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