direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C5⋊C32, C10⋊C32, C40.3C8, C20.3C16, C5⋊2(C2×C32), C8.5(C5⋊C8), C4.3(C5⋊C16), (C2×C20).8C8, C8.39(C2×F5), (C2×C8).21F5, C5⋊2C16.5C4, C10.8(C2×C16), C20.45(C2×C8), (C2×C10).1C16, C40.36(C2×C4), (C2×C40).16C4, C22.2(C5⋊C16), C5⋊2C16.15C22, C4.10(C2×C5⋊C8), C2.2(C2×C5⋊C16), (C2×C4).8(C5⋊C8), (C2×C5⋊2C16).11C2, SmallGroup(320,214)
Series: Derived ►Chief ►Lower central ►Upper central
| C5 — C2×C5⋊C32 |
Generators and relations for C2×C5⋊C32
G = < a,b,c | a2=b5=c32=1, ab=ba, ac=ca, cbc-1=b3 >
Smallest permutation representation of C2×C5⋊C32
►Regular action on 320 points
Generators in S320
(1 94)(2 95)(3 96)(4 65)(5 66)(6 67)(7 68)(8 69)(9 70)(10 71)(11 72)(12 73)(13 74)(14 75)(15 76)(16 77)(17 78)(18 79)(19 80)(20 81)(21 82)(22 83)(23 84)(24 85)(25 86)(26 87)(27 88)(28 89)(29 90)(30 91)(31 92)(32 93)(33 270)(34 271)(35 272)(36 273)(37 274)(38 275)(39 276)(40 277)(41 278)(42 279)(43 280)(44 281)(45 282)(46 283)(47 284)(48 285)(49 286)(50 287)(51 288)(52 257)(53 258)(54 259)(55 260)(56 261)(57 262)(58 263)(59 264)(60 265)(61 266)(62 267)(63 268)(64 269)(97 215)(98 216)(99 217)(100 218)(101 219)(102 220)(103 221)(104 222)(105 223)(106 224)(107 193)(108 194)(109 195)(110 196)(111 197)(112 198)(113 199)(114 200)(115 201)(116 202)(117 203)(118 204)(119 205)(120 206)(121 207)(122 208)(123 209)(124 210)(125 211)(126 212)(127 213)(128 214)(129 289)(130 290)(131 291)(132 292)(133 293)(134 294)(135 295)(136 296)(137 297)(138 298)(139 299)(140 300)(141 301)(142 302)(143 303)(144 304)(145 305)(146 306)(147 307)(148 308)(149 309)(150 310)(151 311)(152 312)(153 313)(154 314)(155 315)(156 316)(157 317)(158 318)(159 319)(160 320)(161 245)(162 246)(163 247)(164 248)(165 249)(166 250)(167 251)(168 252)(169 253)(170 254)(171 255)(172 256)(173 225)(174 226)(175 227)(176 228)(177 229)(178 230)(179 231)(180 232)(181 233)(182 234)(183 235)(184 236)(185 237)(186 238)(187 239)(188 240)(189 241)(190 242)(191 243)(192 244)
(1 144 187 258 114)(2 259 145 115 188)(3 116 260 189 146)(4 190 117 147 261)(5 148 191 262 118)(6 263 149 119 192)(7 120 264 161 150)(8 162 121 151 265)(9 152 163 266 122)(10 267 153 123 164)(11 124 268 165 154)(12 166 125 155 269)(13 156 167 270 126)(14 271 157 127 168)(15 128 272 169 158)(16 170 97 159 273)(17 160 171 274 98)(18 275 129 99 172)(19 100 276 173 130)(20 174 101 131 277)(21 132 175 278 102)(22 279 133 103 176)(23 104 280 177 134)(24 178 105 135 281)(25 136 179 282 106)(26 283 137 107 180)(27 108 284 181 138)(28 182 109 139 285)(29 140 183 286 110)(30 287 141 111 184)(31 112 288 185 142)(32 186 113 143 257)(33 212 74 316 251)(34 317 213 252 75)(35 253 318 76 214)(36 77 254 215 319)(37 216 78 320 255)(38 289 217 256 79)(39 225 290 80 218)(40 81 226 219 291)(41 220 82 292 227)(42 293 221 228 83)(43 229 294 84 222)(44 85 230 223 295)(45 224 86 296 231)(46 297 193 232 87)(47 233 298 88 194)(48 89 234 195 299)(49 196 90 300 235)(50 301 197 236 91)(51 237 302 92 198)(52 93 238 199 303)(53 200 94 304 239)(54 305 201 240 95)(55 241 306 96 202)(56 65 242 203 307)(57 204 66 308 243)(58 309 205 244 67)(59 245 310 68 206)(60 69 246 207 311)(61 208 70 312 247)(62 313 209 248 71)(63 249 314 72 210)(64 73 250 211 315)
(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)
G:=sub<Sym(320)| (1,94)(2,95)(3,96)(4,65)(5,66)(6,67)(7,68)(8,69)(9,70)(10,71)(11,72)(12,73)(13,74)(14,75)(15,76)(16,77)(17,78)(18,79)(19,80)(20,81)(21,82)(22,83)(23,84)(24,85)(25,86)(26,87)(27,88)(28,89)(29,90)(30,91)(31,92)(32,93)(33,270)(34,271)(35,272)(36,273)(37,274)(38,275)(39,276)(40,277)(41,278)(42,279)(43,280)(44,281)(45,282)(46,283)(47,284)(48,285)(49,286)(50,287)(51,288)(52,257)(53,258)(54,259)(55,260)(56,261)(57,262)(58,263)(59,264)(60,265)(61,266)(62,267)(63,268)(64,269)(97,215)(98,216)(99,217)(100,218)(101,219)(102,220)(103,221)(104,222)(105,223)(106,224)(107,193)(108,194)(109,195)(110,196)(111,197)(112,198)(113,199)(114,200)(115,201)(116,202)(117,203)(118,204)(119,205)(120,206)(121,207)(122,208)(123,209)(124,210)(125,211)(126,212)(127,213)(128,214)(129,289)(130,290)(131,291)(132,292)(133,293)(134,294)(135,295)(136,296)(137,297)(138,298)(139,299)(140,300)(141,301)(142,302)(143,303)(144,304)(145,305)(146,306)(147,307)(148,308)(149,309)(150,310)(151,311)(152,312)(153,313)(154,314)(155,315)(156,316)(157,317)(158,318)(159,319)(160,320)(161,245)(162,246)(163,247)(164,248)(165,249)(166,250)(167,251)(168,252)(169,253)(170,254)(171,255)(172,256)(173,225)(174,226)(175,227)(176,228)(177,229)(178,230)(179,231)(180,232)(181,233)(182,234)(183,235)(184,236)(185,237)(186,238)(187,239)(188,240)(189,241)(190,242)(191,243)(192,244), (1,144,187,258,114)(2,259,145,115,188)(3,116,260,189,146)(4,190,117,147,261)(5,148,191,262,118)(6,263,149,119,192)(7,120,264,161,150)(8,162,121,151,265)(9,152,163,266,122)(10,267,153,123,164)(11,124,268,165,154)(12,166,125,155,269)(13,156,167,270,126)(14,271,157,127,168)(15,128,272,169,158)(16,170,97,159,273)(17,160,171,274,98)(18,275,129,99,172)(19,100,276,173,130)(20,174,101,131,277)(21,132,175,278,102)(22,279,133,103,176)(23,104,280,177,134)(24,178,105,135,281)(25,136,179,282,106)(26,283,137,107,180)(27,108,284,181,138)(28,182,109,139,285)(29,140,183,286,110)(30,287,141,111,184)(31,112,288,185,142)(32,186,113,143,257)(33,212,74,316,251)(34,317,213,252,75)(35,253,318,76,214)(36,77,254,215,319)(37,216,78,320,255)(38,289,217,256,79)(39,225,290,80,218)(40,81,226,219,291)(41,220,82,292,227)(42,293,221,228,83)(43,229,294,84,222)(44,85,230,223,295)(45,224,86,296,231)(46,297,193,232,87)(47,233,298,88,194)(48,89,234,195,299)(49,196,90,300,235)(50,301,197,236,91)(51,237,302,92,198)(52,93,238,199,303)(53,200,94,304,239)(54,305,201,240,95)(55,241,306,96,202)(56,65,242,203,307)(57,204,66,308,243)(58,309,205,244,67)(59,245,310,68,206)(60,69,246,207,311)(61,208,70,312,247)(62,313,209,248,71)(63,249,314,72,210)(64,73,250,211,315), (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)>;
G:=Group( (1,94)(2,95)(3,96)(4,65)(5,66)(6,67)(7,68)(8,69)(9,70)(10,71)(11,72)(12,73)(13,74)(14,75)(15,76)(16,77)(17,78)(18,79)(19,80)(20,81)(21,82)(22,83)(23,84)(24,85)(25,86)(26,87)(27,88)(28,89)(29,90)(30,91)(31,92)(32,93)(33,270)(34,271)(35,272)(36,273)(37,274)(38,275)(39,276)(40,277)(41,278)(42,279)(43,280)(44,281)(45,282)(46,283)(47,284)(48,285)(49,286)(50,287)(51,288)(52,257)(53,258)(54,259)(55,260)(56,261)(57,262)(58,263)(59,264)(60,265)(61,266)(62,267)(63,268)(64,269)(97,215)(98,216)(99,217)(100,218)(101,219)(102,220)(103,221)(104,222)(105,223)(106,224)(107,193)(108,194)(109,195)(110,196)(111,197)(112,198)(113,199)(114,200)(115,201)(116,202)(117,203)(118,204)(119,205)(120,206)(121,207)(122,208)(123,209)(124,210)(125,211)(126,212)(127,213)(128,214)(129,289)(130,290)(131,291)(132,292)(133,293)(134,294)(135,295)(136,296)(137,297)(138,298)(139,299)(140,300)(141,301)(142,302)(143,303)(144,304)(145,305)(146,306)(147,307)(148,308)(149,309)(150,310)(151,311)(152,312)(153,313)(154,314)(155,315)(156,316)(157,317)(158,318)(159,319)(160,320)(161,245)(162,246)(163,247)(164,248)(165,249)(166,250)(167,251)(168,252)(169,253)(170,254)(171,255)(172,256)(173,225)(174,226)(175,227)(176,228)(177,229)(178,230)(179,231)(180,232)(181,233)(182,234)(183,235)(184,236)(185,237)(186,238)(187,239)(188,240)(189,241)(190,242)(191,243)(192,244), (1,144,187,258,114)(2,259,145,115,188)(3,116,260,189,146)(4,190,117,147,261)(5,148,191,262,118)(6,263,149,119,192)(7,120,264,161,150)(8,162,121,151,265)(9,152,163,266,122)(10,267,153,123,164)(11,124,268,165,154)(12,166,125,155,269)(13,156,167,270,126)(14,271,157,127,168)(15,128,272,169,158)(16,170,97,159,273)(17,160,171,274,98)(18,275,129,99,172)(19,100,276,173,130)(20,174,101,131,277)(21,132,175,278,102)(22,279,133,103,176)(23,104,280,177,134)(24,178,105,135,281)(25,136,179,282,106)(26,283,137,107,180)(27,108,284,181,138)(28,182,109,139,285)(29,140,183,286,110)(30,287,141,111,184)(31,112,288,185,142)(32,186,113,143,257)(33,212,74,316,251)(34,317,213,252,75)(35,253,318,76,214)(36,77,254,215,319)(37,216,78,320,255)(38,289,217,256,79)(39,225,290,80,218)(40,81,226,219,291)(41,220,82,292,227)(42,293,221,228,83)(43,229,294,84,222)(44,85,230,223,295)(45,224,86,296,231)(46,297,193,232,87)(47,233,298,88,194)(48,89,234,195,299)(49,196,90,300,235)(50,301,197,236,91)(51,237,302,92,198)(52,93,238,199,303)(53,200,94,304,239)(54,305,201,240,95)(55,241,306,96,202)(56,65,242,203,307)(57,204,66,308,243)(58,309,205,244,67)(59,245,310,68,206)(60,69,246,207,311)(61,208,70,312,247)(62,313,209,248,71)(63,249,314,72,210)(64,73,250,211,315), (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) );
G=PermutationGroup([[(1,94),(2,95),(3,96),(4,65),(5,66),(6,67),(7,68),(8,69),(9,70),(10,71),(11,72),(12,73),(13,74),(14,75),(15,76),(16,77),(17,78),(18,79),(19,80),(20,81),(21,82),(22,83),(23,84),(24,85),(25,86),(26,87),(27,88),(28,89),(29,90),(30,91),(31,92),(32,93),(33,270),(34,271),(35,272),(36,273),(37,274),(38,275),(39,276),(40,277),(41,278),(42,279),(43,280),(44,281),(45,282),(46,283),(47,284),(48,285),(49,286),(50,287),(51,288),(52,257),(53,258),(54,259),(55,260),(56,261),(57,262),(58,263),(59,264),(60,265),(61,266),(62,267),(63,268),(64,269),(97,215),(98,216),(99,217),(100,218),(101,219),(102,220),(103,221),(104,222),(105,223),(106,224),(107,193),(108,194),(109,195),(110,196),(111,197),(112,198),(113,199),(114,200),(115,201),(116,202),(117,203),(118,204),(119,205),(120,206),(121,207),(122,208),(123,209),(124,210),(125,211),(126,212),(127,213),(128,214),(129,289),(130,290),(131,291),(132,292),(133,293),(134,294),(135,295),(136,296),(137,297),(138,298),(139,299),(140,300),(141,301),(142,302),(143,303),(144,304),(145,305),(146,306),(147,307),(148,308),(149,309),(150,310),(151,311),(152,312),(153,313),(154,314),(155,315),(156,316),(157,317),(158,318),(159,319),(160,320),(161,245),(162,246),(163,247),(164,248),(165,249),(166,250),(167,251),(168,252),(169,253),(170,254),(171,255),(172,256),(173,225),(174,226),(175,227),(176,228),(177,229),(178,230),(179,231),(180,232),(181,233),(182,234),(183,235),(184,236),(185,237),(186,238),(187,239),(188,240),(189,241),(190,242),(191,243),(192,244)], [(1,144,187,258,114),(2,259,145,115,188),(3,116,260,189,146),(4,190,117,147,261),(5,148,191,262,118),(6,263,149,119,192),(7,120,264,161,150),(8,162,121,151,265),(9,152,163,266,122),(10,267,153,123,164),(11,124,268,165,154),(12,166,125,155,269),(13,156,167,270,126),(14,271,157,127,168),(15,128,272,169,158),(16,170,97,159,273),(17,160,171,274,98),(18,275,129,99,172),(19,100,276,173,130),(20,174,101,131,277),(21,132,175,278,102),(22,279,133,103,176),(23,104,280,177,134),(24,178,105,135,281),(25,136,179,282,106),(26,283,137,107,180),(27,108,284,181,138),(28,182,109,139,285),(29,140,183,286,110),(30,287,141,111,184),(31,112,288,185,142),(32,186,113,143,257),(33,212,74,316,251),(34,317,213,252,75),(35,253,318,76,214),(36,77,254,215,319),(37,216,78,320,255),(38,289,217,256,79),(39,225,290,80,218),(40,81,226,219,291),(41,220,82,292,227),(42,293,221,228,83),(43,229,294,84,222),(44,85,230,223,295),(45,224,86,296,231),(46,297,193,232,87),(47,233,298,88,194),(48,89,234,195,299),(49,196,90,300,235),(50,301,197,236,91),(51,237,302,92,198),(52,93,238,199,303),(53,200,94,304,239),(54,305,201,240,95),(55,241,306,96,202),(56,65,242,203,307),(57,204,66,308,243),(58,309,205,244,67),(59,245,310,68,206),(60,69,246,207,311),(61,208,70,312,247),(62,313,209,248,71),(63,249,314,72,210),(64,73,250,211,315)], [(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)]])
80 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 5 | 8A | ··· | 8H | 10A | 10B | 10C | 16A | ··· | 16P | 20A | 20B | 20C | 20D | 32A | ··· | 32AF | 40A | ··· | 40H |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 5 | 8 | ··· | 8 | 10 | 10 | 10 | 16 | ··· | 16 | 20 | 20 | 20 | 20 | 32 | ··· | 32 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 1 | ··· | 1 | 4 | 4 | 4 | 5 | ··· | 5 | 4 | 4 | 4 | 4 | 5 | ··· | 5 | 4 | ··· | 4 |
80 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | - | + | - | ||||||||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | C8 | C16 | C16 | C32 | F5 | C5⋊C8 | C2×F5 | C5⋊C8 | C5⋊C16 | C5⋊C16 | C5⋊C32 |
| kernel | C2×C5⋊C32 | C5⋊C32 | C2×C5⋊2C16 | C5⋊2C16 | C2×C40 | C40 | C2×C20 | C20 | C2×C10 | C10 | C2×C8 | C8 | C8 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 4 | 4 | 8 | 8 | 32 | 1 | 1 | 1 | 1 | 2 | 2 | 8 |
Matrix representation of C2×C5⋊C32 ►in GL6(𝔽641)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 640 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 640 |
| 0 | 0 | 1 | 0 | 0 | 640 |
| 0 | 0 | 0 | 1 | 0 | 640 |
| 0 | 0 | 0 | 0 | 1 | 640 |
| 637 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 470 | 111 | 538 | 240 |
| 0 | 0 | 367 | 351 | 461 | 69 |
| 0 | 0 | 290 | 180 | 572 | 607 |
| 0 | 0 | 401 | 77 | 171 | 530 |
G:=sub<GL(6,GF(641))| [1,0,0,0,0,0,0,640,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,640,640,640,640],[637,0,0,0,0,0,0,1,0,0,0,0,0,0,470,367,290,401,0,0,111,351,180,77,0,0,538,461,572,171,0,0,240,69,607,530] >;
C2×C5⋊C32 in GAP, Magma, Sage, TeX
C_2\times C_5\rtimes C_{32} % in TeX
G:=Group("C2xC5:C32"); // GroupNames label
G:=SmallGroup(320,214);
// by ID
G=gap.SmallGroup(320,214);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,58,80,102,6278,3156]);
// Polycyclic
G:=Group<a,b,c|a^2=b^5=c^32=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^3>;
// generators/relations
Export