Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C33 |
| direct product | C2×M16×C3⋊(C3⋊D3) |
| Fitting | C2×C33×M16 ⋊ C2 |
| Sylow | C33 ⋊ C22×M16 |
4172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×M16×C3⋊D3 |
| maximal normal subgroup of | C2×D3×M16×C3⋊D3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45931);