direct product, abelian, monomial, 2-elementary
Aliases: C23×C36, SmallGroup(288,367)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C23×C36 |
| C1 — C23×C36 |
| C1 — C23×C36 |
Generators and relations for C23×C36
G = < a,b,c,d | a2=b2=c2=d36=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, cd=dc >
Subgroups: 354, all normal (12 characteristic)
C1, C2, C2, C3, C4, C22, C6, C6, C2×C4, C23, C9, C12, C2×C6, C22×C4, C24, C18, C18, C2×C12, C22×C6, C23×C4, C36, C2×C18, C22×C12, C23×C6, C2×C36, C22×C18, C23×C12, C22×C36, C23×C18, C23×C36
Quotients: C1, C2, C3, C4, C22, C6, C2×C4, C23, C9, C12, C2×C6, C22×C4, C24, C18, C2×C12, C22×C6, C23×C4, C36, C2×C18, C22×C12, C23×C6, C2×C36, C22×C18, C23×C12, C22×C36, C23×C18, C23×C36
►Regular action on 288 points
Generators in S288
(1 201)(2 202)(3 203)(4 204)(5 205)(6 206)(7 207)(8 208)(9 209)(10 210)(11 211)(12 212)(13 213)(14 214)(15 215)(16 216)(17 181)(18 182)(19 183)(20 184)(21 185)(22 186)(23 187)(24 188)(25 189)(26 190)(27 191)(28 192)(29 193)(30 194)(31 195)(32 196)(33 197)(34 198)(35 199)(36 200)(37 288)(38 253)(39 254)(40 255)(41 256)(42 257)(43 258)(44 259)(45 260)(46 261)(47 262)(48 263)(49 264)(50 265)(51 266)(52 267)(53 268)(54 269)(55 270)(56 271)(57 272)(58 273)(59 274)(60 275)(61 276)(62 277)(63 278)(64 279)(65 280)(66 281)(67 282)(68 283)(69 284)(70 285)(71 286)(72 287)(73 153)(74 154)(75 155)(76 156)(77 157)(78 158)(79 159)(80 160)(81 161)(82 162)(83 163)(84 164)(85 165)(86 166)(87 167)(88 168)(89 169)(90 170)(91 171)(92 172)(93 173)(94 174)(95 175)(96 176)(97 177)(98 178)(99 179)(100 180)(101 145)(102 146)(103 147)(104 148)(105 149)(106 150)(107 151)(108 152)(109 240)(110 241)(111 242)(112 243)(113 244)(114 245)(115 246)(116 247)(117 248)(118 249)(119 250)(120 251)(121 252)(122 217)(123 218)(124 219)(125 220)(126 221)(127 222)(128 223)(129 224)(130 225)(131 226)(132 227)(133 228)(134 229)(135 230)(136 231)(137 232)(138 233)(139 234)(140 235)(141 236)(142 237)(143 238)(144 239)
(1 233)(2 234)(3 235)(4 236)(5 237)(6 238)(7 239)(8 240)(9 241)(10 242)(11 243)(12 244)(13 245)(14 246)(15 247)(16 248)(17 249)(18 250)(19 251)(20 252)(21 217)(22 218)(23 219)(24 220)(25 221)(26 222)(27 223)(28 224)(29 225)(30 226)(31 227)(32 228)(33 229)(34 230)(35 231)(36 232)(37 86)(38 87)(39 88)(40 89)(41 90)(42 91)(43 92)(44 93)(45 94)(46 95)(47 96)(48 97)(49 98)(50 99)(51 100)(52 101)(53 102)(54 103)(55 104)(56 105)(57 106)(58 107)(59 108)(60 73)(61 74)(62 75)(63 76)(64 77)(65 78)(66 79)(67 80)(68 81)(69 82)(70 83)(71 84)(72 85)(109 208)(110 209)(111 210)(112 211)(113 212)(114 213)(115 214)(116 215)(117 216)(118 181)(119 182)(120 183)(121 184)(122 185)(123 186)(124 187)(125 188)(126 189)(127 190)(128 191)(129 192)(130 193)(131 194)(132 195)(133 196)(134 197)(135 198)(136 199)(137 200)(138 201)(139 202)(140 203)(141 204)(142 205)(143 206)(144 207)(145 267)(146 268)(147 269)(148 270)(149 271)(150 272)(151 273)(152 274)(153 275)(154 276)(155 277)(156 278)(157 279)(158 280)(159 281)(160 282)(161 283)(162 284)(163 285)(164 286)(165 287)(166 288)(167 253)(168 254)(169 255)(170 256)(171 257)(172 258)(173 259)(174 260)(175 261)(176 262)(177 263)(178 264)(179 265)(180 266)
(1 150)(2 151)(3 152)(4 153)(5 154)(6 155)(7 156)(8 157)(9 158)(10 159)(11 160)(12 161)(13 162)(14 163)(15 164)(16 165)(17 166)(18 167)(19 168)(20 169)(21 170)(22 171)(23 172)(24 173)(25 174)(26 175)(27 176)(28 177)(29 178)(30 179)(31 180)(32 145)(33 146)(34 147)(35 148)(36 149)(37 118)(38 119)(39 120)(40 121)(41 122)(42 123)(43 124)(44 125)(45 126)(46 127)(47 128)(48 129)(49 130)(50 131)(51 132)(52 133)(53 134)(54 135)(55 136)(56 137)(57 138)(58 139)(59 140)(60 141)(61 142)(62 143)(63 144)(64 109)(65 110)(66 111)(67 112)(68 113)(69 114)(70 115)(71 116)(72 117)(73 204)(74 205)(75 206)(76 207)(77 208)(78 209)(79 210)(80 211)(81 212)(82 213)(83 214)(84 215)(85 216)(86 181)(87 182)(88 183)(89 184)(90 185)(91 186)(92 187)(93 188)(94 189)(95 190)(96 191)(97 192)(98 193)(99 194)(100 195)(101 196)(102 197)(103 198)(104 199)(105 200)(106 201)(107 202)(108 203)(217 256)(218 257)(219 258)(220 259)(221 260)(222 261)(223 262)(224 263)(225 264)(226 265)(227 266)(228 267)(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)(250 253)(251 254)(252 255)
(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)
G:=sub<Sym(288)| (1,201)(2,202)(3,203)(4,204)(5,205)(6,206)(7,207)(8,208)(9,209)(10,210)(11,211)(12,212)(13,213)(14,214)(15,215)(16,216)(17,181)(18,182)(19,183)(20,184)(21,185)(22,186)(23,187)(24,188)(25,189)(26,190)(27,191)(28,192)(29,193)(30,194)(31,195)(32,196)(33,197)(34,198)(35,199)(36,200)(37,288)(38,253)(39,254)(40,255)(41,256)(42,257)(43,258)(44,259)(45,260)(46,261)(47,262)(48,263)(49,264)(50,265)(51,266)(52,267)(53,268)(54,269)(55,270)(56,271)(57,272)(58,273)(59,274)(60,275)(61,276)(62,277)(63,278)(64,279)(65,280)(66,281)(67,282)(68,283)(69,284)(70,285)(71,286)(72,287)(73,153)(74,154)(75,155)(76,156)(77,157)(78,158)(79,159)(80,160)(81,161)(82,162)(83,163)(84,164)(85,165)(86,166)(87,167)(88,168)(89,169)(90,170)(91,171)(92,172)(93,173)(94,174)(95,175)(96,176)(97,177)(98,178)(99,179)(100,180)(101,145)(102,146)(103,147)(104,148)(105,149)(106,150)(107,151)(108,152)(109,240)(110,241)(111,242)(112,243)(113,244)(114,245)(115,246)(116,247)(117,248)(118,249)(119,250)(120,251)(121,252)(122,217)(123,218)(124,219)(125,220)(126,221)(127,222)(128,223)(129,224)(130,225)(131,226)(132,227)(133,228)(134,229)(135,230)(136,231)(137,232)(138,233)(139,234)(140,235)(141,236)(142,237)(143,238)(144,239), (1,233)(2,234)(3,235)(4,236)(5,237)(6,238)(7,239)(8,240)(9,241)(10,242)(11,243)(12,244)(13,245)(14,246)(15,247)(16,248)