metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic20⋊15C4, C8.9(C4×D5), C40.65(C2×C4), C10.80(C4×D4), C4.Q8.2D5, (C2×C8).58D10, C40⋊8C4.1C2, C4⋊C4.159D10, C5⋊4(Q16⋊C4), C22.82(D4×D5), C20.26(C4○D4), C4.2(Q8⋊2D5), C10.Q16.4C2, (C2×C20).269C23, C20.100(C22×C4), (C2×C40).107C22, Dic10.23(C2×C4), (C2×Dic5).216D4, Dic5⋊3Q8.4C2, (C2×Dic20).13C2, C2.5(SD16⋊D5), C2.10(D20⋊8C4), C10.37(C8.C22), (C4×Dic5).33C22, (C2×Dic10).83C22, C4.41(C2×C4×D5), (C5×C4.Q8).2C2, (C2×C10).274(C2×D4), (C5×C4⋊C4).62C22, (C2×C5⋊2C8).51C22, (C2×C4).372(C22×D5), SmallGroup(320,480)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic20⋊15C4
G = < a,b,c | a40=c4=1, b2=a20, bab-1=a-1, cac-1=a11, cbc-1=a20b >
Subgroups: 358 in 108 conjugacy classes, 49 normal (21 characteristic)
C1, C2, C2, C4, C4, C22, C5, C8, C8, C2×C4, C2×C4, Q8, C10, C10, C42, C4⋊C4, C4⋊C4, C2×C8, C2×C8, Q16, C2×Q8, Dic5, C20, C20, C2×C10, C8⋊C4, Q8⋊C4, C4.Q8, C4×Q8, C2×Q16, C5⋊2C8, C40, Dic10, Dic10, C2×Dic5, C2×Dic5, C2×C20, C2×C20, Q16⋊C4, Dic20, C2×C5⋊2C8, C4×Dic5, C4×Dic5, C10.D4, C5×C4⋊C4, C2×C40, C2×Dic10, C10.Q16, C40⋊8C4, C5×C4.Q8, Dic5⋊3Q8, C2×Dic20, Dic20⋊15C4
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D5, C22×C4, C2×D4, C4○D4, D10, C4×D4, C8.C22, C4×D5, C22×D5, Q16⋊C4, C2×C4×D5, D4×D5, Q8⋊2D5, D20⋊8C4, SD16⋊D5, Dic20⋊15C4
►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)
(1 152 21 132)(2 151 22 131)(3 150 23 130)(4 149 24 129)(5 148 25 128)(6 147 26 127)(7 146 27 126)(8 145 28 125)(9 144 29 124)(10 143 30 123)(11 142 31 122)(12 141 32 121)(13 140 33 160)(14 139 34 159)(15 138 35 158)(16 137 36 157)(17 136 37 156)(18 135 38 155)(19 134 39 154)(20 133 40 153)(41 268 61 248)(42 267 62 247)(43 266 63 246)(44 265 64 245)(45 264 65 244)(46 263 66 243)(47 262 67 242)(48 261 68 241)(49 260 69 280)(50 259 70 279)(51 258 71 278)(52 257 72 277)(53 256 73 276)(54 255 74 275)(55 254 75 274)(56 253 76 273)(57 252 77 272)(58 251 78 271)(59 250 79 270)(60 249 80 269)(81 161 101 181)(82 200 102 180)(83 199 103 179)(84 198 104 178)(85 197 105 177)(86 196 106 176)(87 195 107 175)(88 194 108 174)(89 193 109 173)(90 192 110 172)(91 191 111 171)(92 190 112 170)(93 189 113 169)(94 188 114 168)(95 187 115 167)(96 186 116 166)(97 185 117 165)(98 184 118 164)(99 183 119 163)(100 182 120 162)(201 314 221 294)(202 313 222 293)(203 312 223 292)(204 311 224 291)(205 310 225 290)(206 309 226 289)(207 308 227 288)(208 307 228 287)(209 306 229 286)(210 305 230 285)(211 304 231 284)(212 303 232 283)(213 302 233 282)(214 301 234 281)(215 300 235 320)(216 299 236 319)(217 298 237 318)(218 297 238 317)(219 296 239 316)(220 295 240 315)
