direct product, abelian, monomial
Aliases: C22×C6×C12, SmallGroup(288,1018)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C22×C6×C12 |
| C1 — C22×C6×C12 |
| C1 — C22×C6×C12 |
Generators and relations for C22×C6×C12
G = < a,b,c,d | a2=b2=c6=d12=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, cd=dc >
Subgroups: 708, all normal (8 characteristic)
C1, C2, C2, C3, C4, C22, C6, C2×C4, C23, C32, C12, C2×C6, C22×C4, C24, C3×C6, C3×C6, C2×C12, C22×C6, C23×C4, C3×C12, C62, C22×C12, C23×C6, C6×C12, C2×C62, C23×C12, C2×C6×C12, C22×C62, C22×C6×C12
Quotients: C1, C2, C3, C4, C22, C6, C2×C4, C23, C32, C12, C2×C6, C22×C4, C24, C3×C6, C2×C12, C22×C6, C23×C4, C3×C12, C62, C22×C12, C23×C6, C6×C12, C2×C62, C23×C12, C2×C6×C12, C22×C62, C22×C6×C12
►Regular action on 288 points
Generators in S288
(1 209)(2 210)(3 211)(4 212)(5 213)(6 214)(7 215)(8 216)(9 205)(10 206)(11 207)(12 208)(13 90)(14 91)(15 92)(16 93)(17 94)(18 95)(19 96)(20 85)(21 86)(22 87)(23 88)(24 89)(25 235)(26 236)(27 237)(28 238)(29 239)(30 240)(31 229)(32 230)(33 231)(34 232)(35 233)(36 234)(37 171)(38 172)(39 173)(40 174)(41 175)(42 176)(43 177)(44 178)(45 179)(46 180)(47 169)(48 170)(49 192)(50 181)(51 182)(52 183)(53 184)(54 185)(55 186)(56 187)(57 188)(58 189)(59 190)(60 191)(61 134)(62 135)(63 136)(64 137)(65 138)(66 139)(67 140)(68 141)(69 142)(70 143)(71 144)(72 133)(73 102)(74 103)(75 104)(76 105)(77 106)(78 107)(79 108)(80 97)(81 98)(82 99)(83 100)(84 101)(109 242)(110 243)(111 244)(112 245)(113 246)(114 247)(115 248)(116 249)(117 250)(118 251)(119 252)(120 241)(121 268)(122 269)(123 270)(124 271)(125 272)(126 273)(127 274)(128 275)(129 276)(130 265)(131 266)(132 267)(145 199)(146 200)(147 201)(148 202)(149 203)(150 204)(151 193)(152 194)(153 195)(154 196)(155 197)(156 198)(157 261)(158 262)(159 263)(160 264)(161 253)(162 254)(163 255)(164 256)(165 257)(166 258)(167 259)(168 260)(217 277)(218 278)(219 279)(220 280)(221 281)(222 282)(223 283)(224 284)(225 285)(226 286)(227 287)(228 288)
(1 82)(2 83)(3 84)(4 73)(5 74)(6 75)(7 76)(8 77)(9 78)(10 79)(11 80)(12 81)(13 129)(14 130)(15 131)(16 132)(17 121)(18 122)(19 123)(20 124)(21 125)(22 126)(23 127)(24 128)(25 175)(26 176)(27 177)(28 178)(29 179)(30 180)(31 169)(32 170)(33 171)(34 172)(35 173)(36 174)(37 231)(38 232)(39 233)(40 234)(41 235)(42 236)(43 237)(44 238)(45 239)(46 240)(47 229)(48 230)(49 198)(50 199)(51 200)(52 201)(53 202)(54 203)(55 204)(56 193)(57 194)(58 195)(59 196)(60 197)(61 167)(62 168)(63 157)(64 158)(65 159)(66 160)(67 161)(68 162)(69 163)(70 164)(71 165)(72 166)(85 271)(86 272)(87 273)(88 274)(89 275)(90 276)(91 265)(92 266)(93 267)(94 268)(95 269)(96 270)(97 207)(98 208)(99 209)(100 210)(101 211)(102 212)(103 213)(104 214)(105 215)(106 216)(107 205)(108 206)(109 223)(110 224)(111 225)(112 226)(113 227)(114 228)(115 217)(116 218)(117 219)(118 220)(119 221)(120 222)(133 258)(134 259)(135 260)(136 261)(137 262)(138 263)(139 264)(140 253)(141 254)(142 255)(143 256)(144 257)(145 181)(146 182)(147 183)(148 184)(149 185)(150 186)(151 187)(152 188)(153 189)(154 190)(155 191)(156 192)(241 282)(242 283)(243 284)(244 285)(245 286)(246 287)(247 288)(248 277)(249 278)(250 279)(251 280)(252 281)
