metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20⋊7(C4⋊C4), C4⋊Dic5⋊16C4, (C2×C4).65D20, C10.45(C4×D4), C2.18(C4×D20), C10.6(C4⋊Q8), C10.17(C4×Q8), (C2×C20).52Q8, (C2×C20).469D4, (C2×C42).13D5, C4⋊3(C10.D4), C2.1(C20⋊7D4), C2.1(C20⋊2Q8), (C2×C4).40Dic10, C2.10(C4×Dic10), C22.33(C2×D20), C10.55(C4⋊D4), (C22×C4).394D10, C10.52(C22⋊Q8), C10.2(C42.C2), C2.1(C20.6Q8), C2.1(C20.48D4), C22.39(C4○D20), C22.16(C2×Dic10), C23.261(C22×D5), C10.10C42.9C2, (C22×C20).469C22, (C22×C10).303C23, C5⋊3(C23.65C23), (C22×Dic5).26C22, (C2×C4×C20).9C2, C10.47(C2×C4⋊C4), (C2×C4).108(C4×D5), (C2×C10).23(C2×Q8), C22.116(C2×C4×D5), (C2×C20).396(C2×C4), (C2×C10).423(C2×D4), (C2×C4⋊Dic5).14C2, C2.4(C2×C10.D4), C22.38(C2×C5⋊D4), (C2×C10).64(C4○D4), (C2×C4).237(C5⋊D4), (C2×Dic5).26(C2×C4), (C2×C10).194(C22×C4), (C2×C10.D4).11C2, SmallGroup(320,555)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20⋊7(C4⋊C4)
G = < a,b,c | a20=b4=c4=1, bab-1=a-1, ac=ca, cbc-1=b-1 >
Subgroups: 510 in 170 conjugacy classes, 87 normal (43 characteristic)
C1, C2, C4, C4, C22, C5, C2×C4, C2×C4, C23, C10, C42, C4⋊C4, C22×C4, C22×C4, Dic5, C20, C20, C2×C10, C2.C42, C2×C42, C2×C4⋊C4, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×C10, C23.65C23, C10.D4, C4⋊Dic5, C4⋊Dic5, C4×C20, C22×Dic5, C22×C20, C10.10C42, C2×C10.D4, C2×C4⋊Dic5, C2×C4×C20, C20⋊7(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, D20, C5⋊D4, C22×D5, C23.65C23, C10.D4, C2×Dic10, C2×C4×D5, C2×D20, C4○D20, C2×C5⋊D4, C4×Dic10, C20⋊2Q8, C20.6Q8, C4×D20, C2×C10.D4, C20.48D4, C20⋊7D4, C20⋊7(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)
(1 220 62 150)(2 219 63 149)(3 218 64 148)(4 217 65 147)(5 216 66 146)(6 215 67 145)(7 214 68 144)(8 213 69 143)(9 212 70 142)(10 211 71 141)(11 210 72 160)(12 209 73 159)(13 208 74 158)(14 207 75 157)(15 206 76 156)(16 205 77 155)(17 204 78 154)(18 203 79 153)(19 202 80 152)(20 201 61 151)(21 49 175 292)(22 48 176 291)(23 47 177 290)(24 46 178 289)(25 45 179 288)(26 44 180 287)(27 43 161 286)(28 42 162 285)(29 41 163 284)(30 60 164 283)(31 59 165 282)(32 58 166 281)(33 57 167 300)(34 56 168 299)(35 55 169 298)(36 54 170 297)(37 53 171 296)(38 52 172 295)(39 51 173 294)(40 50 174 293)(81 190 312 274)(82 189 313 273)(83 188 314 272)(84 187 315 271)(85 186 316 270)(86 185 317 269)(87 184 318 268)(88 183 319 267)(89 182 320 266)(90 181 301 265)(91 200 302 264)(92 199 303 263)(93 198 304 262)(94 197 305 261)(95 196 306 280)(96 195 307 279)(97 194 308 278)(98 193 309 277)(99 192 310 276)(100 191 311 275)(101 225 121 251)(102 224 122 250)(103 223 123 249)(104 222 124 248)(105 221 125 247)(106 240 126 246)(107 239 127 245)(108 238 128 244)(109 237 129 243)(110 236 130 242)(111 235 131 241)(112 234 132 260)(113 233 133 259)(114 232 134 258)(115 231 135 257)(116 230 136 256)(117 229 137 255)(118 228 138 254)(119 227 139 253)(120 226 140 252)
(1 129 98 289)(2 130 99 290)(3 131 100 291)(4 132 81 292)(5 133 82 293)(6 134 83 294)(7 135 84 295)(8 136 85 296)(9 137 86 297)(10 138 87 298)(11 139 88 299)(12 140 89 300)(13 121 90 281)(14 122 91 282)(15 123 92 283)(16 124 93 284)(17 125 94 285)(18 126 95 286)(19 127 96 287)(20 128 97 288)(21 147 260 274)(22 148 241 275)(23 149 242 276)(24 150 243 277)(25 151 244 278)(26 152 245 279)(27 153 246 280)(28 154 247 261)(29 155 248 262)(30 156 249 263)(31 157 250 264)(32 158 251 265)(33 159 252 266)(34 160 253 267)(35 141 254 268)(36 142 255 269)(37 143 256 270)(38 144 257 271)(39 145 258 272)(40 146 259 273)(41 77 104 304)(42 78 105 305)(43 79 106 306)(44 80 107 307)(45 61 108 308)(46 62 109 309)(47 63 110 310)(48 64 111 311)(49 65 112 312)(50 66 113 313)(51 67 114 314)(52 68 115 315)(53 69 116 316)(54 70 117 317)(55 71 118 318)(56 72 119 319)(57 73 120 320)(58 74 101 301)(59 75 102 302)(60 76 103 303)(161 203 240 196)(162 204 221 197)(163 205 222 198)(164 206 223 199)(165 207 224 200)(166 208 225 181)(167 209 226 182)(168 210 227 183)(169 211 228 184)(170 212 229 185)(171 213 230 186)(172 214 231 187)(173 215 232 188)(174 216 233 189)(175 217 234 190)(176 218 235 191)(177 219 236 192)(178 220 237 193)(179 201 238 194)(180 202 239 195)
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), (1,220,62,150)(2,219,63,149)(3,218,64,148)(4,217,65,147)(5,216,66,146)(6,215,67,145)(7,214,68,144)(8,213,69,143)(9,212,70,142)(10,211,71,141)(11,210,72,160)(12,209,73,159)(13,208,74,158)(14,207,75,157)(15,206,76,156)(16,205,77,155)(17,204,78,154)(18,203,79,153)(19,202,80,152)(20,201,61,151)(21,49,175,292)(22,48,176,291)(23,47,177,290)(24,46,178,289)(25,45,179,288)(26,44,180,287)(27,43,161,286)(28,42,162,285)(29,41,163,284)(30,60,164,283)(31,59,165,282)(32,58,166,281)(33,57,167,300)(34,56,168,299)(35,55,169,298)(36,54,170,297)(37,53,171,296)(38,52,172,295)(39,51,173,294)(40,50,174,293)(81,190,312,274)(82,189,313,273)(83,188,314,272)(84,187,315,271)(85,186,316,270)(86,185,317,269)(87,184,318,268)(88,183,319,267)(89,182,320,266)(90,181,301,265)(91,200,302,264)(92,199,303,263)(93,198,304,262)(94,197,305,261)(95,196,306,280)(96,195,307,279)(97,194,308,278)(98,193,309,277)(99,192,310,276)(100,191,311,275)(101,225,121,251)(102,224,122,250)(103,223,123,249)(104,222,124,248)(105,221,125,247)(106,240,126,246)(107,239,127,245)(108,238,128,244)(109,237,129,243)(110,236,130,242)(111,235,131,241)(112,234,132,260)(113,233,133,259)(114,232,134,258)(115,231,135,257)(116,230,136,256)(117,229,137,255)(118,228,138,254)(119,227,139,253)(120,226,140,252), (1,129,98,289)(2,130,99,290)(3,131,100,291)(4,132,81,292)(5,133,82,293)(6,134,83,294)(7,135,84,295)(8,136,85,296)(9,137,86,297)(10,138,87,298)(11,139,88,299)(12,140,89,300)(13,121,90,281)(14,122,91,282)(15,123,92,283)(16,124,93,284)(17,125,94,285)(18,126,95,286)(19,127,96,287)(20,128,97,288)(21,147,260,274)(22,148,241,275)(23,149,242,276)(24,150,243,277)(25,151,244,278)(26,152,245,279)(27,153,246,280)(28,154,247,261)(29,155,248,262)(30,156,249,263)(31,157,250,264)(32,158,251,265)(33,159,252,266)(34,160,253,267)(35,141,254,268)(36,142,255,269)(37,143,256,270)(38,144,257,271)(39,145,258,272)(40,146,259,273)(41,77,104,304)(42,78,105,305)(43,79,106,306)(44,80,107,307)(45,61,108,308)(46,62,109,309)(47,63,110,310)(48,64,111,311)(49,65,112,312)(50,66,113,313)(51,67,114,314)(52,68,115,315)(53,69,116,316)(54,70,117,317)(55,71,118,318)(56,72,119,319)(57,73,120,320)(58,74,101,301)(59,75,102,302)(60,76,103,303)(161,203,240,196)(162,204,221,197)(163,205,222,198)(164,206,223,199)(165,207,224,200)(166,208,225,181)(167,209,226,182)(168,210,227,183)(169,211,228,184)(170,212,229,185)(171,213,230,186)(172,214,231,187)(173,215,232,188)(174,216,233,189)(175,217,234,190)(176,218,235,191)(177,219,236,192)(178,220,237,193)(179,201,238,194)(180,202,239,195)>;
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), (1,220,62,150)(2,219,63,149)(3,218,64,148)(4,217,65,147)(5,216,66,146)(6,215,67,145)(7,214,68,144)(8,213,69,143)(9,212,70,142)(10,211,71,141)(11,210,72,160)(12,209,73,159)(13,208,74,158)(14,207,75,157)(15,206,76,156)(16,205,77,155)(17,204,78,154)(18,203,79,153)(19,202,80,152)(20,201,61,151)(21,49,175,292)(22,48,176,291)(23,47,177,290)(24,46,178,289)(25,45,179,288)(26,44,180,287)(27,43,161,286)(28,42,162,285)(29,41,163,284)(30,60,164,283)(31,59,165,282)(32,58,166,281)(33,57,167,300)(34,56,168,299)(35,55,169,298)(36,54,170,297)(37,53,171,296)(38,52,172,295)(39,51,173,294)(40,50,174,293)(81,190,312,274)(82,189,313,273)(83,188,314,272)(84,187,315,271)(85,186,316,270)(86,185,317,269)(87,184,318,268)(88,183,319,267)(89,182,320,266)(90,181,301,265)(91,200,302,264)(92,199,303,263)(93,198,304,262)(94,197,305,261)(95,196,306,280)(96,195,307,279)(97,194,308,278)(98,193,309,277)(99,192,310,276)(100,191,311,275)(101,225,121,251)(102,224,122,250)(103,223,123,249)(104,222,124,248)(105,221,125,247)(106,240,126,246)(107,239,127,245)(108,238,128,244)(109,237,129,243)(110,236,130,242)(111,235,131,241)(112,234,132,260)(113,233,133,259)(114,232,134,258)(115,231,135,257)(116,230,136,256)(117,229,137,255)(118,228,138,254)(119,227,139,253)(120,226,140,252), (1,129,98,289)(2,130,99,290)(3,131,100,291)(4,132,81,292)(5,133,82,293)(6,134,83,294)(7,135,84,295)(8,136,85,296)(9,137,86,297)(10,138,87,298)(11,139,88,299)(12,140,89,300)(13,121,90,281)(14,122,91,282)(15,123,92,283)(16,124,93,284)(17,125,94,285)(18,126,95,286)(19,127,96,287)(20,128,97,288)(21,147,260,274)(22,148,241,275)(23,149,242,276)(24,150,243,277)(25,151,244,278)(26,152,245,279)(27,153,246,280)(28,154,247,261)(29,155,248,262)(30,156,249,263)(31,157,250,264)(32,158,251,265)(33,159,252,266)(34,160,253,267)(35,141,254,268)(36,142,255,269)(37,143,256,270)(38,144,257,271)(39,145,258,272)(40,146,259,273)(41,77,104,304)(42,78,105,305)(43,79,106,306)(44,80,107,307)(45,61,108,308)(46,62,109,309)(47,63,110,310)(48,64,111,311)(49,65,112,312)(50,66,113,313)(51,67,114,314)(52,68,115,315)(53,69,116,316)(54,70,117,317)(55,71,118,318)(56,72,119,319)(57,73,120,320)(58,74,101,301)(59,75,102,302)(60,76,103,303)(161,203,240,196)(162,204,221,197)(163,205,222,198)(164,206,223,199)(165,207,224,200)(166,208,225,181)(167,209,226,182)(168,210,227,183)(169,211,228,184)(170,212,229,185)(171,213,230,186)(172,214,231,187)(173,215,232,188)(174,216,233,189)(175,217,234,190)(176,218,235,191)(177,219,236,192)(178,220,237,193)(179,201,238,194)(180,202,239,195) );
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)], [(1,220,62,150),(2,219,63,149),(3,218,64,148),(4,217,65,147),(5,216,66,146),(6,215,67,145),(7,214,68,144),(8,213,69,143),(9,212,70,142),(10,211,71,141),(11,210,72,160),(12,209,73,159),(13,208,74,158),(14,207,75,157),(15,206,76,156),(16,205,77,155),(17,204,78,154),(18,203,79,153),(19,202,80,152),(20,201,61,151),(21,49,175,292),(22,48,176,291),(23,47,177,290),(24,46,178,289),(25,45,179,288),(26,44,180,287),(27,43,161,286),(28,42,162,285),(29,41,163,284),(30,60,164,283),(31,59,165,282),(32,58,166,281),(33,57,167,300),(34,56,168,299),(35,55,169,298),(36,54,170,297),(37,53,171,296),(38,52,172,295),(39,51,173,294),(40,50,174,293),(81,190,312,274),(82,189,313,273),(83,188,314,272),(84,187,315,271),(85,186,316,270),(86,185,317,269),(87,184,318,268),(88,183,319,267),(89,182,320,266),(90,181,301,265),(91,200,302,264),(92,199,303,263),(93,198,304,262),(94,197,305,261),(95,196,306,280),(96,195,307,279),(97,194,308,278),(98,193,309,277),(99,192,310,276),(100,191,311,275),(101,225,121,251),(102,224,122,250),(103,223,123,249),(104,222,124,248),(105,221,125,247),(106,240,126,246),(107,239,127,245),(108,238,128,244),(109,237,129,243),(110,236,130,242),(111,235,131,241),(112,234,132,260),(113,233,133,259),(114,232,134,258),(115,231,135,257),(116,230,136,256),(117,229,137,255),(118,228,138,254),(119,227,139,253),(120,226,140,252)], [(1,129,98,289),(2,130,99,290),(3,131,100,291),(4,132,81,292),(5,133,82,293),(6,134,83,294),(7,135,84,295),(8,136,85,296),(9,137,86,297),(10,138,87,298),(11,139,88,299),(12,140,89,300),(13,121,90,281),(14,122,91,282),(15,123,92,283),(16,124,93,284),(17,125,94,285),(18,126,95,286),(19,127,96,287),(20,128,97,288),(21,147,260,274),(22,148,241,275),(23,149,242,276),(24,150,243,277),(25,151,244,278),(26,152,245,279),(27,153,246,280),(28,154,247,261),(29,155,248,262),(30,156,249,263),(31,157,250,264),(32,158,251,265),(33,159,252,266),(34,160,253,267),(35,141,254,268),(36,142,255,269),(37,143,256,270),(38,144,257,271),(39,145,258,272),(40,146,259,273),(41,77,104,304),(42,78,105,305),(43,79,106,306),(44,80,107,307),(45,61,108,308),(46,62,109,309),(47,63,110,310),(48,64,111,311),(49,65,112,312),(50,66,113,313),(51,67,114,314),(52,68,115,315),(53,69,116,316),(54,70,117,317),(55,71,118,318),(56,72,119,319),(57,73,120,320),(58,74,101,301),(59,75,102,302),(60,76,103,303),(161,203,240,196),(162,204,221,197),(163,205,222,198),(164,206,223,199),(165,207,224,200),(166,208,225,181),(167,209,226,182),(168,210,227,183),(169,211,228,184),(170,212,229,185),(171,213,230,186),(172,214,231,187),(173,215,232,188),(174,216,233,189),(175,217,234,190),(176,218,235,191),(177,219,236,192),(178,220,237,193),(179,201,238,194),(180,202,239,195)]])
92 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4L | 4M | ··· | 4T | 5A | 5B | 10A | ··· | 10N | 20A | ··· | 20AV |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
92 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | - | + | + | - | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | Q8 | D5 | C4○D4 | D10 | Dic10 | C4×D5 | D20 | C5⋊D4 | C4○D20 |
| kernel | C20⋊7(C4⋊C4) | C10.10C42 | C2×C10.D4 | C2×C4⋊Dic5 | C2×C4×C20 | C4⋊Dic5 | C2×C20 | C2×C20 | C2×C42 | C2×C10 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C2×C4 | C22 |
| # reps | 1 | 2 | 2 | 2 | 1 | 8 | 4 | 4 | 2 | 4 | 6 | 16 | 8 | 8 | 8 | 16 |
Matrix representation of C20⋊7(C4⋊C4) ►in GL6(𝔽41)
| 34 | 40 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 40 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 11 |
| 0 | 0 | 0 | 0 | 30 | 32 |
| 27 | 11 | 0 | 0 | 0 | 0 |
| 27 | 14 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 32 | 0 | 0 |
| 0 | 0 | 22 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 38 | 17 |
| 0 | 0 | 0 | 0 | 38 | 3 |
| 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 1 | 0 | 0 |
| 0 | 0 | 40 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 9 |
| 0 | 0 | 0 | 0 | 32 | 30 |
G:=sub<GL(6,GF(41))| [34,1,0,0,0,0,40,0,0,0,0,0,0,0,34,1,0,0,0,0,40,0,0,0,0,0,0,0,27,30,0,0,0,0,11,32],[27,27,0,0,0,0,11,14,0,0,0,0,0,0,19,22,0,0,0,0,32,22,0,0,0,0,0,0,38,38,0,0,0,0,17,3],[32,0,0,0,0,0,0,32,0,0,0,0,0,0,24,40,0,0,0,0,1,17,0,0,0,0,0,0,11,32,0,0,0,0,9,30] >;
C20⋊7(C4⋊C4) in GAP, Magma, Sage, TeX
C_{20}\rtimes_7(C_4\rtimes C_4) % in TeX
G:=Group("C20:7(C4:C4)"); // GroupNames label
G:=SmallGroup(320,555);
// by ID
G=gap.SmallGroup(320,555);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,253,120,758,58,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^4=c^4=1,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations