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## G = C2×C20⋊C8order 320 = 26·5

### Direct product of C2 and C20⋊C8

Series: Derived Chief Lower central Upper central

 Derived series C1 — C10 — C2×C20⋊C8
 Chief series C1 — C5 — C10 — Dic5 — C2×Dic5 — C2×C5⋊C8 — C22×C5⋊C8 — C2×C20⋊C8
 Lower central C5 — C10 — C2×C20⋊C8
 Upper central C1 — C23 — C22×C4

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 [×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

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

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

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

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

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

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