direct product, metabelian, nilpotent (class 2), monomial
Aliases: D4×C3×C18, C12.26C62, C4⋊(C6×C18), C36⋊9(C2×C6), C12⋊4(C2×C18), (C2×C12)⋊6C18, (C2×C36)⋊14C6, (C6×C36)⋊14C2, (C6×C12).47C6, (C6×C18)⋊9C22, C22⋊3(C6×C18), C23⋊3(C3×C18), (C22×C6)⋊3C18, (C22×C18)⋊9C6, (C2×C6).7C62, C32.5(C6×D4), (C3×C36)⋊14C22, (C2×C62).21C6, C6.13(C2×C62), C62.45(C2×C6), (C6×D4).1C32, C6.21(D4×C32), C6.14(C22×C18), (C3×C18).58C23, C18.28(C22×C6), (D4×C32).16C6, (C2×C6×C18)⋊2C2, C3.1(D4×C3×C6), C2.1(C2×C6×C18), (D4×C3×C6).2C3, (C2×C4)⋊2(C3×C18), (C2×C6)⋊4(C2×C18), (C2×C18)⋊11(C2×C6), (C3×D4).9(C3×C6), (C3×C6).79(C3×D4), (C2×C12).16(C3×C6), (C3×C12).104(C2×C6), (C3×C6).69(C22×C6), (C22×C6).16(C3×C6), SmallGroup(432,403)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D4×C3×C18
G = < a,b,c,d | a3=b18=c4=d2=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=c-1 >
Subgroups: 350 in 270 conjugacy classes, 190 normal (20 characteristic)
C1, C2, C2, C2, C3, C3, C4, C22, C22, C22, C6, C6, C6, C2×C4, D4, C23, C9, C32, C12, C2×C6, C2×C6, C2×C6, C2×D4, C18, C18, C3×C6, C3×C6, C3×C6, C2×C12, C2×C12, C3×D4, C22×C6, C3×C9, C36, C2×C18, C2×C18, C3×C12, C62, C62, C62, C6×D4, C6×D4, C3×C18, C3×C18, C3×C18, C2×C36, D4×C9, C22×C18, C6×C12, D4×C32, C2×C62, C3×C36, C6×C18, C6×C18, C6×C18, D4×C18, D4×C3×C6, C6×C36, D4×C3×C9, C2×C6×C18, D4×C3×C18
Quotients: C1, C2, C3, C22, C6, D4, C23, C9, C32, C2×C6, C2×D4, C18, C3×C6, C3×D4, C22×C6, C3×C9, C2×C18, C62, C6×D4, C3×C18, D4×C9, C22×C18, D4×C32, C2×C62, C6×C18, D4×C18, D4×C3×C6, D4×C3×C9, C2×C6×C18, D4×C3×C18
►On 216 points
Generators in S216
(1 213 32)(2 214 33)(3 215 34)(4 216 35)(5 199 36)(6 200 19)(7 201 20)(8 202 21)(9 203 22)(10 204 23)(11 205 24)(12 206 25)(13 207 26)(14 208 27)(15 209 28)(16 210 29)(17 211 30)(18 212 31)(37 105 156)(38 106 157)(39 107 158)(40 108 159)(41 91 160)(42 92 161)(43 93 162)(44 94 145)(45 95 146)(46 96 147)(47 97 148)(48 98 149)(49 99 150)(50 100 151)(51 101 152)(52 102 153)(53 103 154)(54 104 155)(55 174 128)(56 175 129)(57 176 130)(58 177 131)(59 178 132)(60 179 133)(61 180 134)(62 163 135)(63 164 136)(64 165 137)(65 166 138)(66 167 139)(67 168 140)(68 169 141)(69 170 142)(70 171 143)(71 172 144)(72 173 127)(73 192 110)(74 193 111)(75 194 112)(76 195 113)(77 196 114)(78 197 115)(79 198 116)(80 181 117)(81 182 118)(82 183 119)(83 184 120)(84 185 121)(85 186 122)(86 187 123)(87 188 124)(88 189 125)(89 190 126)(90 191 109)
(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)
(1 81 91 167)(2 82 92 168)(3 83 93 169)(4 84 94 170)(5 85 95 171)(6 86 96 172)(7 87 97 173)(8 88 98 174)(9 89 99 175)(10 90 100 176)(11 73 101 177)(12 74 102 178)(13 75 103 179)(14 76 104 180)(15 77 105 163)(16 78 106 164)(17 79 107 165)(18 80 108 166)(19 123 46 71)(20 124 47 72)(21 125 48 55)(22 126 49 56)(23 109 50 57)(24 110 51 58)(25 111 52 59)(26 112 53 60)(27 113 54 61)(28 114 37 62)(29 115 38 63)(30 116 39 64)(31 117 40 65)(32 118 41 66)(33 119 42 67)(34 120 43 68)(35 121 44 69)(36 122 45 70)(127 201 188 148)(128 202 189 149)(129 203 190 150)(130 204 191 151)(131 205 192 152)(132 206 193 153)(133 207 194 154)(134 208 195 155)(135 209 196 156)(136 210 197 157)(137 211 198 158)(138 212 181 159)(139 213 182 160)(140 214 183 161)(141 215 184 162)(142 216 185 145)(143 199 186 146)(144 200 187 147)
(1 90)(2 73)(3 74)(4 75)(5 76)(6 77)(7 78)(8 79)(9 80)(10 81)(11 82)(12 83)(13 84)(14 85)(15 86)(16 87)(17 88)(18 89)(19 114)(20 115)(21 116)(22 117)(23 118)(24 119)(25 120)(26 121)(27 122)(28 123)(29 124)(30 125)(31 126)(32 109)(33 110)(34 111)(35 112)(36 113)(37 71)(38 72)(39 55)(40 56)(41 57)(42 58)(43 59)(44 60)(45 61)(46 62)(47 63)(48 64)(49 65)(50 66)(51 67)(52 68)(53 69)(54 70)(91 176)(92 177)(93 178)(94 179)(95 180)(96 163)(97 164)(98 165)(99 166)(100 167)(101 168)(102 169)(103 170)(104 171)(105 172)(106 173)(107 174)(108 175)(127 157)(128 158)(129 159)(130 160)(131 161)(132 162)(133 145)(134 146)(135 147)(136 148)(137 149)(138 150)(139 151)(140 152)(141 153)(142 154)(143 155)(144 156)(181 203)(182 204)(183 205)(184 206)(185 207)(186 208)(187 209)(188 210)(189 211)(190 212)(191 213)(192 214)(193 215)(194 216)(195 199)(196 200)(197 201)(198 202)
G:=sub<Sym(216)| (1,213,32)(2,214,33)(3,215,34)(4,216,35)(5,199,36)(6,200,19)(7,201,20)(8,202,21)(9,203,22)(10,204,23)(11,205,24)(12,206,25)(13,207,26)(14,208,27)(15,209,28)(16,210,29)(17,211,30)(18,212,31)(37,105,156)(38,106,157)(39,107,158)(40,108,159)(41,91,160)(42,92,161)(43,93,162)(44,94,145)(45,95,146)(46,96,147)(47,97,148)(48,98,149)(49,99,150)(50,100,151)(51,101,152)(52,102,153)(53,103,154)(54,104,155)(55,174,128)(56,175,129)(57,176,130)(58,177,131)(59,178,132)(60,179,133)(61,180,134)(62,163,135)(63,164,136)(64,165,137)(65,166,138)(66,167,139)(67,168,140)(68,169,141)(69,170,142)(70,171,143)(71,172,144)(72,173,127)(73,192,110)(74,193,111)(75,194,112)(76,195,113)(77,196,114)(78,197,115)(79,198,116)(80,181,117)(81,182,118)(82,183,119)(83,184,120)(84,185,121)(85,186,122)(86,187,123)(87,188,124)(88,189,125)(89,190,126)(90,191,109), (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), (1,81,91,167)(2,82,92,168)(3,83,93,169)(4,84,94,170)(5,85,95,171)(6,86,96,172)(7,87,97,173)(8,88,98,174)(9,89,99,175)(10,90,100,176)(11,73,101,177)(12,74,102,178)(13,75,103,179)(14,76,104,180)(15,77,105,163)(16,78,106,164)(17,79,107,165)(18,80,108,166)(19,123,46,71)(20,124,47,72)(21,125,48,55)(22,126,49,56)(23,109,50,57)(24,110,51,58)(25,111,52,59)(26,112,53,60)(27,113,54,61)(28,114,37,62)(29,115,38,63)(30,116,39,64)(31,117,40,65)(32,118,41,66)(33,119,42,67)(34,120