(1 283 114 256)(2 294 115 267)(3 305 116 278)(4 316 117 249)(5 287 118 260)(6 298 119 271)(7 309 120 242)(8 320 81 253)(9 291 82 264)(10 302 83 275)(11 313 84 246)(12 284 85 257)(13 295 86 268)(14 306 87 279)(15 317 88 250)(16 288 89 261)(17 299 90 272)(18 310 91 243)(19 281 92 254)(20 292 93 265)(21 303 94 276)(22 314 95 247)(23 285 96 258)(24 296 97 269)(25 307 98 280)(26 318 99 251)(27 289 100 262)(28 300 101 273)(29 311 102 244)(30 282 103 255)(31 293 104 266)(32 304 105 277)(33 315 106 248)(34 286 107 259)(35 297 108 270)(36 308 109 241)(37 319 110 252)(38 290 111 263)(39 301 112 274)(40 312 113 245)(41 140 220 196)(42 151 221 167)(43 122 222 178)(44 133 223 189)(45 144 224 200)(46 155 225 171)(47 126 226 182)(48 137 227 193)(49 148 228 164)(50 159 229 175)(51 130 230 186)(52 141 231 197)(53 152 232 168)(54 123 233 179)(55 134 234 190)(56 145 235 161)(57 156 236 172)(58 127 237 183)(59 138 238 194)(60 149 239 165)(61 160 240 176)(62 131 201 187)(63 142 202 198)(64 153 203 169)(65 124 204 180)(66 135 205 191)(67 146 206 162)(68 157 207 173)(69 128 208 184)(70 139 209 195)(71 150 210 166)(72 121 211 177)(73 132 212 188)(74 143 213 199)(75 154 214 170)(76 125 215 181)(77 136 216 192)(78 147 217 163)(79 158 218 174)(80 129 219 185)
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), (1,152,21,132)(2,151,22,131)(3,150,23,130)(4,149,24,129)(5,148,25,128)(6,147,26,127)(7,146,27,126)(8,145,28,125)(9,144,29,124)(10,143,30,123)(11,142,31,122)(12,141,32,121)(13,140,33,160)(14,139,34,159)(15,138,35,158)(16,137,36,157)(17,136,37,156)(18,135,38,155)(19,134,39,154)(20,133,40,153)(41,268,61,248)(42,267,62,247)(43,266,63,246)(44,265,64,245)(45,264,65,244)(46,263,66,243)(47,262,67,242)(48,261,68,241)(49,260,69,280)(50,259,70,279)(51,258,71,278)(52,257,72,277)(53,256,73,276)(54,255,74,275)(55,254,75,274)(56,253,76,273)(57,252,77,272)(58,251,78,271)(59,250,79,270)(60,249,80,269)(81,161,101,181)(82,200,102,180)(83,199,103,179)(84,198,104,178)(85,197,105,177)(86,196,106,176)(87,195,107,175)(88,194,108,174)(89,193,109,173)(90,192,110,172)(91,191,111,171)(92,190,112,170)(93,189,113,169)(94,188,114,168)(95,187,115,167)(96,186,116,166)(97,185,117,165)(98,184,118,164)(99,183,119,163)(100,182,120,162)(201,314,221,294)(202,313,222,293)(203,312,223,292)(204,311,224,291)(205,310,225,290)(206,309,226,289)(207,308,227,288)(208,307,228,287)(209,306,229,286)(210,305,230,285)(211,304,231,284)(212,303,232,283)(213,302,233,282)(214,301,234,281)(215,300,235,320)(216,299,236,319)(217,298,237,318)(218,297,238,317)(219,296,239,316)(220,295,240,315), (1,283,114,256)(2,294,115,267)(3,305,116,278)(4,316,117,249)(5,287,118,260)(6,298,119,271)(7,309,120,242)(8,320,81,253)(9,291,82,264)(10,302,83,275)(11,313,84,246)(12,284,85,257)(13,295,86,268)(14,306,87,279)(15,317,88,250)(16,288,89,261)(17,299,90,272)(18,310,91,243)(19,281,92,254)(20,292,93,265)(21,303,94,276