Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×C3⋊D3×ΓL(1,𝔽25) |
| Fitting | C2×C33×C8 ⋊ C22 |
| Sylow | C33 ⋊ C22×M16 |
2060 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×M16×C3⋊D3, C2×C3⋊D3×#914, C2×C3⋊D3×#911 |
| maximal normal subgroup of | C2×D3×M16×C3⋊D3, C2×C3⋊D3×#914, C2×C3⋊D3×#911 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 42675);