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G = C23×C38order 304 = 24·19

Abelian group of type [2,2,2,38]

direct product, abelian, monomial, 2-elementary

Aliases: C23×C38, SmallGroup(304,42)

Series: Derived Chief Lower central Upper central

C1 — C23×C38
C1C19C38C2×C38C22×C38 — 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 [×15], C22 [×35], C23 [×15], C24, C19, C38 [×15], C2×C38 [×35], C22×C38 [×15], C23×C38
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], C24, C19, C38 [×15], C2×C38 [×35], C22×C38 [×15], C23×C38

Smallest permutation representation of C23×C38
Regular action on 304 points
Generators in S304
(1 190)(2 153)(3 154)(4 155)(5 156)(6 157)(7 158)(8 159)(9 160)(10 161)(11 162)(12 163)(13 164)(14 165)(15 166)(16 167)(17 168)(18 169)(19 170)(20 171)(21 172)(22 173)(23 174)(24 175)(25 176)(26 177)(27 178)(28 179)(29 180)(30 181)(31 182)(32 183)(33 184)(34 185)(35 186)(36 187)(37 188)(38 189)(39 196)(40 197)(41 198)(42 199)(43 200)(44 201)(45 202)(46 203)(47 204)(48 205)(49 206)(50 207)(51 208)(52 209)(53 210)(54 211)(55 212)(56 213)(57 214)(58 215)(59 216)(60 217)(61 218)(62 219)(63 220)(64 221)(65 222)(66 223)(67 224)(68 225)(69 226)(70 227)(71 228)(72 191)(73 192)(74 193)(75 194)(76 195)(77 234)(78 235)(79 236)(80 237)(81 238)(82 239)(83 240)(84 241)(85 242)(86 243)(87 244)(88 245)(89 246)(90 247)(91 248)(92 249)(93 250)(94 251)(95 252)(96 253)(97 254)(98 255)(99 256)(100 257)(101 258)(102 259)(103 260)(104 261)(105 262)(106 263)(107 264)(108 265)(109 266)(110 229)(111 230)(112 231)(113 232)(114 233)(115 281)(116 282)(117 283)(118 284)(119 285)(120 286)(121 287)(122 288)(123 289)(124 290)(125 291)(126 292)(127 293)(128 294)(129 295)(130 296)(131 297)(132 298)(133 299)(134 300)(135 301)(136 302)(137 303)(138 304)(139 267)(140 268)(141 269)(142 270)(143 271)(144 272)(145 273)(146 274)(147 275)(148 276)(149 277)(150 278)(151 279)(152 280)
(1 102)(2 103)(3 104)(4 105)(5 106)(6 107)(7 108)(8 109)(9 110)(10 111)(11 112)(12 113)(13 114)(14 77)(15 78)(16 79)(17 80)(18 81)(19 82)(20 83)(21 84)(22 85)(23 86)(24 87)(25 88)(26 89)(27 90)(28 91)(29 92)(30 93)(31 94)(32 95)(33 96)(34 97)(35 98)(36 99)(37 100)(38 101)(39 146)(40 147)(41 148)(42 149)(43 150)(44 151)(45 152)(46 115)(47 116)(48 117)(49 118)(50 119)(51 120)(52 121)(53 122)(54 123)(55 124)(56 125)(57 126)(58 127)(59 128)(60 129)(61 130)(62 131)(63 132)(64 133)(65 134)(66 135)(67 136)(68 137)(69 138)(70 139)(71 140)(72 141)(73 142)(74 143)(75 144)(76 145)(153 260)(154 261)(155 262)(156 263)(157 264)(158 265)(159 266)(160 229)(161 230)(162 231)(163 232)(164 233)(165 234)(166 235)(167 236)(168 237)(169 238)(170 239)(171 240)(172 241)(173 242)(174 243)(175 244)(176 245)(177 246)(178 247)(179 248)(180 249)(181 250)(182 251)(183 252)(184 253)(185 254)(186 255)(187 256)(188 257)(189 258)(190 259)(191 269)(192 270)(193 271)(194 272)(195 273)(196 274)(197 275)(198 276)(199 277)(200 278)(201 279)(202 280)(203 281)(204 282)(205 283)(206 284)(207 285)(208 286)(209 287)(210 288)(211 289)(212 290)(213 291)(214 292)(215 293)(216 294)(217 295)(218 296)(219 297)(220 298)(221 299)(222 300)(223 301)(224 302)(225 303)(226 304)(227 267)(228 268)
(1 70)(2 71)(3 72)(4 73)(5 74)(6 75)(7 76)(8 39)(9 40)(10 41)(11 42)(12 43)(13 44)(14 45)(15 46)(16 47)(17 48)(18 49)(19 50)(20 51)(21 52)(22 53)(23 54)(24 55)(25 56)(26 57)(27 58)(28 59)(29 60)(30 61)(31 62)(32 63)(33 64)(34 65)(35 66)(36 67)(37 68)(38 69)(77 152)(78 115)(79 116)(80 117)(81 118)(82 119)(83 120)(84 121)(85 122)(86 123)(87 124)(88 125)(89 126)(90 127)(91 128)(92 129)(93 130)(94 131)(95 132)(96 133)(97 134)(98 135)(99 136)(100 137)(101 138)(102 139)(103 140)(104 141)(105 142)(106 143)(107 144)(108 145)(109 146)(110 147)(111 148)(112 149)(113 150)(114 151)(153 228)(154 191)(155 192)(156 193)(157 194)(158 195)(159 196)(160 197)(161 198)(162 199)(163 200)(164 201)(165 202)(166 203)(167 204)(168 205)(169 206)(170 207)(171 208)(172 209)(173 210)(174 211)(175 212)(176 213)(177 214)(178 215)(179 216)(180 217)(181 218)(182 219)(183 220)(184 221)(185 222)(186 223)(187 224)(188 225)(189 226)(190 227)(229 275)(230 276)(231 277)(232 278)(233 279)(234 280)(235 281)(236 282)(237 283)(238 284)(239 285)(240 286)(241 287)(242 288)(243 289)(244 290)(245 291)(246 292)(247 293)(248 294)(249 295)(250 296)(251 297)(252 298)(253 299)(254 300)(255 301)(256 302)(257 303)(258 304)(259 267)(260 268)(261 269)(262 270)(263 271)(264 272)(265 273)(266 274)
(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)| (1,190)(2,153)(3,154)(4,155)(5,156)(6,157)(7,158)(8,159)(9,160)(10,161)(11,162)(12,163)(13,164)(14,165)(15,166)(16,167)(17,168)(18,169)(19,170)(20,171)(21,172)(22,173)(23,174)(24,175)(25,176)(26,177)(27,178)(28,179)(29,180)(30,181)(31,182)(32,183)(33,184)(34,185)(35,186)(36,187)(37,188)(38,189)(39,196)(40,197)(41,198)(42,199)(43,200)(44,201)(45,202)(46,203)(47,204)(48,205)(49,206)(50,207)(51,208)(52,209)(53,210)(54,211)(55,212)(56,213)(57,214)(58,215)(59,216)(60,217)(61,218)(62,219)(63,220)(64,221)(65,222)(66,223)(67,224)(68,225)(69,226)(70,227)(71,228)(72,191)(73,192)(74,193)(75,194)(76,195)(77,234)(78,235)(79,236)(80,237)(81,238)(82,239)(83,240)(84,241)(85,242)(86,243)(87,244)(88,245)(89,246)(90,247)(91,248)(92,249)(93,250)(94,251)(95,252)(96,253)(97,254)(98,255)(99,256)(100,257)(101,258)(102,259)(103,260)(104,261)(105,262)(106,263)(107,264)(108,265)(109,266)(110,229)(111,230)(112,231)(113,232)(114,233)(115,281)(116,282)(117,283)(118,284)(119,285)(120,286)(121,287)(122,288)(123,289)(124,290)(125,291)(126,292)(127,293)(128,294)(129,295)(130,296)(131,297)(132,298)(133,299)(134,300)(135,301)(136,302)(137,303)(138,304)(139,267)(140,268)(141,269)(142,270)(143,271)(144,272)(145,273)(146,274)(147,275)(148,276)(149,277)(150,278)(151,279)(152,280), (1,102)(2,103)(3,104)(4,105)(5,106)(6,107)(7,108)(8,109)(9,110)(10,111)(11,112)(12,113)(13,114)(14,77)(15,78)(16,79)(17,80)(18,81)(19,82)(20,83)(21,84)(22,85)(23,86)(24,87)(25,88)(26,89)(27,90)(28,91)(29,92)(30,93)(31,94)(32,95)(33,96)(34,97)(35,98)(36,99)(37,100)(38,101)(39,146)(40,147)(41,148)(42,149)(43,150)(44,151)(45,152)(46,115)(47,116)(48,117)(49,118)(50,119)(51,120)(52,121)(53,122)(54,123)(55,124)(56,125)(57,126)(58,127)(59,128)(60,129)(61,130)(62,131)(63,132)(64,133)(65,134)(66,135)(67,136)(68,137)(69,138)(70,139)(71,140)(72,141)(73,142)(74,143)(75,144)(76,145)(153,260)(154,261)(155,262)(156,263)(157,264)(158,265)(159,266)(160,229)(161,230)(162,231)(163,232)(164,233)(165,234)(166,235)(167,236)(168,237)(169,238)(170,239)(171,240)(172,241)(173,242)(174,243)(175,244)(176,245)(177,246)(178,247)(179,248)(180,249)(181,250)(182,251)(183,252)(184,253)(185,254)(186,255)(187,256)(188,257)(189,258)(190,259)(191,269)(192,270)(193,271)(194,272)(195,273)(196,274)(197,275)(198,276)(199,277)(200,278)(201,279)(202,280)(203,281)(204,282)(205,283)(206,284)(207,285)(208,286)(209,287)(210,288)(211,289)(212,290)(213,291)(214,292)(215,293)(216,294)(217,295)(218,296)(219,297)(220,298)(221,299)(222,300)(223,301)(224,302)(225,303)(226,304)(227,267)(228,268), (1,70)(2,71)(3,72)(4,73)(5,74)(6,75)(7,76)(8,39)(9,40)(10,41)(11,42)(12,43)(13,44)(14,45)(15,46)(16,47)(17,48)(18,49)(19,50)(20,51)(21,52)(22,53)(23,54)(24,55)(25,56)(26,57)(27,58)(28,59)(29,60)(30,61)(31,62)(32,63)(33,64)(34,65)(35,66)(36,67)(37,68)(38,69)(77,152)(78,115)(79,116)(80,117)(81,118)(82,119)(83,120)(84,121)(85,122)(86,123)(87,124)(88,125)(89,126)(90,127)(91,128)(92,129)(93,130)(94,131)(95,132)(96,133)(97,134)(98,135)(99,136)(100,137)(101,138)(102,139)(103,140)(104,141)(105,142)(106,143)(107,144)(108,145)(109,146)(110,147)(111,148)(112,149)(113,150)(114,151)(153,228)(154,191)(155,192)(156,193)(157,194)(158,195)(159,196)(160,197)(161,198)(162,199)(163,200)(164,201)(165,202)(166,203)(167,204)(168,205)(169,206)(170,207)(171,208)(172,209)(173,210)(174,211)(175,212)(176,213)(177,214)(178,215)(179,216)(180,217)(181,218)(182,219)(183,220)(184,221)(185,222)(186,223)(187,224)(188,225)(189,226)(190,227)(229,275)(230,276)(231,277)(232,278)(233,279)(234,280)(235,281)(236,282)(237,283)(238,284)(239,285)(240,286)(241,287)(242,288)(243,289)(244,290)(245,291)(246,292)(247,293)(248,294)(249,295)(250,296)(251,297)(252,298)(253,299)(254,300)(255,301)(256,302)(257,303)(258,304)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)(265,273)(266,274), (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( (1,190)(2,153)(3,154)(4,155)(5,156)(6,157)(7,158)(8,159)(9,160)(10,161)(11,162)(12,163)(13,164)(14,165)(15,166)(16,167)(17,168)(18,169)(19,170)(20,171)(21,172)(22,173)(23,174)(24,175)(25,176)(26,177)(27,178)(28,179)(29,180)(30,181)(31,182)(32,183)(33,184)(34,185)(35,186)(36,187)(37,188)(38,189)(39,196)(40,197)(41,198)(42,199)(43,200)(44,201)(45,202)(46,203)(47,204)(48,205)(49,206)(50,207)(51,208)(52,209)(53,210)(54,211)(55,212)(56,213)(57,214)(58,215)(59,216)(60,217)(61,218)(62,219)(63,220)(64,221)(65,222)(66,223)(67,224)(68,225)(69,226)(70,227)(71,228)(72,191)(73,192)(74,193)(75,194)(76,195)(77,234)(78,235)(79,236)(80,237)(81,238)(82,239)(83,240)(84,241)(85,242)(86,243)(87,244)(88,245)(89,246)(90,247)(91,248)(92,249)(93,250)(94,251)(95,252)(96,253)(97,254)(98,255)(99,256)(100,257)(101,258)(102,259)(103,260)(104,261)(105,262)(106,263)(107,264)(108,265)(109,266)(110,229)(111,230)(112,231)(113,232)(114,233)(115,281)(116,282)(117,283)(118,284)(119,285)(120,286)(121,287)(122,288)(123,289)(124,290)(125,291)(126,292)(127,293)(128,294)(129,295)(130,296)(131,297)(132,298)(133,299)(134,300)(135,301)(136,302)(137,303)(138,304)(139,267)(140,268)(141,269)(142,270)(143,271)(144,272)(145,273)(146,274)(147,275)(148,276)(149,277)(150,278)(151,279)(152,280), (1,102)(2,103)(3,104)(4,105)(5,106)(6,107)(7,108)(8,109)(9,110)(10,111)(11,112)(12,113)(13,114)(14,77)(15,78)(16,79)(17,80)(18,81)(19,82)(20,83)(21,84)(22,85)(23,86)(24,87)(25,88)(26,89)(27,90)(28,91)(29,92)(30,93)(31,94)(32,95)(33,96)(34,97)(35,98)(36,99)(37,100)(38,101)(39,146)(40,147)(41,148)(42,149)(43,150)(44,151)(45,152)(46,115)(47,116)(48,117)(49,118)(50,119)(51,120)(52,121)(53,122)(54,123)(55,124)(56,125)(57,126)(58,127)(59,128)(60,129)(61,130)(62,131)(63,132)(64,133)(65,134)(66,135)(67,136)(68,137)(69,138)(70,139)(71,140)(72,141)(73,142)(74,143)(75,144)(76,145)(153,260)(154,261)(155,262)(156,263)(157,264)(158,265)(159,266)(160,229)(161,230)(162,231)(163,232)(164,233)(165,234)(166,235)(167,236)(168,237)(169,238)(170,239)(171,240)(172,241)(173,242)(174,243)(175,244)(176,245)(177,246)(178,247)(179,248)(180,249)(181,250)(182,251)(183,252)(184,253)(185,254)(186,255)(187,256)(188,257)(189,258)(190,259)(191,269)(192,270)(193,271)(194,272)(195,273)(196,274)(197,275)(198,276)(199,277)(200,278)(201,279)(202,280)(203,281)(204,282)(205,283)(206,284)(207,285)(208,286)(209,287)(210,288)(211,289)(212,290)(213,291)(214,292)(215,293)(216,294)(217,295)(218,296)(219,297)(220,298)(221,299)(222,300)(223,301)(224,302)(225,303)(226,304)(227,267)(228,268), (1,70)(2,71)(3,72)(4,73)(5,74)(6,75)(7,76)(8,39)(9,40)(10,41)(11,42)(12,43)(13,44)(14,45)(15,46)(16,47)(17,48)(18,49)(19,50)(20,51)(21,52)(22,53)(23,54)(24,55)(25,56)(26,57)(27,58)(28,59)(29,60)(30,61)(31,62)(32,63)(33,64)(34,65)(35,66)(36,67)(37,68)(38,69)(77,152)(78,115)(79,116)(80,117)(81,118)(82,119)(83,120)(84,121)(85,122)(86,123)(87,124)(88,125)(89,126)(90,127)(91,128)(92,129)(93,130)(94,131)(95,132)(96,133)(97,134)(98,135)(99,136)(100,137)(101,138)(102,139)(103,140)(104,141)(105,142)(106,143)(107,144)(108,145)(109,146)(110,147)(111,148)(112,149)(113,150)(114,151)(153,228)(154,191)(155,192)(156,193)(157,194)(158,195)(159,196)(160,197)(161,198)(162,199)(163,200)(164,201)(165,202)(166,203)(167,204)(168,205)(169,206)(170,207)(171,208)(172,209)(173,210)(174,211)(175,212)(176,213)(177,214)(178,215)(179,216)(180,217)(181,218)(182,219)(183,220)(184,221)(185,222)(186,223)(187,224)(188,225)(189,226)(190,227)(229,275)(230,276)(231,277)(232,278)(233,279)(234,280)(235,281)(236,282)(237,283)(238,284)(239,285)(240,286)(241,287)(242,288)(243,289)(244,290)(245,291)(246,292)(247,293)(248,294)(249,295)(250,296)(251,297)(252,298)(253,299)(254,300)(255,301)(256,302)(257,303)(258,304)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)(265,273)(266,274), (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([(1,190),(2,153),(3,154),(4,155),(5,156),(6,157),(7,158),(8,159),(9,160),(10,161),(11,162),(12,163),(13,164),(14,165),(15,166),(16,167),(17,168),(18,169),(19,170),(20,171),(21,172),(22,173),(23,174),(24,175),(25,176),(26,177),(27,178),(28,179),(29,180),(30,181),(31,182),(32,183),(33,184),(34,185),(35,186),(36,187),(37,188),(38,189),(39,196),(40,197),(41,198),(42,199),(43,200),(44,201),(45,202),(46,203),(47,204),(48,205),(49,206),(50,207),(51,208),(52,209),(53,210),(54,211),(55,212),(56,213),(57,214),(58,215),(59,216),(60,217),(61,218),(62,219),(63,220),(64,221),(65,222),(66,223),(67,224),(68,225),(69,226),(70,227),(71,228),(72,191),(73,192),(74,193),(75,194),(76,195),(77,234),(78,235),(79,236),(80,237),(81,238),(82,239),(83,240),(84,241),(85,242),(86,243),(87,244),(88,245),(89,246),(90,247),(91,248),(92,249),(93,250),(94,251),(95,252),(96,253),(97,254),(98,255),(99,256),(100,257),(101,258),(102,259),(103,260),(104,261),(105,262),(106,263),(107,264),(108,265),(109,266),(110,229),(111,230),(112,231),(113,232),(114,233),(115,281),(116,282),(117,283),(118,284),(119,285),(120,286),(121,287),(122,288),(123,289),(124,290),(125,291),(126,292),(127,293),(128,294),(129,295),(130,296),(131,297),(132,298),(133,299),(134,300),(135,301),(136,302),(137,303),(138,304),(139,267),(140,268),(141,269),(142,270),(143,271),(144,272),(145,273),(146,274),(147,275),(148,276),(149,277),(150,278),(151,279),(152,280)], [(1,102),(2,103),(3,104),(4,105),(5,106),(6,107),(7,108),(8,109),(9,110),(10,111),(11,112),(12,113),(13,114),(14,77),(15,78),(16,79),(17,80),(18,81),(19,82),(20,83),(21,84),(22,85),(23,86),(24,87),(25,88),(26,89),(27,90),(28,91),(29,92),(30,93),(31,94),(32,95),(33,96),(34,97),(35,98),(36,99),(37,100),(38,101),(39,146),(40,147),(41,148),(42,149),(43,150),(44,151),(45,152),(46,115),(47,116),(48,117),(49,118),(50,119),(51,120),(52,121),(53,122),(54,123),(55,124),(56,125),(57,126),(58,127),(59,128),(60,129),(61,130),(62,131),(63,132),(64,133),(65,134),(66,135),(67,136),(68,137),(69,138),(70,139),(71,140),(72,141),(73,142),(74,143),(75,144),(76,145),(153,260),(154,261),(155,262),(156,263),(157,264),(158,265),(159,266),(160,229),(161,230),(162,231),(163,232),(164,233),(165,234),(166,235),(167,236),(168,237),(169,238),(170,239),(171,240),(172,241),(173,242),(174,243),(175,244),(176,245),(177,246),(178,247),(179,248),(180,249),(181,250),(182,251),(183,252),(184,253),(185,254),(186,255),(187,256),(188,257),(189,258),(190,259),(191,269),(192,270),(193,271),(194,272),(195,273),(196,274),(197,275),(198,276),(199,277),(200,278),(201,279),(202,280),(203,281),(204,282),(205,283),(206,284),(207,285),(208,286),(209,287),(210,288),(211,289),(212,290),(213,291),(214,292),(215,293),(216,294),(217,295),(218,296),(219,297),(220,298),(221,299),(222,300),(223,301),(224,302),(225,303),(226,304),(227,267),(228,268)], [(1,70),(2,71),(3,72),(4,73),(5,74),(6,75),(7,76),(8,39),(9,40),(10,41),(11,42),(12,43),(13,44),(14,45),(15,46),(16,47),(17,48),(18,49),(19,50),(20,51),(21,52),(22,53),(23,54),(24,55),(25,56),(26,57),(27,58),(28,59),(29,60),(30,61),(31,62),(32,63),(33,64),(34,65),(35,66),(36,67),(37,68),(38,69),(77,152),(78,115),(79,116),(80,117),(81,118),(82,119),(83,120),(84,121),(85,122),(86,123),(87,124),(88,125),(89,126),(90,127),(91,128),(92,129),(93,130),(94,131),(95,132),(96,133),(97,134),(98,135),(99,136),(100,137),(101,138),(102,139),(103,140),(104,141),(105,142),(106,143),(107,144),(108,145),(109,146),(110,147),(111,148),(112,149),(113,150),(114,151),(153,228),(154,191),(155,192),(156,193),(157,194),(158,195),(159,196),(160,197),(161,198),(162,199),(163,200),(164,201),(165,202),(166,203),(167,204),(168,205),(169,206),(170,207),(171,208),(172,209),(173,210),(174,211),(175,212),(176,213),(177,214),(178,215),(179,216),(180,217),(181,218),(182,219),(183,220),(184,221),(185,222),(186,223),(187,224),(188,225),(189,226),(190,227),(229,275),(230,276),(231,277),(232,278),(233,279),(234,280),(235,281),(236,282),(237,283),(238,284),(239,285),(240,286),(241,287),(242,288),(243,289),(244,290),(245,291),(246,292),(247,293),(248,294),(249,295),(250,296),(251,297),(252,298),(253,299),(254,300),(255,301),(256,302),(257,303),(258,304),(259,267),(260,268),(261,269),(262,270),(263,271),(264,272),(265,273),(266,274)], [(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···2O19A···19R38A···38JJ
order12···219···1938···38
size11···11···11···1

304 irreducible representations

dim1111
type++
imageC1C2C19C38
kernelC23×C38C22×C38C24C23
# reps11518270

Matrix representation of C23×C38 in GL4(𝔽191) generated by

1000
0100
0010
000190
,
1000
0100
001900
0001
,
1000
019000
0010
000190
,
139000
03000
00690
000107
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

׿
×
𝔽