C4, C22×C4, C22×C4, C22×C4, Dic5, Dic5, C20, C20, C2×C10, C2×C10, C2×C42, C2×C4⋊C4, C2×C4⋊C4, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×C10, C42⋊9C4, C4×Dic5, C10.D4, C4⋊Dic5, C5×C4⋊C4, C22×Dic5, C22×C20, C22×C20, C2×C4×Dic5, C2×C10.D4, C2×C4⋊Dic5, C10×C4⋊C4, C20⋊5(C4⋊C4)
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D5, C4⋊C4, C22×C4, C2×D4, C2×Q8, D10, C2×C4⋊C4, C4⋊1D4, C4⋊Q8, Dic10, C4×D5, C5⋊D4, C22×D5, C42⋊9C4, C10.D4, C2×Dic10, C2×C4×D5, D4×D5, Q8×D5, C2×C5⋊D4, C20⋊Q8, D5×C4⋊C4, C2×C10.D4, C20⋊D4, Dic5⋊Q8, C20⋊5(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)
(1 242 56 136)(2 251 57 125)(3 260 58 134)(4 249 59 123)(5 258 60 132)(6 247 41 121)(7 256 42 130)(8 245 43 139)(9 254 44 128)(10 243 45 137)(11 252 46 126)(12 241 47 135)(13 250 48 124)(14 259 49 133)(15 248 50 122)(16 257 51 131)(17 246 52 140)(18 255 53 129)(19 244 54 138)(20 253 55 127)(21 152 117 94)(22 141 118 83)(23 150 119 92)(24 159 120 81)(25 148 101 90)(26 157 102 99)(27 146 103 88)(28 155 104 97)(29 144 105 86)(30 153 106 95)(31 142 107 84)(32 151 108 93)(33 160 109 82)(34 149 110 91)(35 158 111 100)(36 147 112 89)(37 156 113 98)(38 145 114 87)(39 154 115 96)(40 143 116 85)(61 262 320 229)(62 271 301 238)(63 280 302 227)(64 269 303 236)(65 278 304 225)(66 267 305 234)(67 276 306 223)(68 265 307 232)(69 274 308 221)(70 263 309 230)(71 272 310 239)(72 261 311 228)(73 270 312 237)(74 279 313 226)(75 268 314 235)(76 277 315 224)(77 266 316 233)(78 275 317 222)(79 264 318 231)(80 273 319 240)(161 204 193 286)(162 213 194 295)(163 202 195 284)(164 211 196 293)(165 220 197 282)(166 209 198 291)(167 218 199 300)(168 207 200 289)(169 216 181 298)(170 205 182 287)(171 214 183 296)(172 203 184 285)(173 212 185 294)(174 201 186 283)(175 210 187 292)(176 219 188 281)(177 208 189 290)(178 217 190 299)(179 206 191 288)(180 215 192 297)
(1 119 221 288)(2 110 222 299)(3 101 223 290)(4 112 224 281)(5 103 225 292)(6 114 226 283)(7 105 227 294)(8 116 228 285)(9 107 229 296)(10 118 230 287)(11 109 231 298)(12 120 232 289)(13 111 233 300)(14 102 234 291)(15 113 235 282)(16 104 236 293)(17 115 237 284)(18 106 238 295)(19 117 239 286)(20 108 240 297)(21 272 204 54)(22 263 205 45)(23 274 206 56)(24 265 207 47)(25 276 208 58)(26 267 209 49)(27 278 210 60)(28 269 211 51)(29 280 212 42)(30 271 213 53)(31 262 214 44)(32 273 215 55)(33 264 216 46)(34 275 217 57)(35 266 218 48)(36 277 219 59)(37 268 220 50)(38 279 201 41)(39 270 202 52)(40 261 203 43)(61 183 254 142)(62 194 255 153)(63 185 256 144)(64 196 257 155)(65 187 258 146)(66 198 259 157)(67 189 260 148)(68 200 241 159)(69 191 242 150)(70 182 243 141)(71 193 244 152)(72 184 245 143)(73 195 246 154)(74 186 247 145)(75 197 248 156)(76 188 249 147)(77 199 250 158)(78 190 251 149)(79 181 252 160)(80 192 253 151)(81 307 168 135)(82 318 169 126)(83 309 170 137)(84 320 171 128)(85 311 172 139)(86 302 173 130)(87 313 174 121)(88 304 175 132)(89 315 176 123)(90 306 177 134)(91 317 178 125)(92 308 179 136)(93 319 180 127)(94 310 161 138)(95 301 162 129)(96 312 163 140)(97 303 164 131)(98 314 165 122)(99 305 166 133)(100 316 167 124)
