Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C4×D3×#638 |
| Fitting | C22×C33×C4 ⋊ C22 |
| Sylow | C33 ⋊ C2×C4×D4 |
2932 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×D4×C3⋊D3 |
| maximal normal subgroup of | C4×D3×D4×C3⋊D3 |
| maximal quotient of | D3×#10592713 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 43356);