Finite Group DatabasebetaFinite Group Databasebeta| order | 3888 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C22×D9×AGL(1,ℤ/9) |
| Fitting | C22×C9×3−1+2 ⋊ C22 |
| derived | C92 ⋊ C24×C3 |
| Sylow | C9×3−1+2 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D9×AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C92 | C24×C3 |
| Frattini | C32 | C22×C3×D32 |
| Fitting | C22×C9×3−1+2 | C22 |
| socle | C22×C32 | C3×D32 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C22 | |
1519 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 1519 conjugacy classes of subgroups — too many to draw. Only its 276 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
240 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.