)(22,314,95,247)(23,285,96,258)(24,296,97,269)(25,307,98,280)(26,318,99,251)(27,289,100,262)(28,300,101,273)(29,311,102,244)(30,282,103,255)(31,293,104,266)(32,304,105,277)(33,315,106,248)(34,286,107,259)(35,297,108,270)(36,308,109,241)(37,319,110,252)(38,290,111,263)(39,301,112,274)(40,312,113,245)(41,140,220,196)(42,151,221,167)(43,122,222,178)(44,133,223,189)(45,144,224,200)(46,155,225,171)(47,126,226,182)(48,137,227,193)(49,148,228,164)(50,159,229,175)(51,130,230,186)(52,141,231,197)(53,152,232,168)(54,123,233,179)(55,134,234,190)(56,145,235,161)(57,156,236,172)(58,127,237,183)(59,138,238,194)(60,149,239,165)(61,160,240,176)(62,131,201,187)(63,142,202,198)(64,153,203,169)(65,124,204,180)(66,135,205,191)(67,146,206,162)(68,157,207,173)(69,128,208,184)(70,139,209,195)(71,150,210,166)(72,121,211,177)(73,132,212,188)(74,143,213,199)(75,154,214,170)(76,125,215,181)(77,136,216,192)(78,147,217,163)(79,158,218,174)(80,129,219,185)>;
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), (1,152,21,132)(2,151,22,131)(3,150,23,130)(4,149,24,129)(5,148,25,128)(6,147,26,127)(7,146,27,126)(8,145,28,125)(9,144,29,124)(10,143,30,123)(11,142,31,122)(12,141,32,121)(13,140,33,160)(14,139,34,159)(15,138,35,158)(16,137,36,157)(17,136,37,156)(18,135,38,155)(19,134,39,154)(20,133,40,153)(41,268,61,248)(42,267,62,247)(43,266,63,246)(44,265,64,245)(45,264,65,244)(46,263,66,243)(47,262,67,242)(48,261,68,241)(49,260,69,280)(50,259,70,279)(51,258,71,278)(52,257,72,277)(53,256,73,276)(54,255,74,275)(55,254,75,274)(56,253,76,273)(57,252,77,272)(58,251,78,271)(59,250,79,270)(60,249,80,269)(81,161,101,181)(82,200,102,180)(83,199,103,179)(84,198,104,178)(85,197,105,177)(86,196,106,176)(87,195,107,175)(88,194,108,174)(89,193,109,173)(90,192,110,172)(91,191,111,171)(92,190,112,170)(93,189,113,169)(94,188,114,168)(95,187,115,167)(96,186,116,166)(97,185,117,165)(98,184,118,164)(99,183,119,163)(100,182,120,162)(201,314,221,294)(202,313,222,293)(203,312,223,292)(204,311,224,291)(205,310,225,290)(206,309,226,289)(207,308,227,288)(208,307,228,287)(209,306,229,286)(210,305,230,285)(211,304,231,284)(212,303,232,283)(213,302,233,282)(214,301,234,281)(215,300,235,320)(216,299,236,319)(217,298,237,318)(218,297,238,317)(219,296,239,316)(220,295,240,315), (1,283,114,256)(2,294,115,267)(3,305,116,278)(4,316,117,249)(5,287,118,260)(6,298,119,271)(7,309,120,242)(8,320,81,253)(9,291,82,264)(10,302,83,275)(11,313,84,246)(12,284,85,257)(13,295,86,268)(14,306,87,279)(15,317,88,250)(16,288,89,261)(17,299,90,272)(18,310,91,243)(19,281,92,254)(20,292,93,265)(21,303,94,276)(22,314,95,247)(23,285,96,258)(24,296,97,269)(25,307,98,280)(26,318,99,251)(27,289,100,262)(28,300,101,273)(29,311,102,244)(30,282,103,255)(31,293,104,266)(32,304,105,277)(33,315,