(17,249)(18,250)(19,251)(20,252)(21,217)(22,218)(23,219)(24,220)(25,221)(26,222)(27,223)(28,224)(29,225)(30,226)(31,227)(32,228)(33,229)(34,230)(35,231)(36,232)(37,86)(38,87)(39,88)(40,89)(41,90)(42,91)(43,92)(44,93)(45,94)(46,95)(47,96)(48,97)(49,98)(50,99)(51,100)(52,101)(53,102)(54,103)(55,104)(56,105)(57,106)(58,107)(59,108)(60,73)(61,74)(62,75)(63,76)(64,77)(65,78)(66,79)(67,80)(68,81)(69,82)(70,83)(71,84)(72,85)(109,208)(110,209)(111,210)(112,211)(113,212)(114,213)(115,214)(116,215)(117,216)(118,181)(119,182)(120,183)(121,184)(122,185)(123,186)(124,187)(125,188)(126,189)(127,190)(128,191)(129,192)(130,193)(131,194)(132,195)(133,196)(134,197)(135,198)(136,199)(137,200)(138,201)(139,202)(140,203)(141,204)(142,205)(143,206)(144,207)(145,267)(146,268)(147,269)(148,270)(149,271)(150,272)(151,273)(152,274)(153,275)(154,276)(155,277)(156,278)(157,279)(158,280)(159,281)(160,282)(161,283)(162,284)(163,285)(164,286)(165,287)(166,288)(167,253)(168,254)(169,255)(170,256)(171,257)(172,258)(173,259)(174,260)(175,261)(176,262)(177,263)(178,264)(179,265)(180,266), (1,150)(2,151)(3,152)(4,153)(5,154)(6,155)(7,156)(8,157)(9,158)(10,159)(11,160)(12,161)(13,162)(14,163)(15,164)(16,165)(17,166)(18,167)(19,168)(20,169)(21,170)(22,171)(23,172)(24,173)(25,174)(26,175)(27,176)(28,177)(29,178)(30,179)(31,180)(32,145)(33,146)(34,147)(35,148)(36,149)(37,118)(38,119)(39,120)(40,121)(41,122)(42,123)(43,124)(44,125)(45,126)(46,127)(47,128)(48,129)(49,130)(50,131)(51,132)(52,133)(53,134)(54,135)(55,136)(56,137)(57,138)(58,139)(59,140)(60,141)(61,142)(62,143)(63,144)(64,109)(65,110)(66,111)(67,112)(68,113)(69,114)(70,115)(71,116)(72,117)(73,204)(74,205)(75,206)(76,207)(77,208)(78,209)(79,210)(80,211)(81,212)(82,213)(83,214)(84,215)(85,216)(86,181)(87,182)(88,183)(89,184)(90,185)(91,186)(92,187)(93,188)(94,189)(95,190)(96,191)(97,192)(98,193)(99,194)(100,195)(101,196)(102,197)(103,198)(104,199)(105,200)(106,201)(107,202)(108,203)(217,256)(218,257)(219,258)(220,259)(221,260)(222,261)(223,262)(224,263)(225,264)(226,265)(227,266)(228,267)(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)(250,253)(251,254)(252,255), (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)>;
G:=Group( (1,201)(2,202)(3,203)(4,204)(5,205)(6,206)(7,207)(8,208)(9,209)(10,210)(11,211)(12,212)(13,213)(14,214)(15,215)(16,216)(17,181)(18,182)(19,183)(20,184)(21,185)(22,186)(23,187)(24,188)(25,189)(26,190)(27,191)(28,192)(29,193)(30,194)(31,195)(32,196)(33,197)(34,198)(35,199)(36,200)(37,288)(38,253)(39,254)(40,255)(41,256)(42,257)(43,258)(44,259)(45,260)(46,261)(47,262)(48,263)(49,264)(50,265)(51,266)(52,267)(53,268)(54,269)(55,270)(56,271)(57,272)(58,273)(59,274)(60,275)(61,276)(62,277)(63,278)(64,279)(65,280)(66,281)(67,282)(68,283)(69,284)(70,285)(71,286)(72,287)(73,153)(74,154)(75,155)(76,156)(77,157