Finite Group DatabasebetaFinite Group Databasebeta| order | 5832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | D32×C9×D9 |
| Fitting, Sylow | C32×C92 ⋊ C23 |
| derived | C32×C9 ⋊ C23×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D32×D9 |
| commutator, hypocenter | C32×C9 | C23×C9 |
| Frattini | C32 | C3×D33 |
| Fitting | C32×C92 | C23 |
| socle | C34 | C22×C3×D3 |
| prime radical | C3×D32×D9 | C3 |
| cosocle | C33×C9 | C23×C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C9 | |
1251 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 1251 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
486 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D32×#92265, D32×D92 |
| maximal normal subgroup of | D32×#92265, D32×D92 |
Past the SmallGroups library coverage — no SmallGroups id.