106,248)(34,286,107,259)(35,297,108,270)(36,308,109,241)(37,319,110,252)(38,290,111,263)(39,301,112,274)(40,312,113,245)(41,140,220,196)(42,151,221,167)(43,122,222,178)(44,133,223,189)(45,144,224,200)(46,155,225,171)(47,126,226,182)(48,137,227,193)(49,148,228,164)(50,159,229,175)(51,130,230,186)(52,141,231,197)(53,152,232,168)(54,123,233,179)(55,134,234,190)(56,145,235,161)(57,156,236,172)(58,127,237,183)(59,138,238,194)(60,149,239,165)(61,160,240,176)(62,131,201,187)(63,142,202,198)(64,153,203,169)(65,124,204,180)(66,135,205,191)(67,146,206,162)(68,157,207,173)(69,128,208,184)(70,139,209,195)(71,150,210,166)(72,121,211,177)(73,132,212,188)(74,143,213,199)(75,154,214,170)(76,125,215,181)(77,136,216,192)(78,147,217,163)(79,158,218,174)(80,129,219,185) );
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)], [(1,152,21,132),(2,151,22,131),(3,150,23,130),(4,149,24,129),(5,148,25,128),(6,147,26,127),(7,146,27,126),(8,145,28,125),(9,144,29,124),(10,143,30,123),(11,142,31,122),(12,141,32,121),(13,140,33,160),(14,139,34,159),(15,138,35,158),(16,137,36,157),(17,136,37,156),(18,135,38,155),(19,134,39,154),(20,133,40,153),(41,268,61,248),(42,267,62,247),(43,266,63,246),(44,265,64,245),(45,264,65,244),(46,263,66,243),(47,262,67,242),(48,261,68,241),(49,260,69,280),(50,259,70,279),(51,258,71,278),(52,257,72,277),(53,256,73,276),(54,255,74,275),(55,254,75,274),(56,253,76,273),(57,252,77,272),(58,251,78,271),(59,250,79,270),(60,249,80,269),(81,161,101,181),(82,200,102,180),(83,199,103,179),(84,198,104,178),(85,197,105,177),(86,196,106,176),(87,195,107,175),(88,194,108,174),(89,193,109,173),(90,192,110,172),(91,191,111,171),(92,190,112,170),(93,189,113,169),(94,188,114,168),(95,187,115,167),(96,186,116,166),(97,185,117,165),(98,184,118,164),(99,183,119,163),(100,182,120,162),(201,314,221,294),(202,313,222,293),(203,312,223,292),(204,311,224,291),(205,310,225,290),(206,309,226,289),(207,308,227,288),(208,307,228,287),(209,306,229,286),(210,305,230,285),(211,304,231,284),(212,303,232,283),(213,302,233,282),(214,301,234,281),(215,300,235,320),(216,299,236,319),(217,298,237,318),(218,297,238,317),(219,296,239,316),(220,295,240,315)], [(1,283,114,256),(2,294,115,267),(3,305,116,278),(4,316,117,249),(5,287,118,260),(6,298,119,271),(7,309,120,242),(8,320,81,253),(9,291,82,264),(10,302,83,275),(11,313,84,246),(12,284,85,257),(13,295,86,268),(14,306,87,279),(15,317,88,250),(16,288,89,261),(17,299,90,272),(18,310,91,243),(19,281,92,254),(20,292,93,265),(21,303,94,276),(22,314,95,247),(23,285,96,258),(24,296,97,269),(25,307,98,280),(26,318,99,251),(27,289,100,262),(28,300,101,273),(29,311,102,244),(30,282,103,255),(31,293,104,266),(32,304,105,277),(33,315,106,248),(34,286,107,259),(35,297,108,270),(36,308,109,241),(37,319