Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | D3×#64102 |
| Fitting | C33×C4⋊C4 ⋊ C22 |
| Sylow | C33 ⋊ C2×C4×D4 |
2932 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10592568, C4×D3×D4×C3⋊D3, D3×#10592484 |
| maximal normal subgroup of | D3×#10592568, C4×D3×D4×C3⋊D3, D3×#10592484 |
| maximal quotient of | D3×#10592568 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 42589);