direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C20⋊C8, C20⋊8(C2×C8), (C2×C20)⋊3C8, C10⋊1(C4⋊C8), (C22×C4).19F5, C23.58(C2×F5), (C22×C20).22C4, C10.19(C22×C8), (C4×Dic5).37C4, Dic5.17(C2×Q8), (C2×Dic5).36Q8, Dic5.35(C2×D4), (C2×C10).7M4(2), C22.26(C4⋊F5), C22.8(C4.F5), Dic5.34(C4⋊C4), (C2×Dic5).178D4, C10.17(C2×M4(2)), C22.41(C22×F5), (C22×Dic5).27C4, (C2×Dic5).338C23, (C4×Dic5).346C22, (C22×Dic5).266C22, C4⋊2(C2×C5⋊C8), C5⋊2(C2×C4⋊C8), (C2×C4)⋊3(C5⋊C8), C2.3(C2×C4⋊F5), C2.4(C22×C5⋊C8), C10.19(C2×C4⋊C4), C2.3(C2×C4.F5), (C22×C5⋊C8).4C2, C22.14(C2×C5⋊C8), (C2×C10).34(C2×C8), (C2×C5⋊C8).33C22, (C2×C4).142(C2×F5), (C2×C4×Dic5).46C2, (C2×C10).25(C4⋊C4), (C2×C20).130(C2×C4), (C22×C10).54(C2×C4), (C2×C10).54(C22×C4), (C2×Dic5).178(C2×C4), SmallGroup(320,1085)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C20⋊C8
G = < a,b,c | a2=b20=c8=1, ab=ba, ac=ca, cbc-1=b3 >
Subgroups: 378 in 138 conjugacy classes, 84 normal (22 characteristic)
C1, C2, C2, C4, C4, C22, C22, C5, C8, C2×C4, C2×C4, C23, C10, C10, C42, C2×C8, C22×C4, C22×C4, Dic5, Dic5, Dic5, C20, C2×C10, C2×C10, C4⋊C8, C2×C42, C22×C8, C5⋊C8, C2×Dic5, C2×Dic5, C2×Dic5, C2×C20, C22×C10, C2×C4⋊C8, C4×Dic5, C2×C5⋊C8, C2×C5⋊C8, C22×Dic5, C22×C20, C20⋊C8, C2×C4×Dic5, C22×C5⋊C8, C2×C20⋊C8
Quotients: C1, C2, C4, C22, C8, C2×C4, D4, Q8, C23, C4⋊C4, C2×C8, M4(2), C22×C4, C2×D4, C2×Q8, F5, C4⋊C8, C2×C4⋊C4, C22×C8, C2×M4(2), C5⋊C8, C2×F5, C2×C4⋊C8, C4.F5, C4⋊F5, C2×C5⋊C8, C22×F5, C20⋊C8, C2×C4.F5, C2×C4⋊F5, C22×C5⋊C8, C2×C20⋊C8
►Regular action on 320 points
Generators in S320
(1 189)(2 190)(3 191)(4 192)(5 193)(6 194)(7 195)(8 196)(9 197)(10 198)(11 199)(12 200)(13 181)(14 182)(15 183)(16 184)(17 185)(18 186)(19 187)(20 188)(21 148)(22 149)(23 150)(24 151)(25 152)(26 153)(27 154)(28 155)(29 156)(30 157)(31 158)(32 159)(33 160)(34 141)(35 142)(36 143)(37 144)(38 145)(39 146)(40 147)(41 313)(42 314)(43 315)(44 316)(45 317)(46 318)(47 319)(48 320)(49 301)(50 302)(51 303)(52 304)(53 305)(54 306)(55 307)(56 308)(57 309)(58 310)(59 311)(60 312)(61 95)(62 96)(63 97)(64 98)(65 99)(66 100)(67 81)(68 82)(69 83)(70 84)(71 85)(72 86)(73 87)(74 88)(75 89)(76 90)(77 91)(78 92)(79 93)(80 94)(101 287)(102 288)(103 289)(104 290)(105 291)(106 292)(107 293)(108 294)(109 295)(110 296)(111 297)(112 298)(113 299)(114 300)(115 281)(116 282)(117 283)(118 284)(119 285)(120 286)(121 244)(122 245)(123 246)(124 247)(125 248)(126 249)(127 250)(128 251)(129 252)(130 253)(131 254)(132 255)(133 256)(134 257)(135 258)(136 259)(137 260)(138 241)(139 242)(140 243)(161 230)(162 231)(163 232)(164 233)(165 234)(166 235)(167 236)(168 237)(169 238)(170 239)(171 240)(172 221)(173 222)(174 223)(175 224)(176 225)(177 226)(178 227)(179 228)(180 229)(201 265)(202 266)(203 267)(204 268)(205 269)(206 270)(207 271)(208 272)(209 273)(210 274)(211 275)(212 276)(213 277)(214 278)(215 279)(216 280)(217 261)(218 262)(219 263)(220 264)