(1 181 40 62 112 123)(2 182 41 63 113 124)(3 183 42 64 114 125)(4 184 43 65 115 126)(5 185 44 66 116 127)(6 186 45 67 117 128)(7 187 46 68 118 129)(8 188 47 69 119 130)(9 189 48 70 120 131)(10 190 37 71 109 132)(11 191 38 72 110 121)(12 192 39 61 111 122)(13 76 151 240 162 220)(14 77 152 229 163 221)(15 78 153 230 164 222)(16 79 154 231 165 223)(17 80 155 232 166 224)(18 81 156 233 167 225)(19 82 145 234 168 226)(20 83 146 235 157 227)(21 84 147 236 158 228)(22 73 148 237 159 217)(23 74 149 238 160 218)(24 75 150 239 161 219)(25 261 287 85 100 200)(26 262 288 86 101 201)(27 263 277 87 102 202)(28 264 278 88 103 203)(29 253 279 89 104 204)(30 254 280 90 105 193)(31 255 281 91 106 194)(32 256 282 92 107 195)(33 257 283 93 108 196)(34 258 284 94 97 197)(35 259 285 95 98 198)(36 260 286 96 99 199)(49 173 134 244 269 208)(50 174 135 245 270 209)(51 175 136 246 271 210)(52 176 137 247 272 211)(53 177 138 248 273 212)(54 178 139 249 274 213)(55 179 140 250 275 214)(56 180 141 251 276 215)(57 169 142 252 265 216)(58 170 143 241 266 205)(59 171 144 242 267 206)(60 172 133 243 268 207)
(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)| (1,209)(2,210)(3,211)(4,212)(5,213)(6,214)(7,215)(8,216)(9,205)(10,206)(11,207)(12,208)(13,90)(14,91)(15,92)(16,93)(17,94)(18,95)(19,96)(20,85)(21,86)(22,87)(23,88)(24,89)(25,235)(26,236)(27,237)(28,238)(29,239)(30,240)(31,229)(32,230)(33,231)(34,232)(35,233)(36,234)(37,171)(38,172)(39,173)(40,174)(41,175)(42,176)(43,177)(44,178)(45,179)(46,180)(47,169)(48,170)(49,192)(50,181)(51,182)(52,183)(53,184)(54,185)(55,186)(56,187)(57,188)(58,189)(59,190)(60,191)(61,134)(62,135)(63,136)(64,137)(65,138)(66,139)(67,140)(68,141)(69,142)(70,143)(71,144)(72,133)(73,102)(74,103)(75,104)(76,105)(77,106)(78,107)(79,108)(80,97)(81,98)(82,99)(83,100)(84,101)(109,242)(110,243)(111,244)(112,245)(113,246)(114,247)(115,248)(116,249)(117,250)(118,251)(119,252)(120,241)(121,268)(122,269)(123,270)(124,271)(125,272)(126,273)(127,274)(128,275)(129,276)(130,265)(131,266)(132,267)(145,199)(146,200)(147,201)(148,202)(149,203)(150,204)(151,193)(152,194)(153,195)(154,196)(155,197)(156,198)(157,261)(158,262)(159,263)(160,264)(161,253)(162,254)(163,255)(164,256)(165,257)(166,258)(167,259)(168,260)(217,277)(218,278)(219,279)(220,280)(221,281)(222,282)(223,283)(224,284)(225,285)(226,286)(227,287)(228,288), (1,82)(2,83)(3,84)(4,73)(5,74)(6,75)(7,76)(8,77)(9,78)(10,79)(11,80)(12,81)(13,129)(14,130)(15,131)(16,132)(17,121)(18,122)(19,123)(20,124)(21,125)(22,126)(23,127)(24,128)(25,175)(26,176)(27,177)(28,178)(29,179)(30,180)(31,169)(32,170)(33,171)(34,172)(35,173)(36,174)(37,231)(38,232)(39,233)(40,234)(41,235)(42,236)(43,237)(44,238)(45,239)(46,240)(47,229)(48,230)(49,198)(50,199)(51,200)(52,201)(53,202)(54,203)(55,204)(56,193)(57,194)(58,195)(59,196)(60,197)(61,167)(62,168)(63,157)(64,158)(65,159)(66,160)(67,161)(68,162)(69,163)(70,164)(71,165)(72,166)(85,271)(86,272)(87,273)(88,274)(89,275)(90,276)(91,265)(92,266)(93,267)(94,268)(95,269)(96,270)(97,207)(98,208)(99,209)(100,210)(101,211)(102,212)(103,213)(104,214)(105,215)(106,216)(107,205)(108,206)(109,223)(110,224)(111,225)(112,226)(113,227)(114,228)(115,217)(116,218)(117,219)(118,220)(119,221)(120,222)(133,258)(134,259)(135,260)(136,261)(137,262)(138,263)(139,264)(140,253)(141,254)(142,255)(143,256)(144,257)(145,181)(146,182)(147,183)(148,184)(149,185)(150,186)(151,187)(152,188)(153,189)(154,190)(155,191)(156,192)(241,282)(242,283)(243,284)(244,285)(245,286)(246,287)(247,288)(248,277)(249,278)(250,279)(251,280)(252,281), (1,181,40,62,112,123)(2,182,41,63,113,124)(3,183,42,64,114,125)(4,184,43,65,115,126)(5,185,44,66,116,127)(6,186,45,67,117,128)(7,187,46,68,118,129)(8,188,47,69,119,130)(9,189,48,70,120,131)(10,190,37,71,109,132)(11,191,38,72,110,121)(12,192,39,61,111,122)(13,76,151,240,162,220)(14,77,152,229,163,221)(15,78,153,230,164,222)(16,79,154,231,165,223)(17,80,155,232,166,224)(18,81,156,233,167,225)(19,82,145,234,168,226)(20,83,146,235,157,227)(21,84,147,236,158,228)(22,73,148,237,159,217)(23,74,149,238,160,218)(24,75,150,239,161,219)(25,261,287,85,100,200)(26,262,288,86,101,201)(27,263,277,87,102,202)(28,264,278,88,103,203)(29,253,279,89,104,204)(30,254,280,90,105,193)(31,255,281,91,106,194)(32,256,282,92,107,195)(33,257,283,93,108,196)(34,258,284,94,97,197)(35,259,285,95,98,198)(36,260,286,96,99,199)(49,173,134,244,269,208)(50,174,135,245,270,209)(51,175,136,246,271,210)(52,176,137,247,272,211)(53,177,138,248,273,212)(54,178,139,249,274,213)(55,179,140,250,275,214)(56,180,141,251,276,215)(57,169,142,252,265,216)(58,170,143,241,266,205)(59,171,144,242,267,206)(60,172,133,243,268,207), (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( (1,209)(2,210)(3,211)(4,212)(5,213)(6,214)(7,215)(8,216)(9,205)(10,206)(11,207)(12,208)(13,90)(14,91)(15,92)(16,93)(17,94)(18,95)(19,96)(20,85)(21,86)(22,87)(23,88)(24,89)(25,235)(26,236)(27,237)(28,238)(29,239)(30,240)(31,229)(32,230)(33,231)(34,232)(35,233)(36,234)(37,171)(38,172)(39,173)(40,174)(41,175)(42,176)(43,177)(44,178)(45,179)(46,180)(47,169)(48,170)(49,192)(50,181)(51,182)(52,183)(53,184)(54,185)(55,186)(56,187)(57