Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×#13166068 |
| Fitting | C24×C33 ⋊ C2×D3 |
| derived | C32×C22⋊A4 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13166068 |
| commutator, cosocle, hypocenter | C32×C22⋊A4 | C22×C3 |
| Frattini | C22 | C3×D3×C3⋊S4 |
| Fitting | C24×C33 | C2×D3 |
| socle | C22×C33 | C2×S4 |
| LCS | G ▷ C32×C22⋊A4 | |
| UCS | C1 ◁ C3 | |
1724 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 1724 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72210357, C3×D3×#10593244, D3×#13166068, … |
| maximal normal subgroup of | C3×#72210357, C3×D3×#10593244, D3×#13166068, … |
Past the SmallGroups library coverage — no SmallGroups id.