,43,68)(35,121,44,69)(36,122,45,70)(127,201,188,148)(128,202,189,149)(129,203,190,150)(130,204,191,151)(131,205,192,152)(132,206,193,153)(133,207,194,154)(134,208,195,155)(135,209,196,156)(136,210,197,157)(137,211,198,158)(138,212,181,159)(139,213,182,160)(140,214,183,161)(141,215,184,162)(142,216,185,145)(143,199,186,146)(144,200,187,147), (1,90)(2,73)(3,74)(4,75)(5,76)(6,77)(7,78)(8,79)(9,80)(10,81)(11,82)(12,83)(13,84)(14,85)(15,86)(16,87)(17,88)(18,89)(19,114)(20,115)(21,116)(22,117)(23,118)(24,119)(25,120)(26,121)(27,122)(28,123)(29,124)(30,125)(31,126)(32,109)(33,110)(34,111)(35,112)(36,113)(37,71)(38,72)(39,55)(40,56)(41,57)(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)(48,64)(49,65)(50,66)(51,67)(52,68)(53,69)(54,70)(91,176)(92,177)(93,178)(94,179)(95,180)(96,163)(97,164)(98,165)(99,166)(100,167)(101,168)(102,169)(103,170)(104,171)(105,172)(106,173)(107,174)(108,175)(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,145)(134,146)(135,147)(136,148)(137,149)(138,150)(139,151)(140,152)(141,153)(142,154)(143,155)(144,156)(181,203)(182,204)(183,205)(184,206)(185,207)(186,208)(187,209)(188,210)(189,211)(190,212)(191,213)(192,214)(193,215)(194,216)(195,199)(196,200)(197,201)(198,202)>;
G:=Group( (1,213,32)(2,214,33)(3,215,34)(4,216,35)(5,199,36)(6,200,19)(7,201,20)(8,202,21)(9,203,22)(10,204,23)(11,205,24)(12,206,25)(13,207,26)(14,208,27)(15,209,28)(16,210,29)(17,211,30)(18,212,31)(37,105,156)(38,106,157)(39,107,158)(40,108,159)(41,91,160)(42,92,161)(43,93,162)(44,94,145)(45,95,146)(46,96,147)(47,97,148)(48,98,149)(49,99,150)(50,100,151)(51,101,152)(52,102,153)(53,103,154)(54,104,155)(55,174,128)(56,175,129)(57,176,130)(58,177,131)(59,178,132)(60,179,133)(61,180,134)(62,163,135)(63,164,136)(64,165,137)(65,166,138)(66,167,139)(67,168,140)(68,169,141)(69,170,142)(70,171,143)(71,172,144)(72,173,127)(73,192,110)(74,193,111)(75,194,112)(76,195,113)(77,196,114)(78,197,115)(79,198,116)(80,181,117)(81,182,118)(82,183,119)(83,184,120)(84,185,121)(85,186,122)(86,187,123)(87,188,124)(88,189,125)(89,190,126)(90,191,109), (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), (1,81,91,167)(2,82,92,168)(3,83,93,169)(4,84,94,170)(5,85,95,171)(6,86,96,172)(7,87,97,173)(8,88,98,174)(9,89,99,175)(10,90,100,176)(11,73,101,177)(12,74,102,178)(13,75,103,179)(14,76,104,180)(15,77,105,163)(16,78,106,164)(17,79,107,165)(18,80,108,166)(19,123,46,71)(20,124,47,72)(21,125,48,55)(22,126,49,56)(23,109,50,57)(24,110,51,58)(25,111,52,59)(26,112,53,60)(27,113,54,61)(28,114,37,62)(29,115,38,63)(30,116,39,64)(31,117,40,65)(32,118,41,66)(33,119,42,67)(34,120,43,68)(35,121,44,69)(36,122,45,70)(127,201,188,148)(128,202,189,149)(129,203,190,150)(130,204,191,151)(131,205,192,152)(132,206,193,153)(133,207,194,154)(134,208,195,155)(135,209,196,156)(136,210,197,157)(137,211,198,158)(138,212,181,159)(139,213,182,160)(140,214,183,161)(141,215,184,162)(142,216,185,145)(143,199,186,146)(144,200,187,147), (1,90)(2,73)(3,74)(4,75)(5,76)(6,77)(7,78)(8,79)(9,80)(10,81)(11,82)(12,83)(13,84)(14,85)(15,86)(16,87)(17,88)(18,89)(19,114)(20,115)(21,116)(22,117)(23,118)(24,119)(25,120)(26,121)(27,122)(28,123)(29,124)(30,125)(31,126)(32,109)(33,110)(34,111)(35,112)(36,113)(37,71)(38,72)(39,55)(40,56)(41,57)(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)(48,64)(49,65)(50,66)(51,67)(52,68)(53,69)(54,70)(91,176)(92,177)(93,178)(94,179)(95,180)(96,163)(97,164)(98,165)(99,166)(100,167)(101,168)(102,169)(103,170)(104,171)(105,172)(106,173)(107,174)(108,175)(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,145)(134,146)(135,147)(136,148)(137,149)(138,150)(139,151)(140,152)(141,153)(142,154)(143,155)(144,156)(181,203)(182,204)(183,205)(184,206)(185,207)(186,208)(187,209)(188,210)(189,211)(190,212)(191,213)(192,214)(193,215)(194,216)(195,199)(196,200)(197,201)(198,202) );
G=PermutationGroup([[(1,213,32),(2,214,33),(3,215,34),(4,216,35),(5,199,36),(6,200,19),(7,201,20),(8,202,21),(9,203,22),(10,204,23),(11,205,24),(12,206,25),(13,207,26),(14,208,27),(15,209,28),(16,210,29),(17,211,30),(18,212,31),(37,105,156),(38,106,157),(39,107,158),(40,108,159),(41,91,160),(42,92,161),(43,93,162),(44,94,145),(45,95,146),(46,96,147),(47,97,148),(48,98,149),(49,99,150),(50,100,151),(51,101,152),(52,102,153),(53,103,154),(54,104,155),(55,174,128),(56,175,129),(57,176,130),(58,177,131),(59,178,132),(60,179,133),(61,180,134),(62,163,135),(63,164,136),(64,165,137),(65,166,138),(66,167,139),(67,168,140),(68,169,141),(69,170,142),(70,171,143),(71,172,144),(72,173,127),(73,192,110),(74,193,111),(75,194,112),(76,195,113),(77,196,114),(78,197,115),(79,198,116),(80,181,117),(81,182,118),(82,183,119),(83,184,120),(84,185,121),(85,186,122),(86,187,123),(87,188,124),(88,189,125),(89,190,126),(90,191,109)], [(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)], [(1,81,91,167),(2,82,92,168),(3,83,93,169),(4,84,94,170),(5,85,95,171),(6,86,96,172),(7,87,97,173),(8,88,98,174),(9,89,99,175),(10,90,100,176),(11,73,101,177),(12,74,102,178),(13,75,103,179),(14,76,104,180),(15,77,105,163),(16,78,106,164),(17,79,107,165),(18,80,108,166),(19,123,46,71),(20,124,47,72),(21,125,48,55),(22,126,49,56),(23,109,50,57),(24,110,51,58),(25,111,52,59),(26,112,53,60),(27,113,54,61),(28,114,37,62),(29,115,38,63),(30,116,39,64),(31,117,40,65),(32,118,41,66),(33,119,42,67),(34,120,43,68),(35,121,44,69),(36,122,45,70),(127,201,188,148),(128,202,189,149),(129,203,190,150),(130,204,191,151),(131,205,192,152),(132,206,193,153),(133,207,194,154),(134,208,195,155),(135,209,196,156),(136,210,197,157),(137