,188)(58,189)(59,190)(60,191)(61,134)(62,135)(63,136)(64,137)(65,138)(66,139)(67,140)(68,141)(69,142)(70,143)(71,144)(72,133)(73,102)(74,103)(75,104)(76,105)(77,106)(78,107)(79,108)(80,97)(81,98)(82,99)(83,100)(84,101)(109,242)(110,243)(111,244)(112,245)(113,246)(114,247)(115,248)(116,249)(117,250)(118,251)(119,252)(120,241)(121,268)(122,269)(123,270)(124,271)(125,272)(126,273)(127,274)(128,275)(129,276)(130,265)(131,266)(132,267)(145,199)(146,200)(147,201)(148,202)(149,203)(150,204)(151,193)(152,194)(153,195)(154,196)(155,197)(156,198)(157,261)(158,262)(159,263)(160,264)(161,253)(162,254)(163,255)(164,256)(165,257)(166,258)(167,259)(168,260)(217,277)(218,278)(219,279)(220,280)(221,281)(222,282)(223,283)(224,284)(225,285)(226,286)(227,287)(228,288), (1,82)(2,83)(3,84)(4,73)(5,74)(6,75)(7,76)(8,77)(9,78)(10,79)(11,80)(12,81)(13,129)(14,130)(15,131)(16,132)(17,121)(18,122)(19,123)(20,124)(21,125)(22,126)(23,127)(24,128)(25,175)(26,176)(27,177)(28,178)(29,179)(30,180)(31,169)(32,170)(33,171)(34,172)(35,173)(36,174)(37,231)(38,232)(39,233)(40,234)(41,235)(42,236)(43,237)(44,238)(45,239)(46,240)(47,229)(48,230)(49,198)(50,199)(51,200)(52,201)(53,202)(54,203)(55,204)(56,193)(57,194)(58,195)(59,196)(60,197)(61,167)(62,168)(63,157)(64,158)(65,159)(66,160)(67,161)(68,162)(69,163)(70,164)(71,165)(72,166)(85,271)(86,272)(87,273)(88,274)(89,275)(90,276)(91,265)(92,266)(93,267)(94,268)(95,269)(96,270)(97,207)(98,208)(99,209)(100,210)(101,211)(102,212)(103,213)(104,214)(105,215)(106,216)(107,205)(108,206)(109,223)(110,224)(111,225)(112,226)(113,227)(114,228)(115,217)(116,218)(117,219)(118,220)(119,221)(120,222)(133,258)(134,259)(135,260)(136,261)(137,262)(138,263)(139,264)(140,253)(141,254)(142,255)(143,256)(144,257)(145,181)(146,182)(147,183)(148,184)(149,185)(150,186)(151,187)(152,188)(153,189)(154,190)(155,191)(156,192)(241,282)(242,283)(243,284)(244,285)(245,286)(246,287)(247,288)(248,277)(249,278)(250,279)(251,280)(252,281), (1,181,40,62,112,123)(2,182,41,63,113,124)(3,183,42,64,114,125)(4,184,43,65,115,126)(5,185,44,66,116,127)(6,186,45,67,117,128)(7,187,46,68,118,129)(8,188,47,69,119,130)(9,189,48,70,120,131)(10,190,37,71,109,132)(11,191,38,72,110,121)(12,192,39,61,111,122)(13,76,151,240,162,220)(14,77,152,229,163,221)(15,78,153,230,164,222)(16,79,154,231,165,223)(17,80,155,232,166,224)(18,81,156,233,167,225)(19,82,145,234,168,226)(20,83,146,235,157,227)(21,84,147,236,158,228)(22,73,148,237,159,217)(23,74,149,238,160,218)(24,75,150,239,161,219)(25,261,287,85,100,200)(26,262,288,86,101,201)(27,263,277,87,102,202)(28,264,278,88,103,203)(29,253,279,89,104,204)(30,254,280,90,105,193)(31,255,281,91,106,194)(32,256,282,92,107,195)(33,257,283,93,108,196)(34,258,284,94,97,197)(35,259,285,95,98,198)(36,260,286,96,99,199)(49,173,134,244,269,208)(50,174,135,245,270,209)(51,175,136,246,271,210)(52,176,137,247,272,211)(53,177,138,248,273,212)(54,178,139,249,274,213)(55,179,140,250,275,214)(56,180,141,251,276,215)(57,169,142,252,265,216)(58,170,143,241,266,205)(59,171,144,242,267,206)(60,172,133,243,268,207), (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([[(1,209),(2,210),(3,211),(4,212),(5,213),(6,214),(7,215),(8,216),(9,205),(10,206),(11,207),(12,208),(13,90),(14,91),(15,92),(16,93),(17,94),(18,95),(19,96),(20,85),(21,86),(22,87),(23,88),(24,89),(25,235),(26,236),(27,237),(28,238),(29,239),(30,240),(31,229),(32,230),(33,231),(34,232),(35,233),(36,234),(37,171),(38,172),(39,173),(40,174),(41,175),(42,176),(43,177),(44,178),(45,179),(46,180),(47,169),(48,170),(49,192),(50,181),(51,182),(52,183),(53,184),(54,185),(55,186),(56,187),(57,188),(58,189),(59,190),(60,191),(61,134),(62,135),(63,136),(64,137),(65,138),(66,139),(67,140),(68,141),(69,142),(70,143),(71,144),(72,133),(73,102),(74,103),(75,104),(76,105),(77,106),(78,107),(79,108),(80,97),(81,98),(82,99),(83,100),(84,101),(109,242),(110,243),(111,244),(112,245),(113,246),(114,247),(115,248),(116,249),(117,250),(118,251),(119,252),(120,241),(121,268),(122,269),(123,270),(124,271),(125,272),(126,273),(127,274),(128,275),(129,276),(130,265),(131,266),(132,267),(145,199),(146,200),(147,201),(148,202),(149,203),(150,204),(151,193),(152,194),(153,195),(154,196),(155,197),(156,198),(157,261),(158,262),(159,263),(160,264),(161,253),(162,254),(163,255),(164,256),(165,257),(166,258),(167,259),(168,260),(217,277),(218,278),(219,279),(220,280),(221,281),(222,282),(223,283),(224,284),(225,285),(226,286),(227,287),(228,288)], [(1,82),(2,83),(3,84),(4,73),(5,74),(6,75),(7,76),(8,77),(9,78),(10,79),(11,80),(12,81),(13,129),(14,130),(15,131),(16,132),(17,121),(18,122),(19,123),(20,124),(21,125),(22,126),(23,127),(24,128),(25,175),(26,176),(27,177),(28,178),(29,179),(30,180),(31,169),(32,170),(33,171),(34,172),(35,173),(36,174),(37,231),(38,232),(39,233),(40,234),(41,235),(42,236),(43,237),(44,238),(45,239),(46,240),(47,229),(48,230),(49,198),(50,199),(51,200),(52,201),(53,202),(54,203),(55,204),(56,193),(57,194),(58,195),(59,196),(60,197),(61,167),(62,168),(63,157),(64,158),(65,159),(66,160),(67,161),(68,162),(69,163),(70,164),(71,165),(72,166),(85,271),(86,272),(87,273),(88,274),(89,275),(90,276),(91,265),(92,266),(93,267),(94,268),(95,269),(96,270),(97,207),(98,208),(99,209),(100,210),(101,211),(102,212),(103,213),(104,214),(105,215),(106,216),(107,205),(108,206),(109,223),(110,224),(111,225),(112,226),(113,227),(114,228),(115,217),(116,218),(117,219),(118,220),(119,221),(120,222),(133,258),(134,259),(135,260),(136,261),(137,262),(138,263),(139,264),(140,253),(141,254),(142,255),(143,256),(144,257),(145,181),(146,182),(147,183),(148,184),(149,185),(150,186),(151,187),(152,188),(153,189),(154,190),(155,191),(156,192),(241,282),(242,283),(243,284),(244,285),(245,286),(246,287),(247,288),(248,277),(249,278),(250,279),(251,280),(252,281)], [(1,181,40,62,112,123),(2,182,41,63,113,124),(3,183,42,64,114,125),(4,184,43,65,115,126),(5,185,44,66,116,127),(6,186,45,67,117,128),(7,187,46,68,118,129),(8,188,47,69,119,130),(9,189,48,70,120,131),(10,190,37,71,109,132),(11,191,38,72,110,121),(12,192,39,61,111,122),(13,76,151,240,162,220),(14,77,152,229,163,221),(15,78,153,230,164,222),(16,79,154,231,165,223),(17,80,155,232,166,224),(18,81,156,233,167,225),(19,82,145,234,168,226),(20,83,146,235,157,227),(21,84,147,236,158,228),(22,73,148,237,159,217),(23,74,149,238,160,218),(24,75,150,239,161,219),(25,261,287,85,100,200),(26,262,288,86,101,201),(27,263,277,87,102,202),(28,264,278,88,103,203),(29,253,279,89,104,204),(30,254,280,90,105,193),(31,255,281,91,106,194),(32,256,282,92,107,195),(33,257,283,93,108,196),(34,258,284,94,97,197),(35,259,285,95,98,198),(36,260,286,96,99,199),(49,173,134,244,269,208),(50,174,135,245,270,209),(51,175,136,246,271,210),(52,176,137,247,272,211),(53,177,138,248,273,212),(54,178,139,249,274,213),(55,179,140,250,275,214),(56,180,141,251,276,215),(57,169,142,252,265,216),(58,170,143,241,266,205),(59,171,144,242,267,206),(60,172,133,243,268,207)], [(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 | ··· | 3H | 4A | ··· | 4P | 6A | ··· | 6DP | 12A | ··· | 12DX |
| order | 1 | 2 | ··· | 2 | 3 | ··· | 3 | 4 | ··· | 4 | 6 | ··· | 6 | 12 | ··· | 12 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
288 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | + | |||||
| image | C1 | C2 | C2 | C3 | C4 | C6 | C6 | C12 |
| kernel | C22×C6×C12 | C2×C6×C12 | C22×C62 | C23×C12 | C2×C62 | C22×C12 | C23×C6 | C22×C6 |
| # reps | 1 | 14 | 1 | 8 | 16 | 112 | 8 | 128 |
Matrix representation of C22×C6×C12 ►in GL4(𝔽13) generated by
| 12 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 1 |
| 12 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 1 |
| 4 | 0 | 0 | 0 |
| 0 | 3 | 0 | 0 |
| 0 | 0 | 9 | 0 |
| 0 | 0 | 0 | 4 |
| 9 | 0 | 0 | 0 |
| 0 | 4 | 0 | 0 |
| 0 | 0 | 2 | 0 |
| 0 | 0 | 0 | 9 |
G:=sub<GL(4,GF(13))| [12,0,0,0,0,12,0,0,0,0,12,0,0,0,0,1],[12,0,0,0,0,1,0,0,0,0,12,0,0,0,0,1],[4,0,0,0,0,3,0,0,0,0,9,0,0,0,0,4],[9,0,0,0,0,4,0,0,0,0,2,0,0,0,0,9] >;
C22×C6×C12 in GAP, Magma, Sage, TeX
C_2^2\times C_6\times C_{12} % in TeX
G:=Group("C2^2xC6xC12"); // GroupNames label
G:=SmallGroup(288,1018);
// by ID
G=gap.SmallGroup(288,1018);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-2,1008]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^6=d^12=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