| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×D3×#805 |
| Fitting | C33×C42 ⋊ C22 |
| Sylow | C33 ⋊ C2×#104 |
906 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#10590393, C3×D3×#5077, D3×#10590397 |
| maximal normal subgroup of | D3×#10590393, C3×D3×#5077, D3×#10590397 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 23471);