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), (1,242,56,136)(2,251,57,125)(3,260,58,134)(4,249,59,123)(5,258,60,132)(6,247,41,121)(7,256,42,130)(8,245,43,139)(9,254,44,128)(10,243,45,137)(11,252,46,126)(12,241,47,135)(13,250,48,124)(14,259,49,133)(15,248,50,122)(16,257,51,131)(17,246,52,140)(18,255,53,129)(19,244,54,138)(20,253,55,127)(21,152,117,94)(22,141,118,83)(23,150,119,92)(24,159,120,81)(25,148,101,90)(26,157,102,99)(27,146,103,88)(28,155,104,97)(29,144,105,86)(30,153,106,95)(31,142,107,84)(32,151,108,93)(33,160,109,82)(34,149,110,91)(35,158,111,100)(36,147,112,89)(37,156,113,98)(38,145,114,87)(39,154,115,96)(40,143,116,85)(61,262,320,229)(62,271,301,238)(63,280,302,227)(64,269,303,236)(65,278,304,225)(66,267,305,234)(67,276,306,223)(68,265,307,232)(69,274,308,221)(70,263,309,230)(71,272,310,239)(72,261,311,228)(73,270,312,237)(74,279,313,226)(75,268,314,235)(76,277,315,224)(77,266,316,233)(78,275,317,222)(79,264,318,231)(80,273,319,240)(161,204,193,286)(162,213,194,295)(163,202,195,284)(164,211,196,293)(165,220,197,282)(166,209,198,291)(167,218,199,300)(168,207,200,289)(169,216,181,298)(170,205,182,287)(171,214,183,296)(172,203,184,285)(173,212,185,294)(174,201,186,283)(175,210,187,292)(176,219,188,281)(177,208,189,290)(178,217,190,299)(179,206,191,288)(180,215,192,297), (1,119,221,288)(2,110,222,299)(3,101,223,290)(4,112,224,281)(5,103,225,292)(6,114,226,283)(7,105,227,294)(8,116,228,285)(9,107,229,296)(10,118,230,287)(11,109,231,298)(12,120,232,289)(13,111,233,300)(14,102,234,291)(15,113,235,282)(16,104,236,293)(17,115,237,284)(18,106,238,295)(19,117,239,286)(20,108,240,297)(21,272,204,54)(22,263,205,45)(23,274,206,56)(24,265,207,47)(25,276,208,58)(26,267,209,49)(27,278,210,60)(28,269,211,51)(29,280,212,42)(30,271,213,53)(31,262,214,44)(32,273,215,55)(33,264,216,46)(34,275,217,57)(35,266,218,48)(36,277,219,59)(37,268,220,50)(38,279,201,41)(39,270,202,52)(40,261,203,43)(61,183,254,142)(62,194,255,153)(63,185,256,144)(64,196,257,155)(65,187,258,146)(66,198,259,157)(67,189,260,148)(68,200,241,159)(69,191,242,150)(70,182,243,141)(71,193,244,152)(72,184,245,143)(73,195,246,154)(74,186,247,145)(75,197,248,156)(76,188,249,147)(77,199,250,158)(78,190,251,149)(79,181,252,160)(80,192,253,151)(81,307,168,135)(82,318,169,126)(83,309,170,137)(84,320,171,128)(85,311,172,139)(86,302,173,130)(87,313,174,121)(88,304,175,132)(89,315,176,123)(90,306,177,134)(91,317,178,125)(92,308,179,136)(93,319,180,127)(94,310,161,138)(95,301,162,129)(96,312,163,140)(97,303,164,131)(98,314,165,122)(99,305,166,133)(100,316,167,124)>;
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), (1,242,56,136)(2,251,57,125)(3,260,58,134)(4,249,59,123)(5,258,60,132)(6,247,41,121)(7,256,42,130)(8,245,43,139)(9,254,44,128)(10,243,45,137)(11,252,46,126)(12,241,47,135)(13,250,48,124)(14,259,49,133)(15,248,50,122)(16,257,51,131)(17,246,52,140)(18,255,53,129)(19,244,54,138)(20,253,55,127)(21,152,117,94)(22,141,118,83)(23,150,119,92)(24,159,120,81)(25,148,101,90)(26,157,102,99)(27,146,103,88)(28,155,104,97)(29,144,105,86)(30,153,106,95)(31,142,107,84)(32,151,108,93)(33,160,109,82)(34,149,110,91)(35,158,111,100)(36,147,112,89)(37,156,113,98)(38,145,114,87)(39,154,115,96)(40,143,116,85)(61,262,320,229)(62,271,301,