direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C40⋊5C4, C23.57D20, C22.15D40, C22.6Dic20, (C2×C40)⋊19C4, C40⋊39(C2×C4), C8⋊7(C2×Dic5), (C2×C8)⋊5Dic5, C2.2(C2×D40), (C2×C10).22D8, C10.15(C2×D8), C10⋊3(C2.D8), (C2×C4).94D20, C20.67(C4⋊C4), (C2×C20).56Q8, C20.74(C2×Q8), (C22×C8).8D5, (C2×C8).306D10, (C2×C20).387D4, (C2×C10).10Q16, C10.10(C2×Q16), C2.3(C2×Dic20), (C22×C40).14C2, C4.17(C4⋊Dic5), (C2×C4).49Dic10, C4.40(C2×Dic10), C22.51(C2×D20), (C2×C20).764C23, C20.229(C22×C4), (C2×C40).379C22, (C22×C4).424D10, (C22×C10).136D4, C4.24(C22×Dic5), C4⋊Dic5.280C22, C22.22(C4⋊Dic5), (C22×C20).516C22, C5⋊4(C2×C2.D8), C10.68(C2×C4⋊C4), C2.11(C2×C4⋊Dic5), (C2×C10).78(C4⋊C4), (C2×C20).472(C2×C4), (C2×C10).154(C2×D4), (C2×C4⋊Dic5).24C2, (C2×C4).82(C2×Dic5), (C2×C4).711(C22×D5), SmallGroup(320,732)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C40⋊5C4
G = < a,b,c | a2=b40=c4=1, ab=ba, ac=ca, cbc-1=b-1 >
Subgroups: 430 in 130 conjugacy classes, 87 normal (25 characteristic)
C1, C2, C2, C4, C4, C4, C22, C22, C5, C8, C2×C4, C2×C4, C2×C4, C23, C10, C10, C4⋊C4, C2×C8, C22×C4, C22×C4, Dic5, C20, C20, C2×C10, C2×C10, C2.D8, C2×C4⋊C4, C22×C8, C40, C2×Dic5, C2×C20, C2×C20, C22×C10, C2×C2.D8, C4⋊Dic5, C4⋊Dic5, C2×C40, C22×Dic5, C22×C20, C40⋊5C4, C2×C4⋊Dic5, C22×C40, C2×C40⋊5C4
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D5, C4⋊C4, D8, Q16, C22×C4, C2×D4, C2×Q8, Dic5, D10, C2.D8, C2×C4⋊C4, C2×D8, C2×Q16, Dic10, D20, C2×Dic5, C22×D5, C2×C2.D8, D40, Dic20, C4⋊Dic5, C2×Dic10, C2×D20, C22×Dic5, C40⋊5C4, C2×D40, C2×Dic20, C2×C4⋊Dic5, C2×C40⋊5C4
►Regular action on 320 points
Generators in S320
(1 126)(2 127)(3 128)(4 129)(5 130)(6 131)(7 132)(8 133)(9 134)(10 135)(11 136)(12 137)(13 138)(14 139)(15 140)(16 141)(17 142)(18 143)(19 144)(20 145)(21 146)(22 147)(23 148)(24 149)(25 150)(26 151)(27 152)(28 153)(29 154)(30 155)(31 156)(32 157)(33 158)(34 159)(35 160)(36 121)(37 122)(38 123)(39 124)(40 125)(41 224)(42 225)(43 226)(44 227)(45 228)(46 229)(47 230)(48 231)(49 232)(50 233)(51 234)(52 235)(53 236)(54 237)(55 238)(56 239)(57 240)(58 201)(59 202)(60 203)(61 204)(62 205)(63 206)(64 207)(65 208)(66 209)(67 210)(68 211)(69 212)(70 213)(71 214)(72 215)(73 216)(74 217)(75 218)(76 219)(77 220)(78 221)(79 222)(80 223)(81 292)(82 293)(83 294)(84 295)(85 296)(86 297)(87 298)(88 299)(89 300)(90 301)(91 302)(92 303)(93 304)(94 305)(95 306)(96 307)(97 308)(98 309)(99 310)(100 311)(101 312)(102 313)(103 314)(104 315)(105 316)(106 317)(107 318)(108 319)(109 320)(110 281)(111 282)(112 283)(113 284)(114 285)(115 286)(116 287)(117 288)(118 289)(119 290)(120 291)(161 271)(162 272)(163 273)(164 274)(165 275)(166 276)(167 277)(168 278)(169 279)(170 280)(171 241)(172 242)(173 243)(174 244)(175 245)(176 246)(177 247)(178 248)(179 249)(180 250)(181 251)(182 252)(183 253)(184 254)(185 255)(186 256)(187 257)(188 258)(189 259)(190 260)(191 261)(192 262)(193 263)(194 264)(195 265)(196 266)(197 267)(198 268)(199 269)(200 270)