,211,198,158),(138,212,181,159),(139,213,182,160),(140,214,183,161),(141,215,184,162),(142,216,185,145),(143,199,186,146),(144,200,187,147)], [(1,90),(2,73),(3,74),(4,75),(5,76),(6,77),(7,78),(8,79),(9,80),(10,81),(11,82),(12,83),(13,84),(14,85),(15,86),(16,87),(17,88),(18,89),(19,114),(20,115),(21,116),(22,117),(23,118),(24,119),(25,120),(26,121),(27,122),(28,123),(29,124),(30,125),(31,126),(32,109),(33,110),(34,111),(35,112),(36,113),(37,71),(38,72),(39,55),(40,56),(41,57),(42,58),(43,59),(44,60),(45,61),(46,62),(47,63),(48,64),(49,65),(50,66),(51,67),(52,68),(53,69),(54,70),(91,176),(92,177),(93,178),(94,179),(95,180),(96,163),(97,164),(98,165),(99,166),(100,167),(101,168),(102,169),(103,170),(104,171),(105,172),(106,173),(107,174),(108,175),(127,157),(128,158),(129,159),(130,160),(131,161),(132,162),(133,145),(134,146),(135,147),(136,148),(137,149),(138,150),(139,151),(140,152),(141,153),(142,154),(143,155),(144,156),(181,203),(182,204),(183,205),(184,206),(185,207),(186,208),(187,209),(188,210),(189,211),(190,212),(191,213),(192,214),(193,215),(194,216),(195,199),(196,200),(197,201),(198,202)]])
270 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3A | ··· | 3H | 4A | 4B | 6A | ··· | 6X | 6Y | ··· | 6BD | 9A | ··· | 9R | 12A | ··· | 12P | 18A | ··· | 18BB | 18BC | ··· | 18DV | 36A | ··· | 36AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | ··· | 3 | 4 | 4 | 6 | ··· | 6 | 6 | ··· | 6 | 9 | ··· | 9 | 12 | ··· | 12 | 18 | ··· | 18 | 18 | ··· | 18 | 36 | ··· | 36 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 |
270 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | |||||||||||||||
| image | C1 | C2 | C2 | C2 | C3 | C3 | C6 | C6 | C6 | C6 | C6 | C6 | C9 | C18 | C18 | C18 | D4 | C3×D4 | C3×D4 | D4×C9 |
| kernel | D4×C3×C18 | C6×C36 | D4×C3×C9 | C2×C6×C18 | D4×C18 | D4×C3×C6 | C2×C36 | D4×C9 | C22×C18 | C6×C12 | D4×C32 | C2×C62 | C6×D4 | C2×C12 | C3×D4 | C22×C6 | C3×C18 | C18 | C3×C6 | C6 |
| # reps | 1 | 1 | 4 | 2 | 6 | 2 | 6 | 24 | 12 | 2 | 8 | 4 | 18 | 18 | 72 | 36 | 2 | 12 | 4 | 36 |
Matrix representation of D4×C3×C18 ►in GL3(𝔽37) generated by
| 1 | 0 | 0 |
| 0 | 10 | 0 |
| 0 | 0 | 10 |
| 4 | 0 | 0 |
| 0 | 36 | 0 |
| 0 | 0 | 36 |
| 36 | 0 | 0 |
| 0 | 0 | 1 |
| 0 | 36 | 0 |
| 36 | 0 | 0 |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
G:=sub<GL(3,GF(37))| [1,0,0,0,10,0,0,0,10],[4,0,0,0,36,0,0,0,36],[36,0,0,0,0,36,0,1,0],[36,0,0,0,0,1,0,1,0] >;
D4×C3×C18 in GAP, Magma, Sage, TeX
D_4\times C_3\times C_{18} % in TeX
G:=Group("D4xC3xC18"); // GroupNames label
G:=SmallGroup(432,403);
// by ID
G=gap.SmallGroup(432,403);
# by ID
G:=PCGroup([7,-2,-2,-2,-3,-3,-2,-3,1037,528]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^18=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations