direct product, abelian, monomial, 2-elementary
Aliases: C23×C38, SmallGroup(304,42)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C23×C38 |
| C1 — C23×C38 |
| C1 — C23×C38 |
Generators and relations for C23×C38
G = < a,b,c,d | a2=b2=c2=d38=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, cd=dc >
Subgroups: 134, all normal (4 characteristic)
C1, C2, C22, C23, C24, C19, C38, C2×C38, C22×C38, C23×C38
Quotients: C1, C2, C22, C23, C24, C19, C38, C2×C38, C22×C38, C23×C38
►Regular action on 304 points
Generators in S304
(1 173)(2 174)(3 175)(4 176)(5 177)(6 178)(7 179)(8 180)(9 181)(10 182)(11 183)(12 184)(13 185)(14 186)(15 187)(16 188)(17 189)(18 190)(19 153)(20 154)(21 155)(22 156)(23 157)(24 158)(25 159)(26 160)(27 161)(28 162)(29 163)(30 164)(31 165)(32 166)(33 167)(34 168)(35 169)(36 170)(37 171)(38 172)(39 215)(40 216)(41 217)(42 218)(43 219)(44 220)(45 221)(46 222)(47 223)(48 224)(49 225)(50 226)(51 227)(52 228)(53 191)(54 192)(55 193)(56 194)(57 195)(58 196)(59 197)(60 198)(61 199)(62 200)(63 201)(64 202)(65 203)(66 204)(67 205)(68 206)(69 207)(70 208)(71 209)(72 210)(73 211)(74 212)(75 213)(76 214)(77 266)(78 229)(79 230)(80 231)(81 232)(82 233)(83 234)(84 235)(85 236)(86 237)(87 238)(88 239)(89 240)(90 241)(91 242)(92 243)(93 244)(94 245)(95 246)(96 247)(97 248)(98 249)(99 250)(100 251)(101 252)(102 253)(103 254)(104 255)(105 256)(106 257)(107 258)(108 259)(109 260)(110 261)(111 262)(112 263)(113 264)(114 265)(115 273)(116 274)(117 275)(118 276)(119 277)(120 278)(121 279)(122 280)(123 281)(124 282)(125 283)(126 284)(127 285)(128 286)(129 287)(130 288)(131 289)(132 290)(133 291)(134 292)(135 293)(136 294)(137 295)(138 296)(139 297)(140 298)(141 299)(142 300)(143 301)(144 302)(145 303)(146 304)(147 267)(148 268)(149 269)(150 270)(151 271)(152 272)
(1 77)(2 78)(3 79)(4 80)(5 81)(6 82)(7 83)(8 84)(9 85)(10 86)(11 87)(12 88)(13 89)(14 90)(15 91)(16 92)(17 93)(18 94)(19 95)(20 96)(21 97)(22 98)(23 99)(24 100)(25 101)(26 102)(27 103)(28 104)(29 105)(30 106)(31 107)(32 108)(33 109)(34 110)(35 111)(36 112)(37 113)(38 114)(39 148)(40 149)(41 150)(42 151)(43 152)(44 115)(45 116)(46 117)(47 118)(48 119)(49 120)(50 121)(51 122)(52 123)(53 124)(54 125)(55 126)(56 127)(57 128)(58 129)(59 130)(60 131)(61 132)(62 133)(63 134)(64 135)(65 136)(66 137)(67 138)(68 139)(69 140)(70 141)(71 142)(72 143)(73 144)(74 145)(75 146)(76 147)(153 246)(154 247)(155 248)(156 249)(157 250)(158 251)(159 252)(160 253)(161 254)(162 255)(163 256)(164 257)(165 258)(166 259)(167 260)(168 261)(169 262)(170 263)(171 264)(172 265)(173 266)(174 229)(175 230)(176 231)(177 232)(178 233)(179 234)(180 235)(181 236)(182 237)(183 238)(184 239)(185 240)(186 241)(187 242)(188 243)(189 244)(190 245)(191 282)(192 283)(193 284)(194 285)(195 286)(196 287)(197 288)(198 289)(199 290)(200 291)(201 292)(202 293)(203 294)(204 295)(205 296)(206 297)(207 298)(208 299)(209 300)(210 301)(211 302)(212 303)(213 304)(214 267)(215 268)(216 269)(217 270)(218 271)(219 272)(220 273)(221 274)(222 275)(223 276)(224 277)(225 278)(226 279)(227 280)(228 281)