(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)
(1 294 264 232)(2 293 265 231)(3 292 266 230)(4 291 267 229)(5 290 268 228)(6 289 269 227)(7 288 270 226)(8 287 271 225)(9 286 272 224)(10 285 273 223)(11 284 274 222)(12 283 275 221)(13 282 276 220)(14 281 277 219)(15 320 278 218)(16 319 279 217)(17 318 280 216)(18 317 241 215)(19 316 242 214)(20 315 243 213)(21 314 244 212)(22 313 245 211)(23 312 246 210)(24 311 247 209)(25 310 248 208)(26 309 249 207)(27 308 250 206)(28 307 251 205)(29 306 252 204)(30 305 253 203)(31 304 254 202)(32 303 255 201)(33 302 256 240)(34 301 257 239)(35 300 258 238)(36 299 259 237)(37 298 260 236)(38 297 261 235)(39 296 262 234)(40 295 263 233)(41 134 115 162)(42 133 116 161)(43 132 117 200)(44 131 118 199)(45 130 119 198)(46 129 120 197)(47 128 81 196)(48 127 82 195)(49 126 83 194)(50 125 84 193)(51 124 85 192)(52 123 86 191)(53 122 87 190)(54 121 88 189)(55 160 89 188)(56 159 90 187)(57 158 91 186)(58 157 92 185)(59 156 93 184)(60 155 94 183)(61 154 95 182)(62 153 96 181)(63 152 97 180)(64 151 98 179)(65 150 99 178)(66 149 100 177)(67 148 101 176)(68 147 102 175)(69 146 103 174)(70 145 104 173)(71 144 105 172)(72 143 106 171)(73 142 107 170)(74 141 108 169)(75 140 109 168)(76 139 110 167)(77 138 111 166)(78 137 112 165)(79 136 113 164)(80 135 114 163)
G:=sub<Sym(320)| (1,126)(2,127)(3,128)(4,129)(5,130)(6,131)(7,132)(8,133)(9,134)(10,135)(11,136)(12,137)(13,138)(14,139)(15,140)(16,141)(17,142)(18,143)(19,144)(20,145)(21,146)(22,147)(23,148)(24,149)(25,150)(26,151)(27,152)(28,153)(29,154)(30,155)(31,156)(32,157)(33,158)(34,159)(35,160)(36,121)(37,122)(38,123)(39,124)(40,125)(41,224)(42,225)(43,226)(44,227)(45,228)(46,229)(47,230)(48,231)(49,232)(50,233)(51,234)(52,235)(53,236)(54,237)(55,238)(56,239)(57,240)(58,201)(59,202)(60,203)(61,204)(62,205)(63,206)(64,207)(65,208)(66,209)(67,210)(68,211)(69,212)(70,213)(71,214)(72,215)(73,216)(74,217)(75,218)(76,219)(77,220)(78,221)(79,222)(80,223)(81,292)(82,293)(83,294)(84,295)(85,296)(86,297)(87,298)(88,299)(89,300)(90,301)(91,302)(92,303)(93,304)(94,305)(95,306)(96,307)(97,308)(98,309)(99,310)(100,311)(101,312)(102,313)(103,314)(104,315)(105,316)(106,317)(107,318)(108,319)(109,320)(110,281)(111,282)(112,283)(113,284)(114,285)(115,286)(116,287)(117,288)(118,289)(119,290)(120,291)(161,271)(162,272)(163,273)(164,274)(165,275)(166,276)(167,277)(168,278)(169,279)(170,280)(171,241)(172,242)(173,243)(174,244)(175,245)(176,246)(177,247)(178,248)(179,249)(180,250)(181,251)(182,252)(183,253)(184,254)(185,255)(186,256)(187,257)(188,258)(189,259)(190,260)(191,261)(192,262)(193,263)(194,264)(195,265)(196,266)(197,267)(198,268)(199,269)(200,270), (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), (1,294,264,232)(2,293,265,231)(3,292,266,230)(4,291,267,229)(5,290,268,228)(6,289,269,227)(7,288,270,226)(8,287,271,225)(9,286,272,224)(10,285,273,223)(11,284,274,222)(12,283,275,221)(13,282,276,220)(14,281,277,219)(15,320,278,218)(16,319,279,217)(17,318,280,216)(18,317,241,215)(19,316,242,214)(20,315,243,213)(21,314,244,212)(22,313,245,211)(23,312,246,210)(24,311,247,209)(25,310,248,208)(26,309,249,207)(27,308,250,206)(28,307,251,205)(29,306,252,204)(30,305,253,203)(31,304,254,202)(32,303,255,201)(33,302,256,240)(34,301,257,239)(35,300,258,238)(36,299,259,237)(37,298,260,236)(38,297,261,235)(39,296,262,234)(40,295,263,233)(41,134,115,162)(42,133,116,161)(43,132,117,200)(44,131,118,199)(45,130,119,198)(46,129,120,197)(47,128,81,196)(48,127,82,195)(49,126,83,194)(50,125,84,193)(51,124,85,192)(52,123,86,191)(53,122,87,190)(54,121,88,189)(55,160,89,188)(56,159,90,187)(57,158,91,186)(58,157,92,185)(59,156,93,184)(60,155,94,183)(61,154,95,182)(62,153,96,181)(63,152,97,180)(64,151,98,179)(65,150,99,178)(66,149,100,177)(67,148,101,176)(68,147,102,175)(69,146,103,174)(70,145,104,173)(71,144,105,172)(72,143,106,171)(73,142,107,170)(74,141,108,169)(75,140,109,168)(76,139,110,167)(77,138,111,166)(78,137,112,165)(79,136,113,164)(80,135,114,163)>;
G:=Group( (1,126)(2,127)(3,128)(4,129)(5,130)(6,131)(7,132)(8,133)(9,134)(10,135)(11,136)(12,137)(13,138)(14,139)(15,140)(16,141)(17,142)(18,143)(19,144)(20,145)(21,146)(22,147)(23,148)(24,149)(25,150)(26,151)(27,152)(28,153)(29,154)(30,155)(31,156)(32,157)(33,158)(34,159)(35,160)(36,121)(37,122)(38,123)(39,124)(40,125)(41,224)(42,225)(43,226)(44,227)(45,228)(46,229)(47,230)(48,231)(49,232)(50,233)(51,234)(52,235)(53,236)(54,237)(55,238)(56,239)(57,240)(58,201)(59,202)(60,203)(61,204)(62,205)(63,206)(64,207)(65,208)(66,209)(67,210)(68,211)(69,212)(70,213)(71,214)(72,215)(73,216)(74,217)(75,218)(76,219)(77,220)(78,221)(79,222)(80,223)(81,292)(82,293)(83,294)(84,295)(85,296)(86,297)(87,298)(88,299)(89,300)(90,301)(91,302)(92,303)(93,304)(94,305)(95,306)(96,307)(97,308)(98,309)(99,310)(100,311)(101,312)(102,313)(103,314)(104,315)(105,316)(106,317)(107,318)(108,319)(109,320)(110,281)(111,282)(112,283)(113,284)(114,285)(115,286)(116,287)(117,288)(118,289)(119,290)(120,291)(161,271)(162,272)(163,273)(164,274)(165,275)(166,276)(167,277)(168,278)(169,279)(170,280)(171,241)(172,242)(173,243)(174,244)(175,245)(176,246)(177,247)(178,248)(179,249)(180,250)(181,251)(182,252)(183,253)(184,254)(185,255)(186,256)(187,257)(188,258)(189,259)(190,260)(191,261)(192,262)(193,263)(194,264)(195,265)(196,266)(197,267)(198,268)(199,269)(200,270), (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), (1,294,264,232)(2,293,265,231)(3,292,266,230)(4,291