)(78,158)(79,159)(80,160)(81,161)(82,162)(83,163)(84,164)(85,165)(86,166)(87,167)(88,168)(89,169)(90,170)(91,171)(92,172)(93,173)(94,174)(95,175)(96,176)(97,177)(98,178)(99,179)(100,180)(101,145)(102,146)(103,147)(104,148)(105,149)(106,150)(107,151)(108,152)(109,240)(110,241)(111,242)(112,243)(113,244)(114,245)(115,246)(116,247)(117,248)(118,249)(119,250)(120,251)(121,252)(122,217)(123,218)(124,219)(125,220)(126,221)(127,222)(128,223)(129,224)(130,225)(131,226)(132,227)(133,228)(134,229)(135,230)(136,231)(137,232)(138,233)(139,234)(140,235)(141,236)(142,237)(143,238)(144,239), (1,233)(2,234)(3,235)(4,236)(5,237)(6,238)(7,239)(8,240)(9,241)(10,242)(11,243)(12,244)(13,245)(14,246)(15,247)(16,248)(17,249)(18,250)(19,251)(20,252)(21,217)(22,218)(23,219)(24,220)(25,221)(26,222)(27,223)(28,224)(29,225)(30,226)(31,227)(32,228)(33,229)(34,230)(35,231)(36,232)(37,86)(38,87)(39,88)(40,89)(41,90)(42,91)(43,92)(44,93)(45,94)(46,95)(47,96)(48,97)(49,98)(50,99)(51,100)(52,101)(53,102)(54,103)(55,104)(56,105)(57,106)(58,107)(59,108)(60,73)(61,74)(62,75)(63,76)(64,77)(65,78)(66,79)(67,80)(68,81)(69,82)(70,83)(71,84)(72,85)(109,208)(110,209)(111,210)(112,211)(113,212)(114,213)(115,214)(116,215)(117,216)(118,181)(119,182)(120,183)(121,184)(122,185)(123,186)(124,187)(125,188)(126,189)(127,190)(128,191)(129,192)(130,193)(131,194)(132,195)(133,196)(134,197)(135,198)(136,199)(137,200)(138,201)(139,202)(140,203)(141,204)(142,205)(143,206)(144,207)(145,267)(146,268)(147,269)(148,270)(149,271)(150,272)(151,273)(152,274)(153,275)(154,276)(155,277)(156,278)(157,279)(158,280)(159,281)(160,282)(161,283)(162,284)(163,285)(164,286)(165,287)(166,288)(167,253)(168,254)(169,255)(170,256)(171,257)(172,258)(173,259)(174,260)(175,261)(176,262)(177,263)(178,264)(179,265)(180,266), (1,150)(2,151)(3,152)(4,153)(5,154)(6,155)(7,156)(8,157)(9,158)(10,159)(11,160)(12,161)(13,162)(14,163)(15,164)(16,165)(17,166)(18,167)(19,168)(20,169)(21,170)(22,171)(23,172)(24,173)(25,174)(26,175)(27,176)(28,177)(29,178)(30,179)(31,180)(32,145)(33,146)(34,147)(35,148)(36,149)(37,118)(38,119)(39,120)(40,121)(41,122)(42,123)(43,124)(44,125)(45,126)(46,127)(47,128)(48,129)(49,130)(50,131)(51,132)(52,133)(53,134)(54,135)(55,136)(56,137)(57,138)(58,139)(59,140)(60,141)(61,142)(62,143)(63,144)(64,109)(65,110)(66,111)(67,112)(68,113)(69,114)(70,115)(71,116)(72,117)(73,204)(74,205)(75,206)(76,207)(77,208)(78,209)(79,210)(80,211)(81,212)(82,213)(83,214)(84,215)(85,216)(86,181)(87,182)(88,183)(89,184)(90,185)(91,186)(92,187)(93,188)(94,189)(95,190)(96,191)(97,192)(98,193)(99,194)(100,195)(101,196)(102,197)(103,198)(104,199)(105,200)(106,201)(107,202)(108,203)(217,256)(218,257)(219,258)(220,259)(221,260)(222,261)(223,262)(224,263)(225,264)(226,265)(227,266)(228,267)(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)(250,253)(251,254)(252,255), (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) );
