direct product, abelian, monomial, 2-elementary
Aliases: C22×C80, SmallGroup(320,1003)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C22×C80 |
| C1 — C22×C80 |
| C1 — C22×C80 |
Generators and relations for C22×C80
G = < a,b,c | a2=b2=c80=1, ab=ba, ac=ca, bc=cb >
Subgroups: 98, all normal (16 characteristic)
C1, C2, C2, C4, C4, C22, C5, C8, C8, C2×C4, C23, C10, C10, C16, C2×C8, C22×C4, C20, C20, C2×C10, C2×C16, C22×C8, C40, C40, C2×C20, C22×C10, C22×C16, C80, C2×C40, C22×C20, C2×C80, C22×C40, C22×C80
Quotients: C1, C2, C4, C22, C5, C8, C2×C4, C23, C10, C16, C2×C8, C22×C4, C20, C2×C10, C2×C16, C22×C8, C40, C2×C20, C22×C10, C22×C16, C80, C2×C40, C22×C20, C2×C80, C22×C40, C22×C80
►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 81)(37 82)(38 83)(39 84)(40 85)(41 86)(42 87)(43 88)(44 89)(45 90)(46 91)(47 92)(48 93)(49 94)(50 95)(51 96)(52 97)(53 98)(54 99)(55 100)(56 101)(57 102)(58 103)(59 104)(60 105)(61 106)(62 107)(63 108)(64 109)(65 110)(66 111)(67 112)(68 113)(69 114)(70 115)(71 116)(72 117)(73 118)(74 119)(75 120)(76 121)(77 122)(78 123)(79 124)(80 125)(161 282)(162 283)(163 284)(164 285)(165 286)(166 287)(167 288)(168 289)(169 290)(170 291)(171 292)(172 293)(173 294)(174 295)(175 296)(176 297)(177 298)(178 299)(179 300)(180 301)(181 302)(182 303)(183 304)(184 305)(185 306)(186 307)(187 308)(188 309)(189 310)(190 311)(191 312)(192 313)(193 314)(194 315)(195 316)(196 317)(197 318)(198 319)(199 320)(200 241)(201 242)(202 243)(203 244)(204 245)(205 246)(206 247)(207 248)(208 249)(209 250)(210 251)(211 252)(212 253)(213 254)(214 255)(215 256)(216 257)(217 258)(218 259)(219 260)(220 261)(221 262)(222 263)(223 264)(224 265)(225 266)(226 267)(227 268)(228 269)(229 270)(230 271)(231 272)(232 273)(233 274)(234 275)(235 276)(236 277)(237 278)(238 279)(239 280)(240 281)
(1 263)(2 264)(3 265)(4 266)(5 267)(6 268)(7 269)(8 270)(9 271)(10 272)(11 273)(12 274)(13 275)(14 276)(15 277)(16 278)(17 279)(18 280)(19 281)(20 282)(21 283)(22 284)(23 285)(24 286)(25 287)(26 288)(27 289)(28 290)(29 291)(30 292)(31 293)(32 294)(33 295)(34 296)(35 297)(36 298)(37 299)(38 300)(39 301)(40 302)(41 303)(42 304)(43 305)(44 306)(45 307)(46 308)(47 309)(48 310)(49 311)(50 312)(51 313)(52 314)(53 315)(54 316)(55 317)(56 318)(57 319)(58 320)(59 241)(60 242)(61 243)(62 244)(63 245)(64 246)(65 247)(66 248)(67 249)(68 250)(69 251)(70 252)(71 253)(72 254)(73 255)(74 256)(75 257)(76 258)(77 259)(78 260)(79 261)(80 262)(81 177)(82 178)(83 179)(84 180)(85 181)(86 182)(87 183)(88 184)(89 185)(90 186)(91 187)(92 188)(93 189)(94 190)(95 191)(96 192)(97 193)(98 194)(99 195)(100 196)(101 197)(102 198)(103 199)(104 200)(105 201)(106 202)(107 203)(108 204)(109 205)(110 206)(111 207)(112 208)(113 209)(114 210)(115 211)(116 212)(117 213)(118 214)(119 215)(120 216)(121 217)(122 218)(123 219)(124 220)(125 221)(126 222)(127 223)(128 224)(129 225)(130 226)(131 227)(132 228)(133 229)(134 230)(135 231)(136 232)(137 233)(138 234)(139 235)(140 236)(141 237)(142 238)(143 239)(144 240)(145 161)(146 162)(147 163)(148 164)(149 165)(150 166)(151 167)(152 168)(153 169)(154 170)(155 171)(156 172)(157 173)(158 174)(159 175)(160 176)
(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)| (1,126)(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)(36,81)(37,82)(38,83)(39,84)(40,85)(41,86)(42,87)(43,88)(44,89)(45,90)(46,91)(47,92)(48,93)(49,94)(50,95)(51,96)(52,97)(53,98)(54,99)(55,100)(56,101)(57,102)(58,103)(59,104)(60,105)(61,106)(62,107)(63,108)(64,109)(65,110)(66,111)(67,112)(68,113)(69,114)(70,115)(71,116)(72,117)(73,118)(74,119)(75,120)(76,121)(77,122)(78,123)(79,124)(80,125)(161,282)(162,283)(163,284)(164,285)(165,286)(166,287)(167,288)(168,289)(169,290)(170,291)(171,292)(172,293)(173,294)(174,295)(175,296)(176,297)(177,298)(178,299)(179,300)(180,301)(181,302)(182,303)(183,304)(184,305)(185,306)(186,307)(187,308)(188,309)(189,310)(190,311)(191,312)(192,313)(193,314)(194,315)(195,316)(196,317)(197,318)(198,319)(199,320)(200,241)(201,242)(202,243)(203,244)(204,245)(205,246)(206,247)(207,248)(208,249)(209,250)(210,251)(211,252)(212,253)(213,254)(214,255)(215,256)(216,257)(217,258)(218,259)(219,260)(220,261)(221,262)(222,263)(223,264)(224,265)(225,266)(226,267)(227,268)(228,269)(229,270)(230,271)(231,272)(232,273)(233,274)(234,275)(235,276)(236,277)(237,278)(238,279)(239,280)(240,281), (1,263)(2,264)(3,265)(4,266)(5,267)(6,268)(7,269)(8,270)(9,271)(10,272)(11,273)(12,274)(13,275)(14,276)(15,277)(16,278)(17,279)(18,280)(19,281)(20,282)(21,283)(22,284)(23,285)(24,286)(25,287)(26,288)(27,289)(28,290)(29,291)(30,292)(31,293)(32,294)(33,295)(34,296)(35,297)(36,298)(37,299)(38,300)(39,301)(40,302)(41,303)(42,304)(43,305)(44,306)(45,307)(46,308)(47,309)(48,310)(49,311)(50,312)(51,313)(52,314)(53,315)(54,316)(55,317)(56,318)(57,319)(58,320)(59,241)(60,242)(61,243)(62,244)(63,245)(64,246)(65,247)(66,248)(67,249)(68,250)(69,251)(70,252)(71,253)(72,254)(73,255)(74,256)(75,257)(76,258)(77,259)(78,260)(79,261)(80,262)(81,177)(82,178)(83,179)(84,180)(85,181)(86,182)(87,183)(88,184)(89,185)(90,186)(91,187)(92,188)(93,189)(94,190)(95,191)(96,192)(97,193)(98,194)(99,195)(100,196)(101,197)(102,198)(103,199)(104,200)(105,201)(106,202)(107,203)(108,204)(109,205)(110,206)(111,207)(112,208)(113,209)(114,210)(115,211)(116,212)(117,213)(118,214)(119,215)(120,216)(121,217)(122,218)(123,219)(124,220)(125,221)(126,222)(127,223)(128,224)(129,225)(130,226)(131,227)(132,228)(133,229)(134,230)(135,231)(136,232)(137,233)(138,234)(139,235)(140,236)(141,237)(142,238)(143,239)(144,240)(145,161)(146,162)(147,163)(148,164)(149,165)(150,166)(151,167)(152,168)(153,169)(154,170)(155,171)(156,172)(157,173)(158,174)(159,175)(160,176), (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( (1,126)(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)(36,81)(37,82)(38,83)(39,84)(40,85)(41,86)(42,87)(43,88)(44,89)(45,90)(46,91)(47,92)(48,93)(49,94)(50,95)(51,96)(52,97)(53,98)(54,99)(55,100)(56,101)(57,102)(58,103)(59,104)(60,105)(61,106)(62,107)(63,108)(64,109)(65,110)(66,111)(67,112)(68,113)(69,114)(70,115)(71,116)(72,117)(73,118)(74,119)(75,120)(76,121)(77,122)(78,123)(79,124)(80,125)(161,282)(162,283)(163,284)(164,285)(165,286)(166,287)(167,288)(168,289)(169,290)(170,291)(171,292)(172,293)(173,294)(174,295)(175,296)(176,297)(177,298)(178,299)(179,300)(180,301)(181,302)(182,303)(183,304)(184,305)(185,306)(186,307)(187,308)(188,309)(189,310)(190,311)(191,312)(192,313)(193,314)(194,315)(195,316)(196,317)(197,318)(198,319)(199,320)(200,241)(201,242)(202,243)(203,244)(204,245)(205,246)(206,247)(207,248)(208,249)(209,250)(210,251)(211,252)(212,253)(213,254)(214,255)(215,256)(216,257)(217,258)(218,259)(219,260)(220,261)(221,262)(222,263)(223,264)(224,265)(225,266)(226,267)(227,268)(228,269)(229,270)(230,271)(231,272)(232,273)(233,274)(234,275)(235,276)(236,277)(237,278)(238,279)(239,280)(240,281), (1,263)(2,264)(3,265)(4,266)(5,267)(6,268)(7,269)(8,270)(9,271)(10,272)(11,273)(12,274)(13,275)(14,276)(15,277)(16,278)(17,279)(18,280)(19,281)(20,282)(21,283)(22,284)(23,285)(24,286)(25,287)(26,288)(27,289)(28,290)(29,291)(30,292)(31,293)(32,294)(33,295)(34,296)(35,297)(36,298)(37,299)(38,300)(39,301)(40,302)(41,303)(42,304)(43,305)(44,306)(45,307)(46,308)(47,309)(48,310)(49,311)(50,312)(51,313)(52,314)(53,315)(54,316)(55,317)(56,318)(57,319)(58,320)(59,241)(60,242)(61,243)(62,244)(63,245)(64,246)(65,247)(66,248)(67,249)(68,250)(69,251)(70,252)(71,253)(72,254)(73,255)(74,256)(75,257)(76,258)(77,259)(78,260)(79,261)(80,262)(81,177)(82,178)(83,179)(84,180)(85,181)(86,182)(87,183)(88,184)(89,185)(90,186)(91,187)(92,188)(93,189)(94,190)(95,191)(96,192)(97,193)(98,194)(99,195)(100,196)(101,197)(102,198)(103,199)(104,200)(105,201)(106,202)(107,203)(108,204)(109,205)(110,206)(111,207)(112,208)(113,209)(114,210)(115,211)(116,212)(117,213)(118,214)(119,215)(120,216)(121,217)(122,218)(123,219)(124,220)(125,221)(126,222)(127,223)(128,224)(129,225)(130,226)(131,227)(132,228)(133,229)(134,230)(135,231)(136,232)(137,233)(138,234)(139,235)(140,236)(141,237)(142,238)(143,239)(144,240)(145,161)(146,162)(147,163)(148,164)(149,165)(150,166)(151,167)(152,168)(153,169)(154,170)(155,171)(156,172)(157,173)(158,174)(159,175)(160,176), (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([[(1,126),(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),(36,81),(37,82),(38,83),(39,84),(40,85),(41,86),(42,87),(43,88),(44,89),(45,90),(46,91),(47,92),(48,93),(49,94),(50,95),(51,96),(52,97),(53,98),(54,99),(55,100),(56,101),(57,102),(58,103),(59,104),(60,105),(61,106),(62,107),(63,108),(64,109),(65,110),(66,111),(67,112),(68,113),(69,114),(70,115),(71,116),(72,117),(73,118),(74,119),(75,120),(76,121),(77,122),(78,123),(79,124),(80,125),(161,282),(162,283),(163,284),(164,285),(165,286),(166,287),(167,288),(168,289),(169,290),(170,291),(171,292),(172,293),(173,294),(174,295),(175,296),(176,297),(177,298),(178,299),(179,300),(180,301),(181,302),(182,303),(183,304),(184,305),(185,306),(186,307),(187,308),(188,309),(189,310),(190,311),(191,312),(192,313),(193,314),(194,315),(195,316),(196,317),(197,318),(198,319),(199,320),(200,241),(201,242),(202,243),(203,244),(204,245),(205,246),(206,247),(207,248),(208,249),(209,250),(210,251),(211,252),(212,253),(213,254),(214,255),(215,256),(216,257),(217,258),(218,259),(219,260),(220,261),(221,262),(222,263),(223,264),(224,265),(225,266),(226,267),(227,268),(228,269),(229,270),(230,271),(231,272),(232,273),(233,274),(234,275),(235,276),(236,277),(237,278),(238,279),(239,280),(240,281)], [(1,263),(2,264),(3,265),(4,266),(5,267),(6,268),(7,269),(8,270),(9,271),(10,272),(11,273),(12,274),(13,275),(14,276),(15,277),(16,278),(17,279),(18,280),(19,281),(20,282),(21,283),(22,284),(23,285),(24,286),(25,287),(26,288),(27,289),(28,290),(29,291),(30,292),(31,293),(32,294),(33,295),(34,296),(35,297),(36,298),(37,299),(38,300),(39,301),(40,302),(41,303),(42,304),(43,305),(44,306),(45,307),(46,308),(47,309),(48,310),(49,311),(50,312),(51,313),(52,314),(53,315),(54,316),(55,317),(56,318),(57,319),(58,320),(59,241),(60,242),(61,243),(62,244),(63,245),(64,246),(65,247),(66,248),(67,249),(68,250),(69,251),(70,252),(71,253),(72,254),(73,255),(74,256),(75,257),(76,258),(77,259),(78,260),(79,261),(80,262),(81,177),(82,178),(83,179),(84,180),(85,181),(86,182),(87,183),(88,184),(89,185),(90,186),(91,187),(92,188),(93,189),(94,190),(95,191),(96,192),(97,193),(98,194),(99,195),(100,196),(101,197),(102,198),(103,199),(104,200),(105,201),(106,202),(107,203),(108,204),(109,205),(110,206),(111,207),(112,208),(113,209),(114,210),(115,211),(116,212),(117,213),(118,214),(119,215),(120,216),(121,217),(122,218),(123,219),(124,220),(125,221),(126,222),(127,223),(128,224),(129,225),(130,226),(131,227),(132,228),(133,229),(134,230),(135,231),(136,232),(137,233),(138,234),(139,235),(140,236),(141,237),(142,238),(143,239),(144,240),(145,161),(146,162),(147,163),(148,164),(149,165),(150,166),(151,167),(152,168),(153,169),(154,170),(155,171),(156,172),(157,173),(158,174),(159,175),(160,176)], [(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)]])
320 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4H | 5A | 5B | 5C | 5D | 8A | ··· | 8P | 10A | ··· | 10AB | 16A | ··· | 16AF | 20A | ··· | 20AF | 40A | ··· | 40BL | 80A | ··· | 80DX |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 5 | 5 | 5 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 16 | ··· | 16 | 20 | ··· | 20 | 40 | ··· | 40 | 80 | ··· | 80 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
320 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | + | |||||||||||||
| image | C1 | C2 | C2 | C4 | C4 | C5 | C8 | C8 | C10 | C10 | C16 | C20 | C20 | C40 | C40 | C80 |
| kernel | C22×C80 | C2×C80 | C22×C40 | C2×C40 | C22×C20 | C22×C16 | C2×C20 | C22×C10 | C2×C16 | C22×C8 | C2×C10 | C2×C8 | C22×C4 | C2×C4 | C23 | C22 |
| # reps | 1 | 6 | 1 | 6 | 2 | 4 | 12 | 4 | 24 | 4 | 32 | 24 | 8 | 48 | 16 | 128 |
Matrix representation of C22×C80 ►in GL3(𝔽241) generated by
| 1 | 0 | 0 |
| 0 | 240 | 0 |
| 0 | 0 | 1 |
| 1 | 0 | 0 |
| 0 | 240 | 0 |
| 0 | 0 | 240 |
| 111 | 0 | 0 |
| 0 | 136 | 0 |
| 0 | 0 | 73 |
G:=sub<GL(3,GF(241))| [1,0,0,0,240,0,0,0,1],[1,0,0,0,240,0,0,0,240],[111,0,0,0,136,0,0,0,73] >;
C22×C80 in GAP, Magma, Sage, TeX
C_2^2\times C_{80} % in TeX
G:=Group("C2^2xC80"); // GroupNames label
G:=SmallGroup(320,1003);
// by ID
G=gap.SmallGroup(320,1003);
# by ID
G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-2,280,102,124]);
// Polycyclic
G:=Group<a,b,c|a^2=b^2=c^80=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations