Finite Group DatabasebetaFinite Group Databasebeta| order | 27324 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,ℤ/9)×AGL(1,𝔽23) |
| Fitting, Hall | C23×3−1+2 ⋊ C22×C11 |
| derived | C9×C23 ⋊ C22×C3×C11 |
| Hall | 3−1+2×C23⋊C11 ⋊ C22 |
| Hall | D23×AGL(1,ℤ/9) ⋊ C11 |
| Hall | C23⋊C11 ⋊ C2×AGL(1,ℤ/9) |
| Sylow | 3−1+2 ⋊ C2×AGL(1,𝔽23) |
| Sylow | C23 ⋊ C2×C11×AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C9×C23 | C22×C3×C11 |
| Frattini | C3 | C3×D3×AGL(1,𝔽23) |
| Fitting | C23×3−1+2 | C22×C11 |
| socle | C3×C23 | C2×C3×D3×C11 |
| LCS | G ▷ C9×C23 | |
| UCS | C1 | |
128 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 207 |
230 conjugacy classes — view the full character table.
| holomorph of | C9×C23 |
Past the SmallGroups library coverage — no SmallGroups id.