Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27 |
| direct product | C3×D9×#120 |
| Fitting | C3×C9×#120 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×#120 |
2116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D9×#120, #120×D27⋊C3 |
| maximal normal subgroup of | D3×D9×#120 |
| maximal quotient of | #120×D27⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18816);