Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C33 |
| direct product | #106×C3⋊(C3⋊D3) |
| Fitting | C33×#106 ⋊ C2 |
| Sylow | C33 ⋊ C2×#106 |
1820 conjugacy classes of subgroups; only the 427 normal subgroups are shown.
This group has 1820 conjugacy classes of subgroups — too many to draw. Only its 427 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×#106, C3⋊(C3⋊D3)×#442, #72245230 |
| maximal normal subgroup of | D3×C3⋊D3×#106, C3⋊(C3⋊D3)×#442, #72245230 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 29562);