metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C20)⋊8C8, C10.16(C4×C8), C10.14(C4⋊C8), C20.73(C4⋊C4), (C2×C20).63Q8, (C2×C42).1D5, (C2×C20).487D4, (C2×C4).163D20, C2.2(C20⋊3C8), (C2×C10).38C42, (C22×C20).41C4, (C2×C4).53Dic10, C10.11(C8⋊C4), (C22×C4).7Dic5, C10.27(C22⋊C8), (C22×C4).451D10, (C2×C10).39M4(2), C4.45(D10⋊C4), C22.16(C4×Dic5), C23.37(C2×Dic5), C20.107(C22⋊C4), C2.1(C20.55D4), C4.29(C10.D4), C22.17(C4⋊Dic5), C5⋊3(C22.7C42), C2.2(C42.D5), C22.7(C4.Dic5), (C22×C20).548C22, C22.22(C23.D5), C2.1(C10.10C42), C10.21(C2.C42), C2.5(C4×C5⋊2C8), (C2×C4×C20).24C2, (C2×C5⋊2C8)⋊12C4, (C2×C4)⋊2(C5⋊2C8), (C2×C10).56(C2×C8), (C2×C4).170(C4×D5), (C2×C10).62(C4⋊C4), (C2×C20).417(C2×C4), C22.10(C2×C5⋊2C8), (C2×C4).267(C5⋊D4), (C22×C5⋊2C8).15C2, (C22×C10).190(C2×C4), (C2×C10).148(C22⋊C4), SmallGroup(320,82)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C20)⋊8C8
G = < a,b,c | a2=b20=c8=1, ab=ba, ac=ca, cbc-1=ab9 >
Subgroups: 246 in 118 conjugacy classes, 75 normal (25 characteristic)
C1, C2, C2, C4, C4, C22, C22, C5, C8, C2×C4, C2×C4, C2×C4, C23, C10, C10, C42, C2×C8, C22×C4, C22×C4, C20, C20, C2×C10, C2×C10, C2×C42, C22×C8, C5⋊2C8, C2×C20, C2×C20, C2×C20, C22×C10, C22.7C42, C2×C5⋊2C8, C2×C5⋊2C8, C4×C20, C22×C20, C22×C20, C22×C5⋊2C8, C2×C4×C20, (C2×C20)⋊8C8
Quotients: C1, C2, C4, C22, C8, C2×C4, D4, Q8, D5, C42, C22⋊C4, C4⋊C4, C2×C8, M4(2), Dic5, D10, C2.C42, C4×C8, C8⋊C4, C22⋊C8, C4⋊C8, C5⋊2C8, Dic10, C4×D5, D20, C2×Dic5, C5⋊D4, C22.7C42, C2×C5⋊2C8, C4.Dic5, C4×Dic5, C10.D4, C4⋊Dic5, D10⋊C4, C23.D5, C4×C5⋊2C8, C42.D5, C20⋊3C8, C20.55D4, C10.10C42, (C2×C20)⋊8C8
►Regular action on 320 points
Generators in S320
(1 168)(2 169)(3 170)(4 171)(5 172)(6 173)(7 174)(8 175)(9 176)(10 177)(11 178)(12 179)(13 180)(14 161)(15 162)(16 163)(17 164)(18 165)(19 166)(20 167)(21 54)(22 55)(23 56)(24 57)(25 58)(26 59)(27 60)(28 41)(29 42)(30 43)(31 44)(32 45)(33 46)(34 47)(35 48)(36 49)(37 50)(38 51)(39 52)(40 53)(61 125)(62 126)(63 127)(64 128)(65 129)(66 130)(67 131)(68 132)(69 133)(70 134)(71 135)(72 136)(73 137)(74 138)(75 139)(76 140)(77 121)(78 122)(79 123)(80 124)(81 101)(82 102)(83 103)(84 104)(85 105)(86 106)(87 107)(88 108)(89 109)(90 110)(91 111)(92 112)(93 113)(94 114)(95 115)(96 116)(97 117)(98 118)(99 119)(100 120)(141 272)(142 273)(143 274)(144 275)(145 276)(146 277)(147 278)(148 279)(149 280)(150 261)(151 262)(152 263)(153 264)(154 265)(155 266)(156 267)(157 268)(158 269)(159 270)(160 271)(181 212)(182 213)(183 214)(184 215)(185 216)(186 217)(187 218)(188 219)(189 220)(190 201)(191 202)(192 203)(193 204)(194 205)(195 206)(196 207)(197 208)(198 209)(199 210)(200 211)(221 316)(222 317)(223 318)(224 319)(225 320)(226 301)(227 302)(228 303)(229 304)(230 305)(231 306)(232 307)(233 308)(234 309)(235 310)(236 311)(237 312)(238 313)(239 314)(240 315)(241 292)(242 293)(243 294)(244 295)(245 296)(246 297)(247 298)(248 299)(249 300)(250 281)(251 282)(252 283)(253 284)(254 285)(255 286)(256 287)(257 288)(258 289)(259 290)(260 291)
