Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×C3×#64269 |
| Fitting | C25×C32 ⋊ D3 |
1670 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 1670 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72220155, C22×C3×#64269 |
| maximal normal subgroup of | C22×C3×#64269 |
| maximal quotient of | C2×#72220152, C2×C3×#10593663, C22×C3×#64269 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47455);