,110,252),(38,290,111,263),(39,301,112,274),(40,312,113,245),(41,140,220,196),(42,151,221,167),(43,122,222,178),(44,133,223,189),(45,144,224,200),(46,155,225,171),(47,126,226,182),(48,137,227,193),(49,148,228,164),(50,159,229,175),(51,130,230,186),(52,141,231,197),(53,152,232,168),(54,123,233,179),(55,134,234,190),(56,145,235,161),(57,156,236,172),(58,127,237,183),(59,138,238,194),(60,149,239,165),(61,160,240,176),(62,131,201,187),(63,142,202,198),(64,153,203,169),(65,124,204,180),(66,135,205,191),(67,146,206,162),(68,157,207,173),(69,128,208,184),(70,139,209,195),(71,150,210,166),(72,121,211,177),(73,132,212,188),(74,143,213,199),(75,154,214,170),(76,125,215,181),(77,136,216,192),(78,147,217,163),(79,158,218,174),(80,129,219,185)]])
50 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 5A | 5B | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 20A | 20B | 20C | 20D | 20E | ··· | 20L | 40A | ··· | 40H |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 10 | 10 | 10 | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 4 | 4 | 20 | 20 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
50 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D5 | C4○D4 | D10 | D10 | C4×D5 | C8.C22 | Q8⋊2D5 | D4×D5 | SD16⋊D5 |
| kernel | Dic20⋊15C4 | C10.Q16 | C40⋊8C4 | C5×C4.Q8 | Dic5⋊3Q8 | C2×Dic20 | Dic20 | C2×Dic5 | C4.Q8 | C20 | C4⋊C4 | C2×C8 | C8 | C10 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 1 | 2 | 1 | 8 | 2 | 2 | 2 | 4 | 2 | 8 | 2 | 2 | 2 | 8 |
Matrix representation of Dic20⋊15C4 ►in GL6(𝔽41)
| 0 | 1 | 0 | 0 | 0 | 0 |
| 40 | 6 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 20 | 32 | 5 |
| 0 | 0 | 6 | 0 | 34 | 39 |
| 0 | 0 | 28 | 15 | 35 | 8 |
| 0 | 0 | 20 | 8 | 35 | 28 |
| 39 | 25 | 0 | 0 | 0 | 0 |
| 13 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 2 | 40 | 0 |
| 0 | 0 | 34 | 8 | 20 | 21 |
| 0 | 0 | 8 | 40 | 28 | 1 |
| 0 | 0 | 1 | 20 | 22 | 34 |
| 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 39 | 0 |
| 0 | 0 | 0 | 0 | 40 | 1 |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 1 | 40 | 1 | 0 |
G:=sub<GL(6,GF(41))| [0,40,0,0,0,0,1,6,0,0,0,0,0,0,19,6,28,20,0,0,20,0,15,8,0,0,32,34,35,35,0,0,5,39,8,28],[39,13,0,0,0,0,25,2,0,0,0,0,0,0,12,34,8,1,0,0,2,8,40,20,0,0,40,20,28,22,0,0,0,21,1,34],[32,0,0,0,0,0,0,32,0,0,0,0,0,0,40,0,1,1,0,0,0,0,0,40,0,0,39,40,1,1,0,0,0,1,0,0] >;
Dic20⋊15C4 in GAP, Magma, Sage, TeX
{\rm Dic}_{20}\rtimes_{15}C_4 % in TeX
G:=Group("Dic20:15C4"); // GroupNames label
G:=SmallGroup(320,480);
// by ID
G=gap.SmallGroup(320,480);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,344,758,135,100,570,297,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^40=c^4=1,b^2=a^20,b*a*b^-1=a^-1,c*a*c^-1=a^11,c*b*c^-1=a^20*b>;
// generators/relations