G=PermutationGroup([[(1,201),(2,202),(3,203),(4,204),(5,205),(6,206),(7,207),(8,208),(9,209),(10,210),(11,211),(12,212),(13,213),(14,214),(15,215),(16,216),(17,181),(18,182),(19,183),(20,184),(21,185),(22,186),(23,187),(24,188),(25,189),(26,190),(27,191),(28,192),(29,193),(30,194),(31,195),(32,196),(33,197),(34,198),(35,199),(36,200),(37,288),(38,253),(39,254),(40,255),(41,256),(42,257),(43,258),(44,259),(45,260),(46,261),(47,262),(48,263),(49,264),(50,265),(51,266),(52,267),(53,268),(54,269),(55,270),(56,271),(57,272),(58,273),(59,274),(60,275),(61,276),(62,277),(63,278),(64,279),(65,280),(66,281),(67,282),(68,283),(69,284),(70,285),(71,286),(72,287),(73,153),(74,154),(75,155),(76,156),(77,157),(78,158),(79,159),(80,160),(81,161),(82,162),(83,163),(84,164),(85,165),(86,166),(87,167),(88,168),(89,169),(90,170),(91,171),(92,172),(93,173),(94,174),(95,175),(96,176),(97,177),(98,178),(99,179),(100,180),(101,145),(102,146),(103,147),(104,148),(105,149),(106,150),(107,151),(108,152),(109,240),(110,241),(111,242),(112,243),(113,244),(114,245),(115,246),(116,247),(117,248),(118,249),(119,250),(120,251),(121,252),(122,217),(123,218),(124,219),(125,220),(126,221),(127,222),(128,223),(129,224),(130,225),(131,226),(132,227),(133,228),(134,229),(135,230),(136,231),(137,232),(138,233),(139,234),(140,235),(141,236),(142,237),(143,238),(144,239)], [(1,233),(2,234),(3,235),(4,236),(5,237),(6,238),(7,239),(8,240),(9,241),(10,242),(11,243),(12,244),(13,245),(14,246),(15,247),(16,248),(17,249),(18,250),(19,251),(20,252),(21,217),(22,218),(23,219),(24,220),(25,221),(26,222),(27,223),(28,224),(29,225),(30,226),(31,227),(32,228),(33,229),(34,230),(35,231),(36,232),(37,86),(38,87),(39,88),(40,89),(41,90),(42,91),(43,92),(44,93),(45,94),(46,95),(47,96),(48,97),(49,98),(50,99),(51,100),(52,101),(53,102),(54,103),(55,104),(56,105),(57,106),(58,107),(59,108),(60,73),(61,74),(62,75),(63,76),(64,77),(65,78),(66,79),(67,80),(68,81),(69,82),(70,83),(71,84),(72,85),(109,208),(110,209),(111,210),(112,211),(113,212),(114,213),(115,214),(116,215),(117,216),(118,181),(119,182),(120,183),(121,184),(122,185),(123,186),(124,187),(125,188),(126,189),(127,190),(128,191),(129,192),(130,193),(131,194),(132,195),(133,196),(134,197),(135,198),(136,199),(137,200),(138,201),(139,202),(140,203),(141,204),(142,205),(143,206),(144,207),(145,267),(146,268),(147,269),(148,270),(149,271),(150,272),(151,273),(152,274),(153,275),(154,276),(155,277),(156,278),(157,279),(158,280),(159,281),(160,282),(161,283),(162,284),(163,285),(164,286),(165,287),(166,288),(167,253),(168,254),(169,255),(170,256),(171,257),(172,258),(173,259),(174,260),(175,261),(176,262),(177,263),(178,264),(179,265),(180,266)], [(1,150),(2,151),(3,152),(4,153),(5,154),(6,155),(7,156),(8,157),(9,158),(10,159),(11,160),(12,161),(13,162),(14,163),(15,164),(16,165),(17,166),(18,167),(19,168),(20,169),(21,170),(22,171),(23,172),(24,173),(25,174),(26,175),(27,176),(28,177),(29,178),(30,179),(31,180),(32,145),(33,146),(34,147),(35,148),(36,149),(37,118),(38,119),(39,120),(40,121),(41,122),(42,123),(43,124),(44,125),(45,126),(46,127),(47,128),(48,129),(49,130),(50,131),(51,132),(52,133),(53,134),(54,135),(55,136),(56,137),(57,138),(58,139),(59,140),(60,141),(61,142),(62,143),(63,144),(64,109),(65,110),(66,111),(67,112),(68,113),(69,114),(70,115),(71,116),(72,117),(73,204),(74,205),(75,206),(76,207),(77,208),(78,209),(79,210),(80,211),(81,212),(82,213),(83,214),(84,215),(85,216),(86,181),(87,182),(88,183),(89,184),(90,185),(91,186),(92,187),(93,188),(94,189),(95,190),(96,191),(97,192),(98,193),(99,194),(100,195),(101,196),(102,197),(103,198),(104,199),(105,200),(106,201),(107,202),(108,203),(217,256),(218,257),(219,258),(220,259),(221,260),(222,261),(223,262),(224,263),(225,264),(226,265),(227,266),(228,267),(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),(250,253),(251,254),(252,255)], [(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)]])
288 conjugacy classes
| class | 1 | 2A | ··· | 2O | 3A | 3B | 4A | ··· | 4P | 6A | ··· | 6AD | 9A | ··· | 9F | 12A | ··· | 12AF | 18A | ··· | 18CL | 36A | ··· | 36CR |
| order | 1 | 2 | ··· | 2 | 3 | 3 | 4 | ··· | 4 | 6 | ··· | 6 | 9 | ··· | 9 | 12 | ··· | 12 | 18 | ··· | 18 | 36 | ··· | 36 |
| size | 1 | 1 | ··· | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
288 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | + | |||||||||
| image | C1 | C2 | C2 | C3 | C4 | C6 | C6 | C9 | C12 | C18 | C18 | C36 |
| kernel | C23×C36 | C22×C36 | C23×C18 | C23×C12 | C22×C18 | C22×C12 | C23×C6 | C23×C4 | C22×C6 | C22×C4 | C24 | C23 |
| # reps | 1 | 14 | 1 | 2 | 16 | 28 | 2 | 6 | 32 | 84 | 6 | 96 |
Matrix representation of C23×C36 ►in GL4(𝔽37) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 36 |
| 36 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 36 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 36 | 0 |
| 0 | 0 | 0 | 36 |
| 31 | 0 | 0 | 0 |
| 0 | 6 | 0 | 0 |
| 0 | 0 | 34 | 0 |
| 0 | 0 | 0 | 6 |
G:=sub<GL(4,GF(37))| [1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,36],[36,0,0,0,0,1,0,0,0,0,36,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,36,0,0,0,0,36],[31,0,0,0,0,6,0,0,0,0,34,0,0,0,0,6] >;
C23×C36 in GAP, Magma, Sage, TeX
C_2^3\times C_{36} % in TeX
G:=Group("C2^3xC36"); // GroupNames label
G:=SmallGroup(288,367);
// by ID
G=gap.SmallGroup(288,367);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-2,-3,336,242]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^2=d^36=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