238)(63,280,302,227)(64,269,303,236)(65,278,304,225)(66,267,305,234)(67,276,306,223)(68,265,307,232)(69,274,308,221)(70,263,309,230)(71,272,310,239)(72,261,311,228)(73,270,312,237)(74,279,313,226)(75,268,314,235)(76,277,315,224)(77,266,316,233)(78,275,317,222)(79,264,318,231)(80,273,319,240)(161,204,193,286)(162,213,194,295)(163,202,195,284)(164,211,196,293)(165,220,197,282)(166,209,198,291)(167,218,199,300)(168,207,200,289)(169,216,181,298)(170,205,182,287)(171,214,183,296)(172,203,184,285)(173,212,185,294)(174,201,186,283)(175,210,187,292)(176,219,188,281)(177,208,189,290)(178,217,190,299)(179,206,191,288)(180,215,192,297), (1,119,221,288)(2,110,222,299)(3,101,223,290)(4,112,224,281)(5,103,225,292)(6,114,226,283)(7,105,227,294)(8,116,228,285)(9,107,229,296)(10,118,230,287)(11,109,231,298)(12,120,232,289)(13,111,233,300)(14,102,234,291)(15,113,235,282)(16,104,236,293)(17,115,237,284)(18,106,238,295)(19,117,239,286)(20,108,240,297)(21,272,204,54)(22,263,205,45)(23,274,206,56)(24,265,207,47)(25,276,208,58)(26,267,209,49)(27,278,210,60)(28,269,211,51)(29,280,212,42)(30,271,213,53)(31,262,214,44)(32,273,215,55)(33,264,216,46)(34,275,217,57)(35,266,218,48)(36,277,219,59)(37,268,220,50)(38,279,201,41)(39,270,202,52)(40,261,203,43)(61,183,254,142)(62,194,255,153)(63,185,256,144)(64,196,257,155)(65,187,258,146)(66,198,259,157)(67,189,260,148)(68,200,241,159)(69,191,242,150)(70,182,243,141)(71,193,244,152)(72,184,245,143)(73,195,246,154)(74,186,247,145)(75,197,248,156)(76,188,249,147)(77,199,250,158)(78,190,251,149)(79,181,252,160)(80,192,253,151)(81,307,168,135)(82,318,169,126)(83,309,170,137)(84,320,171,128)(85,311,172,139)(86,302,173,130)(87,313,174,121)(88,304,175,132)(89,315,176,123)(90,306,177,134)(91,317,178,125)(92,308,179,136)(93,319,180,127)(94,310,161,138)(95,301,162,129)(96,312,163,140)(97,303,164,131)(98,314,165,122)(99,305,166,133)(100,316,167,124) );
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)], [(1,242,56,136),(2,251,57,125),(3,260,58,134),(4,249,59,123),(5,258,60,132),(6,247,41,121),(7,256,42,130),(8,245,43,139),(9,254,44,128),(10,243,45,137),(11,252,46,126),(12,241,47,135),(13,250,48,124),(14,259,49,133),(15,248,50,122),(16,257,51,131),(17,246,52,140),(18,255,53,129),(19,244,54,138),(20,253,55,127),(21,152,117,94),(22,141,118,83),(23,150,119,92),(24,159,120,81),(25,148,101,90),(26,157,102,99),(27,146,103,88),(28,155,104,97),(29,144,105,86),(30,153,106,95),(31,142,107,84),(32,151,108,93),(33,160,109,82),(34,149,110,91),(35,158,111,100),(36,147,112,89),(37,156,113,98),(38,145,114,87),(39,154,115,96),(40,143,116,85),(61,262,320,229),(62,271,301,238),(63,280,302,227),(64,269,303,236),(65,278,304,225),(66,267,305,234),(67,276,306,223),(68,265,307,232),(69,274,308,221),(70,263,309,230),(71,272,310,239),(72,261,311,228),(73,270,312,237),(74,279,313,226),(75,268,314,235),(76,277,315,224),(77,266,316,233),(78,275,317,222),(79,264,318,231),(80,273,319,240),(161,204,193,286),(162,213,194,295),(163,202,195,284),(164,211,196,293),(165,220,197,282),(166,209,198,291),(167,218,199,300),(168,207,200,289),(169,216,181,298),(170,205,182,287),(171,214,183,296),(172,203,184,285),(173,212,185,294),(174,201,186,283),(175,210,187,292),(176,219,188,281),(177,208,189,290),(178,217,190,299),(179,206,191,288),(180,215,192,297)], [(1,119,221,288),(2,110,222,299),(3,101,223,290),(4,112,224,281),(5,103,225,292),(6,114,226,283),(7,105,227,294),(8,116,228,285),(9,107,229,296),(10,118,230,287),(11,109,231,298),(12,120,232,289),(13,111,233,300),(14,102,234,291),(15,113,235,282),(16,104,236,293),(17,115,237,284),(18,106,238,295),(19,117,239,286),(20,108,240,297),(21,272,204,54),(22,263,205,45),(23,274,206,56),(24,265,207,47),(25,276,208,58),(26,267,209,49),(27,278,210,60),(28,269,211,51),(29,280,212,42),(30,271,213,53),(31,262,214,44),(32,273,215,55),(33,264,216,46),(34,275,217,57),(35,266,218,48),(36,277,219,59),(37,268,220,50),(38,279,201,41),(39,270,202,52),(40,261,203,43),(61,183,254,142),(62,194,255,153),(63,185,256,144),(64,196,257,155),(65,187,258,146),(66,198,259,157),(67,189,260,148),(68,200,241,159),(69,191,242,150),(70,182,243,141),(71,193,244,152),(72,184,245,143),(73,195,246,154),(74,186,247,145),(75,197,248,156),(76,188,249,147),(77,199,250,158),(78,190,251,149),(79,181,252,160),(80,192,253,151),(81,307,168,135),(82,318,169,126),(83,309,170,137),(84,320,171,128),(85,311,172,139),(86,302,173,130),(87,313,174,121),(88,304,175,132),(89,315,176,123),(90,306,177,134),(91,317,178,125),(92,308,179,136),(93,319,180,127),(94,310,161,138),(95,301,162,129),(96,312,163,140),(97,303,164,131),(98,314,165,122),(99,305,166,133),(100,316,167,124)]])
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 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | - | + | + | - | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | Q8 | D4 | Q8 | D5 | D10 | Dic10 | C4×D5 | C5⋊D4 | D4×D5 | Q8×D5 |
| kernel | C20⋊5(C4⋊C4) | 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 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C22 | C22 |
| # reps | 1 | 1 | 4 | 1 | 1 | 8 | 4 | 4 | 2 | 2 | 2 | 6 | 8 | 8 | 8 | 4 | 4 |
Matrix representation of C20⋊5(C4⋊C4) ►in GL6(𝔽41)
| 35 | 1 | 0 | 0 | 0 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 1 | 0 | 0 |
| 0 | 0 | 33 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 38 |
| 0 | 0 | 0 | 0 | 38 | 21 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 6 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 15 | 0 | 0 |
| 0 | 0 | 2 | 25 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 3 |
| 0 | 0 | 0 | 0 | 3 | 20 |
| 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 28 | 0 | 0 |
| 0 | 0 | 22 | 30 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 40 | 0 |
G:=sub<GL(6,GF(41))| [35,40,0,0,0,0,1,0,0,0,0,0,0,0,34,33,0,0,0,0,1,1,0,0,0,0,0,0,20,38,0,0,0,0,38,21],[1,6,0,0,0,0,0,40,0,0,0,0,0,0,16,2,0,0,0,0,15,25,0,0,0,0,0,0,21,3,0,0,0,0,3,20],[9,0,0,0,0,0,0,9,0,0,0,0,0,0,11,22,0,0,0,0,28,30,0,0,0,0,0,0,0,40,0,0,0,0,1,0] >;
C20⋊5(C4⋊C4) in GAP, Magma, Sage, TeX
C_{20}\rtimes_5(C_4\rtimes C_4) % in TeX
G:=Group("C20:5(C4:C4)"); // GroupNames label
G:=SmallGroup(320,603);
// by ID
G=gap.SmallGroup(320,603);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,232,422,387,58,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^4=c^4=1,b*a*b^-1=a^9,c*a*c^-1=a^11,c*b*c^-1=b^-1>;
// generators/relations