Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C24 |
| direct product | AGL(1,ℤ/9)×#1020 |
| Fitting | C24×3−1+2 ⋊ C2×D3 |
| derived | C9×C22⋊A4 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C9×C22⋊A4 | C22×C3 |
| Frattini | C3 | C3×D3×#1020 |
| Fitting | C24×3−1+2 | C2×D3 |
| socle | C24×C3 | C3×D32 |
| LCS | G ▷ C9×C22⋊A4 | |
| UCS | C1 | |
1584 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 1584 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
100 conjugacy classes — view the full character table.
| maximal quotient of | AGL(1,ℤ/9)×#5935, AGL(1,ℤ/9)×#5934 |
Past the SmallGroups library coverage — no SmallGroups id.