Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#13181790 |
| Fitting, socle | C24×C32 ⋊ D32 |
| derived | C3×A42 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13181790 |
| commutator, cosocle, hypocenter | C3×A42 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C32 | D32 |
| LCS | G ▷ C3×A42 | |
| UCS | C1 ◁ C3 | |
1559 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 1559 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
117 conjugacy classes — view the full character table.
| maximal subgroup of | #72222957, #72222979, C3×D3×S42, … |
| maximal normal subgroup of | #72222979, C3×D3×S42, D3×#13181790 |
Past the SmallGroups library coverage — no SmallGroups id.