metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C40.26D4, Dic5⋊1Q16, C4.27(D4×D5), C20.51(C2×D4), C5⋊3(C4⋊Q16), C5⋊2C8.33D4, (C2×Q16).3D5, C2.16(D5×Q16), (C2×C8).241D10, C8.18(C5⋊D4), (C2×Q8).60D10, (C10×Q16).4C2, C10.26(C2×Q16), (C8×Dic5).4C2, (C2×C40).93C22, C22.274(D4×D5), C2.24(C20⋊D4), C10.33(C4⋊1D4), (C2×C20).455C23, (C2×Dic20).11C2, Dic5⋊Q8.7C2, (C2×Dic5).161D4, (Q8×C10).84C22, (C4×Dic5).274C22, (C2×Dic10).134C22, C4.14(C2×C5⋊D4), (C2×C5⋊Q16).8C2, (C2×C10).366(C2×D4), (C2×C4).543(C22×D5), (C2×C5⋊2C8).284C22, SmallGroup(320,808)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C40.26D4
G = < a,b,c | a40=b4=1, c2=a20, bab-1=a9, cac-1=a-1, cbc-1=b-1 >
Subgroups: 430 in 122 conjugacy classes, 47 normal (21 characteristic)
C1, C2, C2, C4, C4, C22, C5, C8, C8, C2×C4, C2×C4, Q8, C10, C10, C42, C4⋊C4, C2×C8, C2×C8, Q16, C2×Q8, C2×Q8, Dic5, Dic5, C20, C20, C2×C10, C4×C8, C4⋊Q8, C2×Q16, C2×Q16, C5⋊2C8, C40, Dic10, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C5×Q8, C4⋊Q16, Dic20, C2×C5⋊2C8, C4×Dic5, C10.D4, C5⋊Q16, C2×C40, C5×Q16, C2×Dic10, Q8×C10, C8×Dic5, C2×Dic20, C2×C5⋊Q16, Dic5⋊Q8, C10×Q16, C40.26D4
Quotients: C1, C2, C22, D4, C23, D5, Q16, C2×D4, D10, C4⋊1D4, C2×Q16, C5⋊D4, C22×D5, C4⋊Q16, D4×D5, C2×C5⋊D4, D5×Q16, C20⋊D4, C40.26D4
►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 43 232 296)(2 52 233 305)(3 61 234 314)(4 70 235 283)(5 79 236 292)(6 48 237 301)(7 57 238 310)(8 66 239 319)(9 75 240 288)(10 44 201 297)(11 53 202 306)(12 62 203 315)(13 71 204 284)(14 80 205 293)(15 49 206 302)(16 58 207 311)(17 67 208 320)(18 76 209 289)(19 45 210 298)(20 54 211 307)(21 63 212 316)(22 72 213 285)(23 41 214 294)(24 50 215 303)(25 59 216 312)(26 68 217 281)(27 77 218 290)(28 46 219 299)(29 55 220 308)(30 64 221 317)(31 73 222 286)(32 42 223 295)(33 51 224 304)(34 60 225 313)(35 69 226 282)(36 78 227 291)(37 47 228 300)(38 56 229 309)(39 65 230 318)(40 74 231 287)(81 276 197 156)(82 245 198 125)(83 254 199 134)(84 263 200 143)(85 272 161 152)(86 241 162 121)(87 250 163 130)(88 259 164 139)(89 268 165 148)(90 277 166 157)(91 246 167 126)(92 255 168 135)(93 264 169 144)(94 273 170 153)(95 242 171 122)(96 251 172 131)(97 260 173 140)(98 269 174 149)(99 278 175 158)(100 247 176 127)(101 256 177 136)(102 265 178 145)(103 274 179 154)(104 243 180 123)(105 252 181 132)(106 261 182 141)(107 270 183 150)(108 279 184 159)(109 248 185 128)(110 257 186 137)(111 266 187 146)(112 275 188 155)(113 244 189 124)(114 253 190 133)(115 262 191 142)(116 271 192 151)(117 280 193 160)(118 249 194 129)(119 258 195 138)(120 267 196 147)
(1 245 21 265)(2 244 22 264)(3 243 23 263)(4 242 24 262)(5 241 25 261)(6 280 26 260)(7 279 27 259)(8 278 28 258)(9 277 29 257)(10 276 30 256)(11 275 31 255)(12 274 32 254)(13 273 33 253)(14 272 34 252)(15 271 35 251)(16 270 36 250)(17 269 37 249)(18 268 38 248)(19 267 39 247)(20 266 40 246)(41 84 61 104)(42 83 62 103)(43 82 63 102)(44 81 64 101)(45 120 65 100)(46 119 66 99)(47 118 67 98)(48 117 68 97)(49 116 69 96)(50 115 70 95)(51 114 71 94)(52 113 72 93)(53 112 73 92)(54 111 74 91)(55 110 75 90)(56 109 76 89)(57 108 77 88)(58 107 78 87)(59 106 79 86)(60 105 80 85)(121 216 141 236)(122 215 142 235)(123 214 143 234)(124 213 144 233)(125 212 145 232)(126 211 146 231)(127 210 147 230)(128 209 148 229)(129 208 149 228)(130 207 150 227)(131 206 151 226)(132 205 152 225)(133 204 153 224)(134 203 154 223)(135 202 155 222)(136 201 156 221)(137 240 157 220)(138 239 158 219)(139 238 159 218)(140 237 160 217)(161 313 181 293)(162 312 182 292)(163 311 183 291)(164 310 184 290)(165 309 185 289)(166 308 186 288)(167 307 187 287)(168 306 188 286)(169 305 189 285)(170 304 190 284)(171 303 191 283)(172 302 192 282)(173 301 193 281)(174 300 194 320)(175 299 195 319)(176 298 196 318)(177 297 197 317)(178 296 198 316)(179 295 199 315)(180 294 200 314)
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), (1,43,232,296)(2,52,233,305)(3,61,234,314)(4,70,235,283)(5,79,236,292)(6,48,237,301)(7,57,238,310)(8,66,239,319)(9,75,240,288)(10,44,201,297)(11,53,202,306)(12,62,203,315)(13,71,204,284)(14,80,205,293)(15,49,206,302)(16,58,207,311)(17,67,208,320)(18,76,209,289)(19,45,210,298)(20,54,211,307)(21,63,212,316)(22,72,213,285)(23,41,214,294)(24,50,215,303)(25,59,216,312)(26,68,217,281)(27,77,218,290)(28,46,219,299)(29,55,220,308)(30,64,221,317)(31,73,222,286)(32,42,223,295)(33,51,224,304)(34,60,225,313)(35,69,226,282)(36,78,227,291)(37,47,228,300)(38,56,229,309)(39,65,230,318)(40,74,231,287)(81,276,197,156)(82,245,198,125)(83,254,199,134)(84,263,200,143)(85,272,161,152)(86,241,162,121)(87,250,163,130)(88,259,164,139)(89,268,165,148)(90,277,166,157)(91,246,167,126)(92,255,168,135)(93,264,169,144)(94,273,170,153)(95,242,171,122)(96,251,172,131)(97,260,173,140)(98,269,174,149)(99,278,175,158)(100,247,176,127)(101,256,177,136)(102,265,178,145)(103,274,179,154)(104,243,180,123)(105,252,181,132)(106,261,182,141)(107,270,183,150)(108,279,184,159)(109,248,185,128)(110,257,186,137)(111,266,187,146)(112,275,188,155)(113,244,189,124)(114,253,190,133)(115,262,191,142)(116,271,192,151)(117,280,193,160)(118,249,194,129)(119,258,195,138)(120,267,196,147), (1,245,21,265)(2,244,22,264)(3,243,23,263)(4,242,24,262)(5,241,25,261)(6,280,26,260)(7,279,27,259)(8,278,28,258)(9,277,29,257)(10,276,30,256)(11,275,31,255)(12,274,32,254)(13,273,33,253)(14,272,34,252)(15,271,35,251)(16,270,36,250)(17,269,37,249)(18,268,38,248)(19,267,39,247)(20,266,40,246)(41,84,61,104)(42,83,62,103)(43,82,63,102)(44,81,64,101)(45,120,65,100)(46,119,66,99)(47,118,67,98)(48,117,68,97)(49,116,69,96)(50,115,70,95)(51,114,71,94)(52,113,72,93)(53,112,73,92)(54,111,74,91)(55,110,75,90)(56,109,76,89)(57,108,77,88)(58,107,78,87)(59,106,79,86)(60,105,80,85)(121,216,141,236)(122,215,142,235)(123,214,143,234)(124,213,144,233)(125,212,145,232)(126,211,146,231)(127,210,147,230)(128,209,148,229)(129,208,149,228)(130,207,150,227)(131,206,151,226)(132,205,152,225)(133,204,153,224)(134,203,154,223)(135,202,155,222)(136,201,156,221)(137,240,157,220)(138,239,158,219)(139,238,159,218)(140,237,160,217)(161,313,181,293)(162,312,182,292)(163,311,183,291)(164,310,184,290)(165,309,185,289)(166,308,186,288)(167,307,187,287)(168,306,188,286)(169,305,189,285)(170,304,190,284)(171,303,191,283)(172,302,192,282)(173,301,193,281)(174,300,194,320)(175,299,195,319)(176,298,196,318)(177,297,197,317)(178,296,198,316)(179,295,199,315)(180,294,200,314)>;
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), (1,43,232,296)(2,52,233,305)(3,61,234,314)(4,70,235,283)(5,79,236,292)(6,48,237,301)(7,57,238,310)(8,66,239,319)(9,75,240,288)(10,44,201,297)(11,53,202,306)(12,62,203,315)(13,71,204,284)(14,80,205,293)(15,49,206,302)(16,58,207,311)(17,67,208,320)(18,76,209,289)(19,45,210,298)(20,54,211,307)(21,63,212,316)(22,72,213,285)(23,41,214,294)(24,50,215,303)(25,59,216,312)(26,68,217,281)(27,77,218,290)(28,46,219,299)(29,55,220,308)(30,64,221,317)(31,73,222,286)(32,42,223,295)(33,51,224,304)(34,60,225,313)(35,69,226,282)(36,78,227,291)(37,47,228,300)(38,56,229,309)(39,65,230,318)(40,74,231,287)(81,276,197,156)(82,245,198,125)(83,254,199,134)(84,263,200,143)(85,272,161,152)(86,241,162,121)(87,250,163,130)(88,259,164,139)(89,268,165,148)(90,277,166,157)(91,246,167,126)(92,255,168,135)(93,264,169,144)(94,273,170,153)(95,242,171,122)(96,251,172,131)(97,260,173,140)(98,269,174,149)(99,278,175,158)(100,247,176,127)(101,256,177,136)(102,265,178,145)(103,274,179,154)(104,243,180,123)(105,252,181,132)(106,261,182,141)(107,270,183,150)(108,279,184,159)(109,248,185,128)(110,257,186,137)(111,266,187,146)(112,275,188,155)(113,244,189,124)(114,253,190,133)(115,262,191,142)(116,271,192,151)(117,280,193,160)(118,249,194,129)(119,258,195,138)(120,267,196,147), (1,245,21,265)(2,244,22,264)(3,243,23,263)(4,242,24,262)(5,241,25,261)(6,280,26,260)(7,279,27,259)(8,278,28,258)(9,277,29,257)(10,276,30,256)(11,275,31,255)(12,274,32,254)(13,273,33,253)(14,272,34,252)(15,271,35,251)(16,270,36,250)(17,269,37,249)(18,268,38,248)(19,267,39,247)(20,266,40,246)(41,84,61,104)(42,83,62,103)(43,82,63,102)(44,81,64,101)(45,120,65,100)(46,119,66,99)(47,118,67,98)(48,117,68,97)(49,116,69,96)(50,115,70,95)(51,114,71,94)(52,113,72,93)(53,112,73,92)(54,111,74,91)(55,110,75,90)(56,109,76,89)(57,108,77,88)(58,107,78,87)(59,106,79,86)(60,105,80,85)(121,216,141,236)(122,215,142,235)(123,214,143,234)(124,213,144,233)(125,212,145,232)(126,211,146,231)(127,210,147,230)(128,209,148,229)(129,208,149,228)(130,207,150,227)(131,206,151,226)(132,205,152,225)(133,204,153,224)(134,203,154,223)(135,202,155,222)(136,201,156,221)(137,240,157,220)(138,239,158,219)(139,238,159,218)(140,237,160,217)(161,313,181,293)(162,312,182,292)(163,311,183,291)(164,310,184,290)(165,309,185,289)(166,308,186,288)(167,307,187,287)(168,306,188,286)(169,305,189,285)(170,304,190,284)(171,303,191,283)(172,302,192,282)(173,301,193,281)(174,300,194,320)(175,299,195,319)(176,298,196,318)(177,297,197,317)(178,296,198,316)(179,295,199,315)(180,294,200,314) );
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)], [(1,43,232,296),(2,52,233,305),(3,61,234,314),(4,70,235,283),(5,79,236,292),(6,48,237,301),(7,57,238,310),(8,66,239,319),(9,75,240,288),(10,44,201,297),(11,53,202,306),(12,62,203,315),(13,71,204,284),(14,80,205,293),(15,49,206,302),(16,58,207,311),(17,67,208,320),(18,76,209,289),(19,45,210,298),(20,54,211,307),(21,63,212,316),(22,72,213,285),(23,41,214,294),(24,50,215,303),(25,59,216,312),(26,68,217,281),(27,77,218,290),(28,46,219,299),(29,55,220,308),(30,64,221,317),(31,73,222,286),(32,42,223,295),(33,51,224,304),(34,60,225,313),(35,69,226,282),(36,78,227,291),(37,47,228,300),(38,56,229,309),(39,65,230,318),(40,74,231,287),(81,276,197,156),(82,245,198,125),(83,254,199,134),(84,263,200,143),(85,272,161,152),(86,241,162,121),(87,250,163,130),(88,259,164,139),(89,268,165,148),(90,277,166,157),(91,246,167,126),(92,255,168,135),(93,264,169,144),(94,273,170,153),(95,242,171,122),(96,251,172