Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | D3×#63648 |
| Fitting | C2×C33×C8 ⋊ C22 |
| Sylow | C33 ⋊ C2×#102 |
1412 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10592410, D3×C3⋊D3×#102, D3×#10592484 |
| maximal normal subgroup of | D3×#10592410, D3×C3⋊D3×#102, D3×#10592484 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 26095);