Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×D3×#932 |
| Fitting | C2×C33×D4 ⋊ C22 |
| Sylow | C33 ⋊ C2×AGL(1,ℤ/8) |
1618 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10595100, C3×D3×#5077, D3×#10591522 |
| maximal normal subgroup of | D3×#10595100, C3×D3×#5077, D3×#10591522 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 40852);