(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)
(1 310 43 103 298 208 69 269)(2 224 44 92 299 186 70 147)(3 308 45 101 300 206 71 267)(4 222 46 90 281 184 72 145)(5 306 47 119 282 204 73 265)(6 240 48 88 283 182 74 143)(7 304 49 117 284 202 75 263)(8 238 50 86 285 200 76 141)(9 302 51 115 286 220 77 261)(10 236 52 84 287 198 78 159)(11 320 53 113 288 218 79 279)(12 234 54 82 289 196 80 157)(13 318 55 111 290 216 61 277)(14 232 56 100 291 194 62 155)(15 316 57 109 292 214 63 275)(16 230 58 98 293 192 64 153)(17 314 59 107 294 212 65 273)(18 228 60 96 295 190 66 151)(19 312 41 105 296 210 67 271)(20 226 42 94 297 188 68 149)(21 102 258 207 124 268 179 309)(22 91 259 185 125 146 180 223)(23 120 260 205 126 266 161 307)(24 89 241 183 127 144 162 221)(25 118 242 203 128 264 163 305)(26 87 243 181 129 142 164 239)(27 116 244 201 130 262 165 303)(28 85 245 199 131 160 166 237)(29 114 246 219 132 280 167 301)(30 83 247 197 133 158 168 235)(31 112 248 217 134 278 169 319)(32 81 249 195 135 156 170 233)(33 110 250 215 136 276 171 317)(34 99 251 193 137 154 172 231)(35 108 252 213 138 274 173 315)(36 97 253 191 139 152 174 229)(37 106 254 211 140 272 175 313)(38 95 255 189 121 150 176 227)(39 104 256 209 122 270 177 311)(40 93 257 187 123 148 178 225)
G:=sub<Sym(320)| (1,168)(2,169)(3,170)(4,171)(5,172)(6,173)(7,174)(8,175)(9,176)(10,177)(11,178)(12,179)(13,180)(14,161)(15,162)(16,163)(17,164)(18,165)(19,166)(20,167)(21,54)(22,55)(23,56)(24,57)(25,58)(26,59)(27,60)(28,41)(29,42)(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52)(40,53)(61,125)(62,126)(63,127)(64,128)(65,129)(66,130)(67,131)(68,132)(69,133)(70,134)(71,135)(72,136)(73,137)(74,138)(75,139)(76,140)(77,121)(78,122)(79,123)(80,124)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)(91,111)(92,112)(93,113)(94,114)(95,115)(96,116)(97,117)(98,118)(99,119)(100,120)(141,272)(142,273)(143,274)(144,275)(145,276)(146,277)(147,278)(148,279)(149,280)(150,261)(151,262)(152,263)(153,264)(154,265)(155,266)(156,267)(157,268)(158,269)(159,270)(160,271)(181,212)(182,213)(183,214)(184,215)(185,216)(186,217)(187,218)(188,219)(189,220)(190,201)(191,202)(192,203)(193,204)(194,205)(195,206)(196,207)(197,208)(198,209)(199,210)(200,211)(221,316)(222,317)(223,318)(224,319)(225,320)(226,301)(227,302)(228,303)(229,304)(230,305)(231,306)(232,307)(233,308)(234,309)(235,310)(236,311)(237,312)(238,313)(239,314)(240,315)(241,292)(242,293)(243,294)(244,295)(245,296)(246,297)(247,298)(248,299)(249,300)(250,281)(251,282)(252,283)(253,284)(254,285)(255,286)(256,287)(257,288)(258,289)(259,290)(260,291), (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), (1,310,43,103,298,208,69,269)(2,224,44,92,299,186,70,147)(3,308,45,101,300,206,71,267)(4,222,46,90,281,184,72,145)(5,306,47,119,282,204,73,265)(6,240,48,88,283,182,74,143)(7,304,49,117,284,202,75,263)(8,238,50,86,285,200,76,141)(9,302,51,115,286,220,77,261)(10,236,52,84,287,198,78,159)(11,320,53,113,288,218,79,279)(12,234,54,82,289,196,80,157)(13,318,55,111,290,216,61,277)(14,232,56,100,291,194,62,155)(15,316,57,109,292,214,63,275)(16,230,58,98,293,192,64,153)(17,314,59,107,294,212,65,273)(18,228,60,96,295,190,66,151)(19,312,41,105,296,210,67,271)(20,226,42,94,297,188,68,149)(21,102,258,207,124,268,179,309)(22,91,259,185,125,146,180,223)(23,120,260,205,126,266,161,307)(24,89,241,183,127,144,162,221)(25,118,242,203,128,264,163,305)(26,87,243,181,129,142,164,239)(27,116,244,201,130,262,165,303)(28,85,245,199,131,160,166,237)(29,114,246,219,132,280,167,301)(30,83,247,197,133,158,168,235)(31,112,248,217,134,278,169,319)(32,81,249,195,135,156,170,233)(33,110,250,215,136,276,171,317)(34,99,251,193,137,154,172,231)(35,108,252,213,138,274,173,315)(36,97,253,191,139,152,174,229)(37,106,254,211,140,272,175,313)(38,95,255,189,121,150,176,227)(39,104,256,209,122,270,177,311)(40,93,257,187,123,148,178,225)>;
G:=Group( (1,168)(2,169)(3,170)(4,171)(5,172)(6,173)(7,174)(8,175)(9,176)(10,177)(11,178)(12,179)(13,180)(14,161)(15,162)(16,163)(17,164)(18,165)(19,166)(20,167)(21,54)(22,55)(23,56)(24,57)(25,58)(26,59)(27,60)(28,41)(29,42)(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52)(40,53)(61,125)(62,126)(63,127)(64,128)(65,129)(66,130)(67,131)(68,132)(69,133)(70,134)(71,135)(72,136)(73,137)(74,138)(75,139)(76,140)(77,121)(78,122)(79,123)(80,124)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)(91,111)(92,112)(93,113)(94,114)(95,115)(96,116)(97,117)(98,118)(99,119)(100,120)(141,272)(142,273)(143,274)(144,275)(145,276)(146,277)(147,278)(148,279)(149,280)(150,261)(151,262)(152,263)(153,264)(154,265)(155,266)(156,267)(157,268)(158,269)(159,270)(160,271)(181,212)(182,213)(183,214)(184,215)(185,216)(186,217)(187,218)(188,219)(189,220)(190,201)(191,202)(192,203)(193,204)(194,205)(195,206)(196,207)(197,208)(198,209)(199,210)(200,211)(221,316)(222,317)(223,318)(224,319)(225,320)(226,301)(227,302)(228,303)(229,304)(230,305)(231,306)(232,307)(233,308)(234,309)(235,310)(236,311)(237,312)(238,313)(239,314)(240,315)(241,292)(242,293)(243,294)(244,295)(245,296)(246,297)(247,298)(248,299)(249,300)(250,281)(251,282)(252,283)(253,284)(254,285)(255,286)(256,287)(257,288)(258,289)(259,290)(260,291), (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), (1,310,43,103,298,208,69,269)(2,224,44,92,299,186,70,147)(3,308,45,101,300,206,71,267)(4,222,46,90,281,184,72,145)(5,306,47,119,282