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G = (C2×C20)⋊8C8order 320 = 26·5

1st semidirect product of C2×C20 and C8 acting via C8/C4=C2

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(C203C8), (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), C53(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×C52C8), (C2×C4×C20).24C2, (C2×C52C8)⋊12C4, (C2×C4)⋊2(C52C8), (C2×C10).56(C2×C8), (C2×C4).170(C4×D5), (C2×C10).62(C4⋊C4), (C2×C20).417(C2×C4), C22.10(C2×C52C8), (C2×C4).267(C5⋊D4), (C22×C52C8).15C2, (C22×C10).190(C2×C4), (C2×C10).148(C22⋊C4), SmallGroup(320,82)

Series: Derived Chief Lower central Upper central

C1C10 — (C2×C20)⋊8C8
C1C5C10C20C2×C20C22×C20C22×C52C8 — (C2×C20)⋊8C8
C5C10 — (C2×C20)⋊8C8
C1C22×C4C2×C42

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 [×3], C2 [×4], C4 [×4], C4 [×4], C22 [×3], C22 [×4], C5, C8 [×4], C2×C4 [×2], C2×C4 [×8], C2×C4 [×4], C23, C10 [×3], C10 [×4], C42 [×2], C2×C8 [×8], C22×C4, C22×C4 [×2], C20 [×4], C20 [×4], C2×C10 [×3], C2×C10 [×4], C2×C42, C22×C8 [×2], C52C8 [×4], C2×C20 [×2], C2×C20 [×8], C2×C20 [×4], C22×C10, C22.7C42, C2×C52C8 [×4], C2×C52C8 [×4], C4×C20 [×2], C22×C20, C22×C20 [×2], C22×C52C8 [×2], C2×C4×C20, (C2×C20)⋊8C8
Quotients: C1, C2 [×3], C4 [×6], C22, C8 [×4], C2×C4 [×3], D4 [×3], Q8, D5, C42, C22⋊C4 [×3], C4⋊C4 [×3], C2×C8 [×2], M4(2) [×2], Dic5 [×2], D10, C2.C42, C4×C8, C8⋊C4, C22⋊C8 [×2], C4⋊C8 [×2], C52C8 [×4], Dic10, C4×D5 [×2], D20, C2×Dic5, C5⋊D4 [×2], C22.7C42, C2×C52C8 [×2], C4.Dic5 [×2], C4×Dic5, C10.D4 [×2], C4⋊Dic5, D10⋊C4 [×2], C23.D5, C4×C52C8, C42.D5, C203C8 [×2], C20.55D4 [×2], C10.10C42, (C2×C20)⋊8C8

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

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

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

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

104 conjugacy classes

class 1 2A···2G4A···4H4I···4P5A5B8A···8P10A···10N20A···20AV
order12···24···44···4558···810···1020···20
size11···11···12···22210···102···22···2

104 irreducible representations

dim111111222222222222
type++++-+-+-+
imageC1C2C2C4C4C8D4Q8D5M4(2)Dic5D10C52C8Dic10C4×D5D20C5⋊D4C4.Dic5
kernel(C2×C20)⋊8C8C22×C52C8C2×C4×C20C2×C52C8C22×C20C2×C20C2×C20C2×C20C2×C42C2×C10C22×C4C22×C4C2×C4C2×C4C2×C4C2×C4C2×C4C22
# reps121841631244216484816

Matrix representation of (C2×C20)⋊8C8 in GL5(𝔽41)

10000
01000
00100
000400
000040
,
400000
05000
021800
0003211
0003027
,
30000
031800
043800
0002827
0001813

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

׿
×
𝔽