,267,229)(5,290,268,228)(6,289,269,227)(7,288,270,226)(8,287,271,225)(9,286,272,224)(10,285,273,223)(11,284,274,222)(12,283,275,221)(13,282,276,220)(14,281,277,219)(15,320,278,218)(16,319,279,217)(17,318,280,216)(18,317,241,215)(19,316,242,214)(20,315,243,213)(21,314,244,212)(22,313,245,211)(23,312,246,210)(24,311,247,209)(25,310,248,208)(26,309,249,207)(27,308,250,206)(28,307,251,205)(29,306,252,204)(30,305,253,203)(31,304,254,202)(32,303,255,201)(33,302,256,240)(34,301,257,239)(35,300,258,238)(36,299,259,237)(37,298,260,236)(38,297,261,235)(39,296,262,234)(40,295,263,233)(41,134,115,162)(42,133,116,161)(43,132,117,200)(44,131,118,199)(45,130,119,198)(46,129,120,197)(47,128,81,196)(48,127,82,195)(49,126,83,194)(50,125,84,193)(51,124,85,192)(52,123,86,191)(53,122,87,190)(54,121,88,189)(55,160,89,188)(56,159,90,187)(57,158,91,186)(58,157,92,185)(59,156,93,184)(60,155,94,183)(61,154,95,182)(62,153,96,181)(63,152,97,180)(64,151,98,179)(65,150,99,178)(66,149,100,177)(67,148,101,176)(68,147,102,175)(69,146,103,174)(70,145,104,173)(71,144,105,172)(72,143,106,171)(73,142,107,170)(74,141,108,169)(75,140,109,168)(76,139,110,167)(77,138,111,166)(78,137,112,165)(79,136,113,164)(80,135,114,163) );
G=PermutationGroup([[(1,126),(2,127),(3,128),(4,129),(5,130),(6,131),(7,132),(8,133),(9,134),(10,135),(11,136),(12,137),(13,138),(14,139),(15,140),(16,141),(17,142),(18,143),(19,144),(20,145),(21,146),(22,147),(23,148),(24,149),(25,150),(26,151),(27,152),(28,153),(29,154),(30,155),(31,156),(32,157),(33,158),(34,159),(35,160),(36,121),(37,122),(38,123),(39,124),(40,125),(41,224),(42,225),(43,226),(44,227),(45,228),(46,229),(47,230),(48,231),(49,232),(50,233),(51,234),(52,235),(53,236),(54,237),(55,238),(56,239),(57,240),(58,201),(59,202),(60,203),(61,204),(62,205),(63,206),(64,207),(65,208),(66,209),(67,210),(68,211),(69,212),(70,213),(71,214),(72,215),(73,216),(74,217),(75,218),(76,219),(77,220),(78,221),(79,222),(80,223),(81,292),(82,293),(83,294),(84,295),(85,296),(86,297),(87,298),(88,299),(89,300),(90,301),(91,302),(92,303),(93,304),(94,305),(95,306),(96,307),(97,308),(98,309),(99,310),(100,311),(101,312),(102,313),(103,314),(104,315),(105,316),(106,317),(107,318),(108,319),(109,320),(110,281),(111,282),(112,283),(113,284),(114,285),(115,286),(116,287),(117,288),(118,289),(119,290),(120,291),(161,271),(162,272),(163,273),(164,274),(165,275),(166,276),(167,277),(168,278),(169,279),(170,280),(171,241),(172,242),(173,243),(174,244),(175,245),(176,246),(177,247),(178,248),(179,249),(180,250),(181,251),(182,252),(183,253),(184,254),(185,255),(186,256),(187,257),(188,258),(189,259),(190,260),(191,261),(192,262),(193,263),(194,264),(195,265),(196,266),(197,267),(198,268),(199,269),(200,270)], [(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)], [(1,294,264,232),(2,293,265,231),(3,292,266,230),(4,291,267,229),(5,290,268,228),(6,289,269,227),(7,288,270,226),(8,287,271,225),(9,286,272,224),(10,285,273,223),(11,284,274,222),(12,283,275,221),(13,282,276,220),(14,281,277,219),(15,320,278,218),(16,319,279,217),(17,318,280,216),(18,317,241,215),(19,316,242,214),(20,315,243,213),(21,314,244,212),(22,313,245,211),(23,312,246,210),(24,311,247,209),(25,310,248,208),(26,309,249,207),(27,308,250,206),(28,307,251,205),(29,306,252,204),(30,305,253,203),(31,304,254,202),(32,303,255,201),(33,302,256,240),(34,301,257,239),(35,300,258,238),(36,299,259,237),(37,298,260,236),(38,297,261,235),(39,296,262,234),(40,295,263,233),(41,134,115,162),(42,133,116,161),(43,132,117,200),(44,131,118,199),(45,130,119,198),(46,129,120,197),(47,128,81,196),(48,127,82,195),(49,126,83,194),(50,125,84,193),(51,124,85,192),(52,123,86,191),(53,122,87,190),(54,121,88,189),(55,160,89,188),(56,159,90,187),(57,158,91,186),(58,157,92,185),(59,156,93,184),(60,155,94,183),(61,154,95,182),(62,153,96,181),(63,152,97,180),(64,151,98,179),(65,150,99,178),(66,149,100,177),(67,148,101,176),(68,147,102,175),(69,146,103,174),(70,145,104,173),(71,144,105,172),(72,143,106,171),(73,142,107,170),(74,141,108,169),(75,140,109,168),(76,139,110,167),(77,138,111,166),(78,137,112,165),(79,136,113,164),(80,135,114,163)]])
92 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 5A | 5B | 8A | ··· | 8H | 10A | ··· | 10N | 20A | ··· | 20P | 40A | ··· | 40AF |
| order | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
92 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | + | + | - | - | + | + | - | + | + | + | - | |
| image | C1 | C2 | C2 | C2 | C4 | D4 | Q8 | D4 | D5 | D8 | Q16 | Dic5 | D10 | D10 | Dic10 | D20 | D20 | D40 | Dic20 |
| kernel | C2×C40⋊5C4 | C40⋊5C4 | C2×C4⋊Dic5 | C22×C40 | C2×C40 | C2×C20 | C2×C20 | C22×C10 | C22×C8 | C2×C10 | C2×C10 | C2×C8 | C2×C8 | C22×C4 | C2×C4 | C2×C4 | C23 | C22 | C22 |
| # reps | 1 | 4 | 2 | 1 | 8 | 1 | 2 | 1 | 2 | 4 | 4 | 8 | 4 | 2 | 8 | 4 | 4 | 16 | 16 |
Matrix representation of C2×C40⋊5C4 ►in GL4(𝔽41) generated by
| 40 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 |
| 0 | 0 | 18 | 3 |
| 0 | 0 | 38 | 36 |
| 32 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 18 | 35 |
| 0 | 0 | 20 | 23 |
G:=sub<GL(4,GF(41))| [40,0,0,0,0,40,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,40,0,0,0,0,18,38,0,0,3,36],[32,0,0,0,0,1,0,0,0,0,18,20,0,0,35,23] >;
C2×C40⋊5C4 in GAP, Magma, Sage, TeX
C_2\times C_{40}\rtimes_5C_4 % in TeX
G:=Group("C2xC40:5C4"); // GroupNames label
G:=SmallGroup(320,732);
// by ID
G=gap.SmallGroup(320,732);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,422,268,1684,102,12550]);
// Polycyclic
G:=Group<a,b,c|a^2=b^40=c^4=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations