Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×D3×#3753 |
| Fitting | C2×C33×D4 ⋊ C22 |
| Sylow | C33 ⋊ C22×D8 |
2332 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×D8×C3⋊D3, D3×#10592713, D3×#10592484 |
| maximal normal subgroup of | C2×D3×D8×C3⋊D3, D3×#10592713, D3×#10592484 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 43612);