,204,73,265)(6,240,48,88,283,182,74,143)(7,304,49,117,284,202,75,263)(8,238,50,86,285,200,76,141)(9,302,51,115,286,220,77,261)(10,236,52,84,287,198,78,159)(11,320,53,113,288,218,79,279)(12,234,54,82,289,196,80,157)(13,318,55,111,290,216,61,277)(14,232,56,100,291,194,62,155)(15,316,57,109,292,214,63,275)(16,230,58,98,293,192,64,153)(17,314,59,107,294,212,65,273)(18,228,60,96,295,190,66,151)(19,312,41,105,296,210,67,271)(20,226,42,94,297,188,68,149)(21,102,258,207,124,268,179,309)(22,91,259,185,125,146,180,223)(23,120,260,205,126,266,161,307)(24,89,241,183,127,144,162,221)(25,118,242,203,128,264,163,305)(26,87,243,181,129,142,164,239)(27,116,244,201,130,262,165,303)(28,85,245,199,131,160,166,237)(29,114,246,219,132,280,167,301)(30,83,247,197,133,158,168,235)(31,112,248,217,134,278,169,319)(32,81,249,195,135,156,170,233)(33,110,250,215,136,276,171,317)(34,99,251,193,137,154,172,231)(35,108,252,213,138,274,173,315)(36,97,253,191,139,152,174,229)(37,106,254,211,140,272,175,313)(38,95,255,189,121,150,176,227)(39,104,256,209,122,270,177,311)(40,93,257,187,123,148,178,225) );
G=PermutationGroup([[(1,168),(2,169),(3,170),(4,171),(5,172),(6,173),(7,174),(8,175),(9,176),(10,177),(11,178),(12,179),(13,180),(14,161),(15,162),(16,163),(17,164),(18,165),(19,166),(20,167),(21,54),(22,55),(23,56),(24,57),(25,58),(26,59),(27,60),(28,41),(29,42),(30,43),(31,44),(32,45),(33,46),(34,47),(35,48),(36,49),(37,50),(38,51),(39,52),(40,53),(61,125),(62,126),(63,127),(64,128),(65,129),(66,130),(67,131),(68,132),(69,133),(70,134),(71,135),(72,136),(73,137),(74,138),(75,139),(76,140),(77,121),(78,122),(79,123),(80,124),(81,101),(82,102),(83,103),(84,104),(85,105),(86,106),(87,107),(88,108),(89,109),(90,110),(91,111),(92,112),(93,113),(94,114),(95,115),(96,116),(97,117),(98,118),(99,119),(100,120),(141,272),(142,273),(143,274),(144,275),(145,276),(146,277),(147,278),(148,279),(149,280),(150,261),(151,262),(152,263),(153,264),(154,265),(155,266),(156,267),(157,268),(158,269),(159,270),(160,271),(181,212),(182,213),(183,214),(184,215),(185,216),(186,217),(187,218),(188,219),(189,220),(190,201),(191,202),(192,203),(193,204),(194,205),(195,206),(196,207),(197,208),(198,209),(199,210),(200,211),(221,316),(222,317),(223,318),(224,319),(225,320),(226,301),(227,302),(228,303),(229,304),(230,305),(231,306),(232,307),(233,308),(234,309),(235,310),(236,311),(237,312),(238,313),(239,314),(240,315),(241,292),(242,293),(243,294),(244,295),(245,296),(246,297),(247,298),(248,299),(249,300),(250,281),(251,282),(252,283),(253,284),(254,285),(255,286),(256,287),(257,288),(258,289),(259,290),(260,291)], [(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)], [(1,310,43,103,298,208,69,269),(2,224,44,92,299,186,70,147),(3,308,45,101,300,206,71,267),(4,222,46,90,281,184,72,145),(5,306,47,119,282,204,73,265),(6,240,48,88,283,182,74,143),(7,304,49,117,284,202,75,263),(8,238,50,86,285,200,76,141),(9,302,51,115,286,220,77,261),(10,236,52,84,287,198,78,159),(11,320,53,113,288,218,79,279),(12,234,54,82,289,196,80,157),(13,318,55,111,290,216,61,277),(14,232,56,100,291,194,62,155),(15,316,57,109,292,214,63,275),(16,230,58,98,293,192,64,153),(17,314,59,107,294,212,65,273),(18,228,60,96,295,190,66,151),(19,312,41,105,296,210,67,271),(20,226,42,94,297,188,68,149),(21,102,258,207,124,268,179,309),(22,91,259,185,125,146,180,223),(23,120,260,205,126,266,161,307),(24,89,241,183,127,144,162,221),(25,118,242,203,128,264,163,305),(26,87,243,181,129,142,164,239),(27,116,244,201,130,262,165,303),(28,85,245,199,131,160,166,237),(29,114,246,219,132,280,167,301),(30,83,247,197,133,158,168,235),(31,112,248,217,134,278,169,319),(32,81,249,195,135,156,170,233),(33,110,250,215,136,276,171,317),(34,99,251,193,137,154,172,231),(35,108,252,213,138,274,173,315),(36,97,253,191,139,152,174,229),(37,106,254,211,140,272,175,313),(38,95,255,189,121,150,176,227),(39,104,256,209,122,270,177,311),(40,93,257,187,123,148,178,225)]])
104 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4H | 4I | ··· | 4P | 5A | 5B | 8A | ··· | 8P | 10A | ··· | 10N | 20A | ··· | 20AV |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | 2 | 10 | ··· | 10 | 2 | ··· | 2 | 2 | ··· | 2 |
104 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | + | - | + | ||||||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | D4 | Q8 | D5 | M4(2) | Dic5 | D10 | C5⋊2C8 | Dic10 | C4×D5 | D20 | C5⋊D4 | C4.Dic5 |
| kernel | (C2×C20)⋊8C8 | C22×C5⋊2C8 | C2×C4×C20 | C2×C5⋊2C8 | C22×C20 | C2×C20 | C2×C20 | C2×C20 | C2×C42 | C2×C10 | C22×C4 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C2×C4 | C2×C4 | C22 |
| # reps | 1 | 2 | 1 | 8 | 4 | 16 | 3 | 1 | 2 | 4 | 4 | 2 | 16 | 4 | 8 | 4 | 8 | 16 |
Matrix representation of (C2×C20)⋊8C8 ►in GL5(𝔽41)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 5 | 0 | 0 | 0 |
| 0 | 21 | 8 | 0 | 0 |
| 0 | 0 | 0 | 32 | 11 |
| 0 | 0 | 0 | 30 | 27 |
| 3 | 0 | 0 | 0 | 0 |
| 0 | 3 | 18 | 0 | 0 |
| 0 | 4 | 38 | 0 | 0 |
| 0 | 0 | 0 | 28 | 27 |
| 0 | 0 | 0 | 18 | 13 |
G:=sub<GL(5,GF(41))| [1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,40],[40,0,0,0,0,0,5,21,0,0,0,0,8,0,0,0,0,0,32,30,0,0,0,11,27],[3,0,0,0,0,0,3,4,0,0,0,18,38,0,0,0,0,0,28,18,0,0,0,27,13] >;
(C2×C20)⋊8C8 in GAP, Magma, Sage, TeX
(C_2\times C_{20})\rtimes_8C_8 % in TeX
G:=Group("(C2xC20):8C8"); // GroupNames label
G:=SmallGroup(320,82);
// by ID
G=gap.SmallGroup(320,82);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,253,64,184,12550]);
// Polycyclic
G:=Group<a,b,c|a^2=b^20=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=a*b^9>;
// generators/relations