,131),(97,260,173,140),(98,269,174,149),(99,278,175,158),(100,247,176,127),(101,256,177,136),(102,265,178,145),(103,274,179,154),(104,243,180,123),(105,252,181,132),(106,261,182,141),(107,270,183,150),(108,279,184,159),(109,248,185,128),(110,257,186,137),(111,266,187,146),(112,275,188,155),(113,244,189,124),(114,253,190,133),(115,262,191,142),(116,271,192,151),(117,280,193,160),(118,249,194,129),(119,258,195,138),(120,267,196,147)], [(1,245,21,265),(2,244,22,264),(3,243,23,263),(4,242,24,262),(5,241,25,261),(6,280,26,260),(7,279,27,259),(8,278,28,258),(9,277,29,257),(10,276,30,256),(11,275,31,255),(12,274,32,254),(13,273,33,253),(14,272,34,252),(15,271,35,251),(16,270,36,250),(17,269,37,249),(18,268,38,248),(19,267,39,247),(20,266,40,246),(41,84,61,104),(42,83,62,103),(43,82,63,102),(44,81,64,101),(45,120,65,100),(46,119,66,99),(47,118,67,98),(48,117,68,97),(49,116,69,96),(50,115,70,95),(51,114,71,94),(52,113,72,93),(53,112,73,92),(54,111,74,91),(55,110,75,90),(56,109,76,89),(57,108,77,88),(58,107,78,87),(59,106,79,86),(60,105,80,85),(121,216,141,236),(122,215,142,235),(123,214,143,234),(124,213,144,233),(125,212,145,232),(126,211,146,231),(127,210,147,230),(128,209,148,229),(129,208,149,228),(130,207,150,227),(131,206,151,226),(132,205,152,225),(133,204,153,224),(134,203,154,223),(135,202,155,222),(136,201,156,221),(137,240,157,220),(138,239,158,219),(139,238,159,218),(140,237,160,217),(161,313,181,293),(162,312,182,292),(163,311,183,291),(164,310,184,290),(165,309,185,289),(166,308,186,288),(167,307,187,287),(168,306,188,286),(169,305,189,285),(170,304,190,284),(171,303,191,283),(172,302,192,282),(173,301,193,281),(174,300,194,320),(175,299,195,319),(176,298,196,318),(177,297,197,317),(178,296,198,316),(179,295,199,315),(180,294,200,314)]])
50 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 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 | 5 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 8 | 8 | 10 | 10 | 10 | 10 | 40 | 40 | 2 | 2 | 2 | 2 | 2 | 2 | 10 | 10 | 10 | 10 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
50 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | + | + | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D5 | Q16 | D10 | D10 | C5⋊D4 | D4×D5 | D4×D5 | D5×Q16 |
| kernel | C40.26D4 | C8×Dic5 | C2×Dic20 | C2×C5⋊Q16 | Dic5⋊Q8 | C10×Q16 | C5⋊2C8 | C40 | C2×Dic5 | C2×Q16 | Dic5 | C2×C8 | C2×Q8 | C8 | C4 | C22 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 8 | 2 | 4 | 8 | 2 | 2 | 8 |
Matrix representation of C40.26D4 ►in GL4(𝔽41) generated by
| 40 | 34 | 0 | 0 |
| 7 | 7 | 0 | 0 |
| 0 | 0 | 0 | 22 |
| 0 | 0 | 13 | 24 |
| 9 | 0 | 0 | 0 |
| 19 | 32 | 0 | 0 |
| 0 | 0 | 40 | 36 |
| 0 | 0 | 25 | 1 |
| 30 | 32 | 0 | 0 |
| 27 | 11 | 0 | 0 |
| 0 | 0 | 29 | 27 |
| 0 | 0 | 25 | 12 |
G:=sub<GL(4,GF(41))| [40,7,0,0,34,7,0,0,0,0,0,13,0,0,22,24],[9,19,0,0,0,32,0,0,0,0,40,25,0,0,36,1],[30,27,0,0,32,11,0,0,0,0,29,25,0,0,27,12] >;
C40.26D4 in GAP, Magma, Sage, TeX
C_{40}._{26}D_4 % in TeX
G:=Group("C40.26D4"); // GroupNames label
G:=SmallGroup(320,808);
// by ID
G=gap.SmallGroup(320,808);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,253,232,422,135,184,570,297,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^40=b^4=1,c^2=a^20,b*a*b^-1=a^9,c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations