Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C24×C3 |
| direct product | C3×D3×C3⋊#1020 |
| Fitting, socle | C24×C33 ⋊ C2×D3 |
| derived | C32×C22⋊A4 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×C3⋊#1020 |
| commutator, cosocle, hypocenter | C32×C22⋊A4 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C33 | C2×D3 |
| LCS | G ▷ C32×C22⋊A4 | |
| UCS | C1 ◁ C3 | |
3198 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 3198 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#10593244, D3×#13166068, D3×#13181837 |
| maximal normal subgroup of | C3×D3×#10593244, D3×#13166068, D3×#13181837 |
Past the SmallGroups library coverage — no SmallGroups id.