Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#63825 |
| Sylow | C33 ⋊ C2×AGL(1,ℤ/8) |
1618 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10595100, D3×#10590397, D3×#10591510 |
| maximal normal subgroup of | D3×#10595100, D3×#10590397, D3×#10591510 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 36592);