(1 76)(2 39)(3 40)(4 41)(5 42)(6 43)(7 44)(8 45)(9 46)(10 47)(11 48)(12 49)(13 50)(14 51)(15 52)(16 53)(17 54)(18 55)(19 56)(20 57)(21 58)(22 59)(23 60)(24 61)(25 62)(26 63)(27 64)(28 65)(29 66)(30 67)(31 68)(32 69)(33 70)(34 71)(35 72)(36 73)(37 74)(38 75)(77 147)(78 148)(79 149)(80 150)(81 151)(82 152)(83 115)(84 116)(85 117)(86 118)(87 119)(88 120)(89 121)(90 122)(91 123)(92 124)(93 125)(94 126)(95 127)(96 128)(97 129)(98 130)(99 131)(100 132)(101 133)(102 134)(103 135)(104 136)(105 137)(106 138)(107 139)(108 140)(109 141)(110 142)(111 143)(112 144)(113 145)(114 146)(153 194)(154 195)(155 196)(156 197)(157 198)(158 199)(159 200)(160 201)(161 202)(162 203)(163 204)(164 205)(165 206)(166 207)(167 208)(168 209)(169 210)(170 211)(171 212)(172 213)(173 214)(174 215)(175 216)(176 217)(177 218)(178 219)(179 220)(180 221)(181 222)(182 223)(183 224)(184 225)(185 226)(186 227)(187 228)(188 191)(189 192)(190 193)(229 268)(230 269)(231 270)(232 271)(233 272)(234 273)(235 274)(236 275)(237 276)(238 277)(239 278)(240 279)(241 280)(242 281)(243 282)(244 283)(245 284)(246 285)(247 286)(248 287)(249 288)(250 289)(251 290)(252 291)(253 292)(254 293)(255 294)(256 295)(257 296)(258 297)(259 298)(260 299)(261 300)(262 301)(263 302)(264 303)(265 304)(266 267)
(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)
G:=sub<Sym(304)| (1,173)(2,174)(3,175)(4,176)(5,177)(6,178)(7,179)(8,180)(9,181)(10,182)(11,183)(12,184)(13,185)(14,186)(15,187)(16,188)(17,189)(18,190)(19,153)(20,154)(21,155)(22,156)(23,157)(24,158)(25,159)(26,160)(27,161)(28,162)(29,163)(30,164)(31,165)(32,166)(33,167)(34,168)(35,169)(36,170)(37,171)(38,172)(39,215)(40,216)(41,217)(42,218)(43,219)(44,220)(45,221)(46,222)(47,223)(48,224)(49,225)(50,226)(51,227)(52,228)(53,191)(54,192)(55,193)(56,194)(57,195)(58,196)(59,197)(60,198)(61,199)(62,200)(63,201)(64,202)(65,203)(66,204)(67,205)(68,206)(69,207)(70,208)(71,209)(72,210)(73,211)(74,212)(75,213)(76,214)(77,266)(78,229)(79,230)(80,231)(81,232)(82,233)(83,234)(84,235)(85,236)(86,237)(87,238)(88,239)(89,240)(90,241)(91,242)(92,243)(93,244)(94,245)(95,246)(96,247)(97,248)(98,249)(99,250)(100,251)(101,252)(102,253)(103,254)(104,255)(105,256)(106,257)(107,258)(108,259)(109,260)(110,261)(111,262)(112,263)(113,264)(114,265)(115,273)(116,274)(117,275)(118,276)(119,277)(120,278)(121,279)(122,280)(123,281)(124,282)(125,283)(126,284)(127,285)(128,286)(129,287)(130,288)(131,289)(132,290)(133,291)(134,292)(135,293)(136,294)(137,295)(138,296)(139,297)(140,298)(141,299)(142,300)(143,301)(144,302)(145,303)(146,304)(147,267)(148,268)(149,269)(150,270)(151,271)(152,272), (1,77)(2,78)(3,79)(4,80)(5,81)(6,82)(7,83)(8,84)(9,85)(10,86)(11,87)(12,88)(13,89)(14,90)(15,91)(16,92)(17,93)(18,94)(19,95)(20,96)(21,97)(22,98)(23,99)(24,100)(25,101)(26,102)(27,103)(28,104)(29,105)(30,106)(31,107)(32,108)(33,109)(34,110)(35,111)(36,112)(37,113)(38,114)(39,148)(40,149)(41,150)(42,151)(43,152)(44,115)(45,116)(46,117)(47,118)(48,119)(49,120)(50,121)(51,122)(52,123)(53,124)(54,125)(55,126)(56,127)(57,128)(58,129)(59,130)(60,131)(61,132)(62,133)(63,134)(64,135)(65,136)(66,137)(67,138)(68,139)(69,140)(70,141)(71,142)(72,143)(73,144)(74,145)(75,146)(76,147)(153,246)(154,247)(155,248)(156,249)(157,250)(158,251)(159,252)(160,253)(161,254)(162,255)(163,256)(164,257)(165,258)(166,259)(167,260)(168,261)(169,262)(170,263)(171,264)(172,265)(173,266)(174,229)(175,230)(176,231)(177,232)(178,233)(179,234)(180,235)(181,236)(182,237)(183,238)(184,239)(185,240)(186,241)(187,242)(188,243)(189,244)(190,245)(191,282)(192,283)(193,284)(194,285)(195,286)(196,287)(197,288)(198,289)(199,290)(200,291)(201,292)(202,293)(203,294)(204,295)(205,296)(206,297)(207,298)(208,299)(209,300)(210,301)(211,302)(212,303)(213,304)(214,267)(215,268)(216,269)(217,270)(218,271)(219,272)(220,273)(221,274)(222,275)(223,276)(224,277)(225,278)(226,279)(227,280)(228,281), (1,76)(2,39)(3,40)(4,41)(5,42)(6,43)(7,44)(8,45)(9,46)(10,47)(11,48)(12,49)(13,50)(14,51)(15,52)(16,53)(17,54)(18,55)(19,56)(20,57)(21,58)(22,59)(23,60)(24,61)(25,62)(26,63)(27,64)(28,65)(29,66)(30,67)(31,68)(32,69)(33,70)(34,71)(35,72)(36,73)(37,74)(38,75)(77,147)(78,148)(79,149)(80,150)(81,151)(82,152)(83,115)(84,116)(85,117)(86,118)(87,119)(88,120)(89,121)(90,122)(91,123)(92,124)(93,125)(94,126)(95,127)(96,128)(97,129)(98,130)(99,131)(100,132)(101,133)(102,134)(103,135)(104,136)(105,137)(106,138)(107,139)(108,140)(109,141)(110,142)(111,143)(112,144)(113,145)(114,146)(153,194)(154,195)(155,196)(156,197)(157,198)(158,199)(159,200)(160,201)(161,202)(162,203)(163,204)(164,205)(165,206)(166,207)(167,208)(168,209)(169,210)(170,211)(171,212)(172,213)(173,214)(174,215)(175,216)(176,217)(177,218)(178,219)(179,220)(180,221)(181,222)(182,223)(183,224)(184,225)(185,226)(186,227)(187,228)(188,191)(189,192)(190,193)(229,268)(230,269)(231,270)(232,271)(233,272)(234,273)(235,274)(236,275)(237,276)(238,277)(239,278)(240,279)(241,280)(242,281)(243,282)(244,283)(245,284)(246,285)(247,286)(248,287)(249,288)(250,289)(251,290)(252,291)(253,292)(254,293)(255,294)(256,295)(257,296)(258,297)(259,298)(260,299)(261,300)(262,301)(263,302)(264,303)(265,304)(266,267), (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)>;
G:=Group( (1,173)(2,174)(3,175)(4,176)(5,177)(6,178)(7,179)(8,180)(9,181)(10,182)(11,183)(12,184)(13,185)(14,186)(15,187)(16,188)(17,189)(18,190)(19,153)(20,154)(21,155)(22,156)(23,157)(24,158)(25,159)(26,160)(27,161)(28,162)(29,163)(30,164)(31,165)(32,166)(33,167)(34,168)(35,169)(36,170)(37,171)(38,172)(39,215)(40,216)(41,217)(42,218)(43,219)(44,220)(45,221)(46,222)(47,223)(48,224)(49,225)(50,226)(51,227)(52,228)(53,191)(54,192)(55,193)(56,194)(57,195)(58,196)(59,197)(60,198)(61,199)(62,200)(63,201)(64,202)(65,203)(66,204)(67,205)(68,206)(69,207)(70,208)(71,209)(72,210)(73,211)(74,212)(75,213)(76,214)(77,266)(78,229)(79,230)(80,231)(81,232)(82,233)(83,234)(84,235)(85,236)(86,237)(87,238)(88,239)(89,240)(90,241)(91,242)(92,243)(93,244)(94,245)(95,246)(96,247)(97,248)(98,249)(99,250)(100,251)(101,252)(102,253)(103,254)(104,255)(105,256)(106,257)(107,258)(108,259)(109,260)(110,261)(111,262)(112,263)(113,264)(114,265)(115,273)(116,274)(117,275)(118,276)(119,277)(120,278)(121,279)(122,280)(123,281)(124,282)(125,283)(126,284)(127,285)(128,286)(129,287)(130,288)(131,289)(132,290)(133,291)(134,292)(135,293)(136,294)(137,295)(138,296)(139,297)(140,298)(141,299)(142,300)(143,301)(144,302)(145,303)(146,304)(147,267)(148,268)(149,269)(150,270)(151,271)(152,272), (1,77)(2,78)(3,79)(4,80)(5,81)(6,82)(7,83)(8,84)(9,85)(10,86)(11,87)(12,88)(13,89)(14,90)(15,91)(16,92)(17,93)(18,94)(19,95)(20,96)(21,97)(22,98)(23,99)(24,100)(25,101)(26,102)(27,103)(28,104)(29,105)(30,106)(31,107)(32,108)(33,109)(34,110)(35,111)(36,112)(37,113)(38,114)(39,148)(40,149)(41,150)(42,151)(43,152)(44,115)(45,116)(46,117)(47,118)(48,119)(49,120)(50,121)(51,122)(52,123)(53,124)(54,125)(55,126)(56,127)(57,128)(58,129)(59,130)(60,131)(61,132)(62,133)(63,134)(64,135)(65,136)(66,137)(67,138)(68,139)(69,140)(70,141)(71,142)(72,143)(73,144)(74,145)(75,146)(76,147)(153,246)(154,247)(155,248)(156,249)(157,250)(158,251)(159,252)(160,253)(161,254)(162,255)(163,256)(164,257)(165,258)(166,259)(167,260)(168,261)(169,262)(170,263)(171,264)(172,265)(173,266)(174,229)(175,230)(176,231)(177,232)(178,233)(179,234)(180,235)(181,236)(182,237)(183,238)(184,239)(185,240)(186,241)(187,242)(188,243)(189,244)(190,245)(191,282)(192,283)(193,284)(194,285)(195,286)(196,287)(197,288)(198,289)(199,290)(200,291)(201,292)(202,293)(203,294)(204,295)(205,296)(206,297)(207,298)(208,299)(209,300)(210,301)(211,302)(212,303)(213,304)(214,267)(215,268)(216,269)(217,270)(218,271)(219,272)(220,273)(221,274)(222,275)(223,276)(224,277)(225,278)(226,279)(227,280)(228,281), (1,76)(2,39)(3,40)(4,41)(5,42)(6,43)(7,44)(8,45)(9,46)(10,47)(11,48)(12,49)(13,50)(14,51)(15,52)(16,53)(17,54)(18,55)(19,56)(20,57)(21,58)(22,59)(23,60)(24,61)(25,62)(26,63)(27,64)(28,65)(29,66)(30,67)(31,68)(32,69)(33,70)(34,71)(35,72)(36,73)(37,74)(38,75)(77,147)(78,148)(79,149)(80,150)(81,151)(82,152)(83,115)(84,116)(85,117)(86,118)(87,119)(88,120)(89,121)(90,122)(91,123)(92,124)(93,125)(94,126)(95,127)(96,128)(97,129)(98,130)(99,131)(100,132)(101,133)(102,134)(103,135)(104,136)(105,137)(106,138)(107,139)(108,140)(109,141)(110,142)(111,143)(112,144)(113,145)(114,146)(153,194)(154,195)(155,196)(156,197)(157,198)(158,199)(159,200)(160,201)(161,202)(162,203)(163,204)(164,205)(165,206)(166,207)(167,208)(168,209)(169,210)(170,211)(171,212)(172,213)(173,214)(174,215)(175,216)(176,217)(177,218)(178,219)(179,220)(180,221)(181,222)(182,223)(183,224)(184,225)(185,226)(186,227)(187,228)(188,191)(189,192)(190,193)(229,268)(230,269)(231,270)(232,271)(233,272)(234,273)(235,274)(236,275)(237,276)(238,277)(239,278)(240,279)(241,280)(242,281)(243,282)(244,283)(245,284)(246,285)(247,286)(248,287)(249,288)(250,289)(251,290)(252,291)(253,292)(254,293)(255,294)(256,295)(257,296)(258,297)(259,298)(260,299)(261,300)(262,301)(263,302)(264,303)(265,304)(266,267), (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) );
G=PermutationGroup([[(1,173),(2,174),(3,175),(4,176),(5,177),(6,178),(7,179),(8,180),(9,181),(10,182),(11,183),(12,184),(13,185),(14,186),(15,187),(16,188),(17,189),(18,190),(19,153),(20,154),(21,155),(22,156),(23,157),(24,158),(25,159),(26,160),(27,161),(28,162),(29,163),(30,164),(31,165),(32,166),(33,167),(34,168),(35,169),(36,170),(37,171),(38,172),(39,215),(40,216),(41,217),(42,218),(43,219),(44,220),(45,221),(46,222),(47,223),(48,224),(49,225),(50,226),(51,227),(52,228),(53,191),(54,192),(55,193),(56,194),(57,195),(58,196),(59,197),(60,198),(61,199),(62,200),(63,201),(64,202),(65,203),(66,204),(67,205),(68,206),(69,207),(70,208),(71,209),(72,210),(73,211),(74,212),(75,213),(76,214),(77,266),(78,229),(79,230),(80,231),(81,232),(82,233),(83,234),(84,235),(85,236),(86,237),(87,238),(88,239),(89,240),(90,241),(91,242),(92,243),(93,244),(94,245),(95,246),(96,247),(97,248),(98,249),(99,250),(100,251),(101,252),(102,253),(103,254),(104,255),(105,256),(106,257),(107,258),(108,259),(109,260),(110,261),(111,262),(112,263),(113,264),(114,265),(115,273),(116,274),(117,275),(118,276),(119,277),(120,278),(121,279),(122,280),(123,281),(124,282),(125,283),(126,284),(127,285),(128,286),(129,287),(130,288),(131,289),(132,290),(133,291),(134,292),(135,293),(136,294),(137,295),(138,296),(139,297),(140,298),(141,299),(142,300),(143,301),(144,302),(145,303),(146,304),(147,267),(148,268),(149,269),(150,270),(151,271),(152,272)], [(1,77),(2,78),(3,79),(4,80),(5,81),(6,82),(7,83),(8,84),(9,85),(10,86),(11,87),(12,88),(13,89),(14,90),(15,91),(16,92),(17,93),(18,94),(19,95),(20,96),(21,97),(22,98),(23,99),(24,100),(25,101),(26,102),(27,103),(28,104),(29,105),(30,106),(31,107),(32,108),(33,109),(34,110),(35,111),(36,112),(37,113),(38,114),(39,148),(40,149),(41,150),(42,151),(43,152),(44,115),(45,116),(46,117),(47,118),(48,119),(49,120),(50,121),(51,122),(52,123),(53,124),(54,125),(55,126),(56,127),(57,128),(58,129),(59,130),(60,131),(61,132),(62,133),(63,134),(64,135),(65,136),(66,137),(67,138),(68,139),(69,140),(70,141),(71,142),(72,143),(73,144),(74,145),(75,146),(76,147),(153,246),(154,247),(155,248),(156,249),(157,250),(158,251),(159,252),(160,253),(161,254),(162,255),(163,256),(164,257),(165,258),(166,259),(167,260),(168,261),(169,262),(170,263),(171,264),(172,265),(173,266),(174,229),(175,230),(176,231),(177,232),(178,233),(179,234),(180,235),(181,236),(182,237),(183,238),(184,239),(185,240),(186,241),(187,242),(188,243),(189,244),(190,245),(191,282),(192,283),(193,284),(194,285),(195,286),(196,287),(197,288),(198,289),(199,290),(200,291),(201,292),(202,293),(203,294),(204,295),(205,296),(206,297),(207,298),(208,299),(209,300),(210,301),(211,302),(212,303),(213,304),(214,267),(215,268),(216,269),(217,270),(218,271),(219,272),(220,273),(221,274),(222,275),(223,276),(224,277),(225,278),(226,279),(227,280),(228,281)], [(1,76),(2,39),(3,40),(4,41),(5,42),(6,43),(7,44),(8,45),(9,46),(10,47),(11,48),(12,49),(13,50),(14,51),(15,52),(16,53),(17,54),(18,55),(19,56),(20,57),(21,58),(22,59),(23,60),(24,61),(25,62),(26,63),(27,64),(28,65),(29,66),(30,67),(31,68),(32,69),(33,70),(34,71),(35,72),(36,73),(37,74),(38,75),(77,147),(78,148),(79,149),(80,150),(81,151),(82,152),(83,115),(84,116),(85,117),(86,118),(87,119),(88,120),(89,121),(90,122),(91,123),(92,124),(93,125),(94,126),(95,127),(96,128),(97,129),(98,130),(99,131),(100,132),(101,133),(102,134),(103,135),(104,136),(105,137),(106,138),(107,139),(108,140),(109,141),(110,142),(111,143),(112,144),(113,145),(114,146),(153,194),(154,195),(155,196),(156,197),(157,198),(158,199),(159,200),(160,201),(161,202),(162,203),(163,204),(164,205),(165,206),(166,207),(167,208),(168,209),(169,210),(170,211),(171,212),(172,213),(173,214),(174,215),(175,216),(176,217),(177,218),(178,219),(179,220),(180,221),(181,222),(182,223),(183,224),(184,225),(185,226),(186,227),(187,228),(188,191),(189,192),(190,193),(229,268),(230,269),(231,270),(232,271),(233,272),(234,273),(235,274),(236,275),(237,276),(238,277),(239,278),(240,279),(241,280),(242,281),(243,282),(244,283),(245,284),(246,285),(247,286),(248,287),(249,288),(250,289),(251,290),(252,291),(253,292),(254,293),(255,294),(256,295),(257,296),(258,297),(259,298),(260,299),(261,300),(262,301),(263,302),(264,303),(265,304),(266,267)], [(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)]])
304 conjugacy classes
| class | 1 | 2A | ··· | 2O | 19A | ··· | 19R | 38A | ··· | 38JJ |
| order | 1 | 2 | ··· | 2 | 19 | ··· | 19 | 38 | ··· | 38 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
304 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C19 | C38 |
| kernel | C23×C38 | C22×C38 | C24 | C23 |
| # reps | 1 | 15 | 18 | 270 |
Matrix representation of C23×C38 ►in GL4(𝔽191) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 190 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 190 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 190 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 190 |
| 139 | 0 | 0 | 0 |
| 0 | 30 | 0 | 0 |
| 0 | 0 | 69 | 0 |
| 0 | 0 | 0 | 107 |
G:=sub<GL(4,GF(191))| [1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,190],[1,0,0,0,0,1,0,0,0,0,190,0,0,0,0,1],[1,0,0,0,0,190,0,0,0,0,1,0,0,0,0,190],[139,0,0,0,0,30,0,0,0,0,69,0,0,0,0,107] >;
C23×C38 in GAP, Magma, Sage, TeX
C_2^3\times C_{38} % in TeX
G:=Group("C2^3xC38"); // GroupNames label
G:=SmallGroup(304,42);
// by ID
G=gap.SmallGroup(304,42);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-19]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^2=d^38=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,c*d=d*c>;
// generators/relations