(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)
(1 314 230 96 243 289 36 207)(2 301 239 99 244 296 25 210)(3 308 228 82 245 283 34 213)(4 315 237 85 246 290 23 216)(5 302 226 88 247 297 32 219)(6 309 235 91 248 284 21 202)(7 316 224 94 249 291 30 205)(8 303 233 97 250 298 39 208)(9 310 222 100 251 285 28 211)(10 317 231 83 252 292 37 214)(11 304 240 86 253 299 26 217)(12 311 229 89 254 286 35 220)(13 318 238 92 255 293 24 203)(14 305 227 95 256 300 33 206)(15 312 236 98 257 287 22 209)(16 319 225 81 258 294 31 212)(17 306 234 84 259 281 40 215)(18 313 223 87 260 288 29 218)(19 320 232 90 241 295 38 201)(20 307 221 93 242 282 27 204)(41 174 73 137 102 156 262 186)(42 161 62 140 103 143 271 189)(43 168 71 123 104 150 280 192)(44 175 80 126 105 157 269 195)(45 162 69 129 106 144 278 198)(46 169 78 132 107 151 267 181)(47 176 67 135 108 158 276 184)(48 163 76 138 109 145 265 187)(49 170 65 121 110 152 274 190)(50 177 74 124 111 159 263 193)(51 164 63 127 112 146 272 196)(52 171 72 130 113 153 261 199)(53 178 61 133 114 160 270 182)(54 165 70 136 115 147 279 185)(55 172 79 139 116 154 268 188)(56 179 68 122 117 141 277 191)(57 166 77 125 118 148 266 194)(58 173 66 128 119 155 275 197)(59 180 75 131 120 142 264 200)(60 167 64 134 101 149 273 183)
G:=sub<Sym(320)| (1,189)(2,190)(3,191)(4,192)(5,193)(6,194)(7,195)(8,196)(9,197)(10,198)(11,199)(12,200)(13,181)(14,182)(15,183)(16,184)(17,185)(18,186)(19,187)(20,188)(21,148)(22,149)(23,150)(24,151)(25,152)(26,153)(27,154)(28,155)(29,156)(30,157)(31,158)(32,159)(33,160)(34,141)(35,142)(36,143)(37,144)(38,145)(39,146)(40,147)(41,313)(42,314)(43,315)(44,316)(45,317)(46,318)(47,319)(48,320)(49,301)(50,302)(51,303)(52,304)(53,305)(54,306)(55,307)(56,308)(57,309)(58,310)(59,311)(60,312)(61,95)(62,96)(63,97)(64,98)(65,99)(66,100)(67,81)(68,82)(69,83)(70,84)(71,85)(72,86)(73,87)(74,88)(75,89)(76,90)(77,91)(78,92)(79,93)(80,94)(101,287)(102,288)(103,289)(104,290)(105,291)(106,292)(107,293)(108,294)(109,295)(110,296)(111,297)(112,298)(113,299)(114,300)(115,281)(116,282)(117,283)(118,284)(119,285)(120,286)(121,244)(122,245)(123,246)(124,247)(125,248)(126,249)(127,250)(128,251)(129,252)(130,253)(131,254)(132,255)(133,256)(134,257)(135,258)(136,259)(137,260)(138,241)(139,242)(140,243)(161,230)(162,231)(163,232)(164,233)(165,234)(166,235)(167,236)(168,237)(169,238)(170,239)(171,240)(172,221)(173,222)(174,223)(175,224)(176,225)(177,226)(178,227)(179,228)(180,229)(201,265)(202,266)(203,267)(204,268)(205,269)(206,270)(207,271)(208,272)(209,273)(210,274)(211,275)(212,276)(213,277)(214,278)(215,279)(216,280)(217,261)(218,262)(219,263)(220,264), (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), (1,314,230,96,243,289,36,207)(2,301,239,99,244,296,25,210)(3,308,228,82,245,283,34,213)(4,315,237,85,246,290,23,216)(5,302,226,88,247,297,32,219)(6,309,235,91,248,284,21,202)(7,316,224,94,249,291,30,205)(8,303,233,97,250,298,39,208)(9,310,222,100,251,285,28,211)(10,317,231,83,252,292,37,214)(11,304,240,86,253,299,26,217)(12,311,229,89,254,286,35,220)(13,318,238,92,255,293,24,203)(14,305,227,95,256,300,33,206)(15,312,236,98,257,287,22,209)(16,319,225,81,258,294,31,212)(17,306,234,84,259,281,40,215)(18,313,223,87,260,288,29,218)(19,320,232,90,241,295,38,201)(20,307,221,93,242,282,27,204)(41,174,73,137,102,156,262,186)(42,161,62,140,103,143,271,189)(43,168,71,123,104,150,280,192)(44,175,80,126,105,157,269,195)(45,162,69,129,106,144,278,198)(46,169,78,132,107,151,267,181)(47,176,67,135,108,158,276,184)(48,163,76,138,109,145,265,187)(49,170,65,121,110,152,274,190)(50,177,74,124,111,159,263,193)(51,164,63,127,112,146,272,196)(52,171,72,130,113,153,261,199)(53,178,61,133,114,160,270,182)(54,165,70,136,115,147,279,185)(55,172,79,139,116,154,268,188)(56,179,68,122,117,141,277,191)(57,166,77,125,118,148,266,194)(58,173,66,128,119,155,275,197)(59,180,75,131,120,142,264,200)(60,167,64,134,101,149,273,183)>;
G:=Group( (1,189)(2,190)(3,191)(4,192)(5,193)(6,194)(7,195)(8,196)(9,197)(10,198)(11,199)(12,200)(13,181)(14,182)(15,183)(16,184)(17,185)(18,186)(19,187)(20,188)(21,148)(22,149)(23,150)(24,151)(25,152)(26,153)(27,154)(28,155)(29,156)(30,157)(31,158)(32,159)(33,160)(34,141)(35,142)(36,143)(37,144)(38,145)(39,146)(40,147)(41,313)(42,314)(43,315)(44,316)(45,317)(46,318)(47,319)(48,320)(49,301)(50,302)(51,303)(52,304)(53,305)(54,306)(55,307)(56,308)(57,309)(58,310)(59,311)(60,312)(61,95)(62,96)(63,97)(64,98)(65,99)(66,100)(67,81)(68,82)(69,83)(70,84)(71,85)(72,86)(73,87)(74,88)(75,89)(76,90)(77,91)(78,92)(79,93)(80,94)(101,287)(102,288)(103,289)(104,290)(105,291)(106,292)(107,293)(108,294)(109,295)(110,296)(111,297)(112,298)(113,299)(114,300)(115,281)(116,282)(117,283)(118,284)(119,285)(120,286)(121,244)(122,245)(123,246)(124,247)(125,248)(126,249)(127,250)(128,251)(129,252)(130,253)(131,254)(132,255)(133,256)(134,257)(135,258)(136,259)(137,260)(138,241)(139,242)(140,243)(161,230)(162,231)(163,232)(164,233)(165,234)(166,235)(167,236)(168,237)(169,238)(170,239)(171,240)(172,221)(173,222)(174,223)(175,224)(176,225)(177,226)(178,227)(179,228)(180,229)(201,265)(202,266)(203,267)(204,268)(205,269)(206,270)(207,271)(208,272)(209,273)(210,274)(211,275)(212,276)(213,277)(214,278)(215,279)(216,280)(217,261)(218,262)(219,263)(220,264), (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), (1,314,230,96,243,289,36,207)(2,301,239,99,244,296,25,210)(3,308,228,82,245,283,34,213)(4,315,237,85,246,290,23,216)(5,302,226,88,247,297,32,219)(6,309,235,91,248,284,21,202)(7,316,224,94,249,291,30,205)(8,303,233,97,250,298,39,208)(9,310,222,100,251,285,28,211)(10,317,231,83,252,292,37,214)(11,304,240,86,253,299,26,217)(12,311,229,89,254,286,35,220)(13,318,238,92,255,293,24,203)(14,305,227,95,256,300,33,206)(15,312,236,98,257,287,22,209)(16,319,225,81,258,294,31,212)(17,306,234,84,259,281,40,215)(18,313,223,87,260,288,29,218)(19,320,232,90,241,295,38,201)(20,307,221,93,242,282,27,204)(41,174,73,137,102,156,262,186)(42,161,62,140,103,143,271,189)(43,168,71,123,104,150,280,192)(44,175,80,126,105,157,269,195)(45,162,69,129,106,144,278,198)(46,169,78,132,107,151,267,181)(47,176,67,135,108,158,276,184)(48,163,76,138,109,145,265,187)(49,170,65,121,110,152,274,190)(50,177,74,124,111,159,263,193)(51,164,63,127,112,146,272,196)(52,171,72,130,113,153,261,199)(53,178,61,133,114,160,270,182)(54,165,70,136,115,147,279,185)(55,172,79,139,116,154,268,188)(56,179,68,122,117,141,277,191)(57,166,77,125,118,148,266,194)(58,173,66,128,119,155,275,197)(59,180,75,131,120,142,264,200)(60,167,64,134,101,149,273,183) );
G=PermutationGroup([[(1,189),(2,190),(3,191),(4,192),(5,193),(6,194),(7,195),(8,196),(9,197),(10,198),(11,199),(12,200),(13,181),(14,182),(15,183),(16,184),(17,185),(18,186),(19,187),(20,188),(21,148),(22,149),(23,150),(24,151),(25,152),(26,153),(27,154),(28,155),(29,156),(30,157),(31,158),(32,159),(33,160),(34,141),(35,142),(36,143),(37,144),(38,145),(39,146),(40,147),(41,313),(42,314),(43,315),(44,316),(45,317),(46,318),(47,319),(48,320),(49,301),(50,302),(51,303),(52,304),(53,305),(54,306),(55,307),(56,308),(57,309),(58,310),(59,311),(60,312),(61,95),(62,96),(63,97),(64,98),(65,99),(66,100),(67,81),(68,82),(69,83),(70,84),(71,85),(72,86),(73,87),(74,88),(75,89),(76,90),(77,91),(78,92),(79,93),(80,94),(101,287),(102,288),(103,289),(104,290),(105,291),(106,292),(107,293),(108,294),(109,295),(110,296),(111,297),(112,298),(113,299),(114,300),(115,281),(116,282),(117,283),(118,284),(119,285),(120,286),(121,244),(122,245),(123,246),(124,247),(125,248),(126,249),(127,250),(128,251),(129,252),(130,253),(131,254),(132,255),(133,256),(134,257),(135,258),(136,259),(137,260),(138,241),(139,242),(140,243),(161,230),(162,231),(163,232),(164,233),(165,234),(166,235),(167,236),(168,237),(169,238),(170,239),(171,240),(172,221),(173,222),(174,223),(175,224),(176,225),(177,226),(178,227),(179,228),(180,229),(201,265),(202,266),(203,267),(204,268),(205,269),(206,270),(207,271),(208,272),(209,273),(210,274),(211,275),(212,276),(213,277),(214,278),(215,279),(216,280),(217,261),(218,262),(219,263),(220,264)], [(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)], [(1,314,230,96,243,289,36,207),(2,301,239,99,244,296,25,210),(3,308,228,82,245,283,34,213),(4,315,237,85,246,290,23,216),(5,302,226,88,247,297,32,219),(6,309,235,91,248,284,21,202),(7,316,224,94,249,291,30,205),(8,303,233,97,250,298,39,208),(9,310,222,100,251,285,28,211),(10,317,231,83,252,292,37,214),(11,304,240,86,253,299,26,217),(12,311,229,89,254,286,35,220),(13,318,238,92,255,293,24,203),(14,305,227,95,256,300,33,206),(15,312,236,98,257,287,22,209),(16,319,225,81,258,294,31,212),(17,306,234,84,259,281,40,215),(18,313,223,87,260,288,29,218),(19,320,232,90,241,295,38,201),(20,307,221,93,242,282,27,204),(41,174,73,137,102,156,262,186),(42,161,62,140,103,143,271,189),(43,168,71,123,104,150,280,192),(44,175,80,126,105,157,269,195),(45,162,69,129,106,144,278,198),(46,169,78,132,107,151,267,181),(47,176,67,135,108,158,276,184),(48,163,76,138,109,145,265,187),(49,170,65,121,110,152,274,190),(50,177,74,124,111,159,263,193),(51,164,63,127,112,146,272,196),(52,171,72,130,113,153,261,199),(53,178,61,133,114,160,270,182),(54,165,70,136,115,147,279,185),(55,172,79,139,116,154,268,188),(56,179,68,122,117,141,277,191),(57,166,77,125,118,148,266,194),(58,173,66,128,119,155,275,197),(59,180,75,131,120,142,264,200),(60,167,64,134,101,149,273,183)]])
56 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 4M | 4N | 4O | 4P | 5 | 8A | ··· | 8P | 10A | ··· | 10G | 20A | ··· | 20H |
| order | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 5 | ··· | 5 | 10 | 10 | 10 | 10 | 4 | 10 | ··· | 10 | 4 | ··· | 4 | 4 | ··· | 4 |
56 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | - | + | - | + | + | |||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | C4 | C8 | D4 | Q8 | M4(2) | F5 | C5⋊C8 | C2×F5 | C2×F5 | C4.F5 | C4⋊F5 |
| kernel | C2×C20⋊C8 | C20⋊C8 | C2×C4×Dic5 | C22×C5⋊C8 | C4×Dic5 | C22×Dic5 | C22×C20 | C2×C20 | C2×Dic5 | C2×Dic5 | C2×C10 | C22×C4 | C2×C4 | C2×C4 | C23 | C22 | C22 |
| # reps | 1 | 4 | 1 | 2 | 4 | 2 | 2 | 16 | 2 | 2 | 4 | 1 | 4 | 2 | 1 | 4 | 4 |
Matrix representation of C2×C20⋊C8 ►in GL8(𝔽41)
| 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 40 | 2 | 0 | 0 | 0 | 0 | 0 | 0 |
| 40 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 34 | 14 | 0 |
| 0 | 0 | 0 | 0 | 34 | 0 | 7 | 14 |
| 0 | 0 | 0 | 0 | 34 | 27 | 14 | 7 |
| 0 | 0 | 0 | 0 | 7 | 27 | 0 | 14 |
| 22 | 40 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 19 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 14 | 38 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 2 | 9 | 39 |
| 0 | 0 | 0 | 0 | 14 | 0 | 36 | 3 |
| 0 | 0 | 0 | 0 | 0 | 5 | 38 | 12 |
| 0 | 0 | 0 | 0 | 2 | 14 | 36 | 39 |
G:=sub<GL(8,GF(41))| [40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[40,40,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,0,6,9,0,0,0,0,0,0,5,35,0,0,0,0,0,0,0,0,7,34,34,7,0,0,0,0,34,0,27,27,0,0,0,0,14,7,14,0,0,0,0,0,0,14,7,14],[22,1,0,0,0,0,0,0,40,19,0,0,0,0,0,0,0,0,3,14,0,0,0,0,0,0,11,38,0,0,0,0,0,0,0,0,5,14,0,2,0,0,0,0,2,0,5,14,0,0,0,0,9,36,38,36,0,0,0,0,39,3,12,39] >;
C2×C20⋊C8 in GAP, Magma, Sage, TeX
C_2\times C_{20}\rtimes C_8 % in TeX
G:=Group("C2xC20:C8"); // GroupNames label
G:=SmallGroup(320,1085);
// by ID
G=gap.SmallGroup(320,1085);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,422,100,136,6278,1595]);
// 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=b^3>;
// generators/relations