Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27×C3 |
| direct product | C2×C3×#64162 |
| Fitting | C25×C33 ⋊ C2 |
| Sylow | C33 ⋊ C2×#120 |
6964 conjugacy classes of subgroups; only the 750 normal subgroups are shown.
This group has 6964 conjugacy classes of subgroups — too many to draw. Only its 750 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
468 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72220148, C2×#72220152, C2×C3×C3⋊D3×#120, … |
| maximal normal subgroup of | C2×C3×C3⋊D3×#120, C22×C3×#64162 |
| maximal quotient of | C22×C3×#64162, C2×C3×#10592940 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45654);