Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27 |
| direct product | C3×D3×#953 |
| Fitting | C24×C33 ⋊ C22 |
| Sylow | C33 ⋊ C2×#120 |
3790 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#10595527, C3×D3×C3⋊(#120⋊C3), C3×D3×C3⋊#1020, … |
| maximal normal subgroup of | D3×#10595527, C3×D3×C3⋊(#120⋊C3), C3×D3×#5032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 41183);