Finite Group DatabasebetaFinite Group Databasebeta| order | 7920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×S4×AGL(1,𝔽11) |
| Fitting, socle | C22×C3×C11 ⋊ C2×C5×D3 |
| derived | C11×A4 ⋊ C22×C3×C5 |
| Hall | C3×D11×S4 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×C3×S4 |
| Sylow | C11 ⋊ C2×C3×C5×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | S4×AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C11×A4 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C11 | C2×C5×D3 |
| LCS | G ▷ C11×A4 | |
| UCS | C1 ◁ C3 | |
280 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 132 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | D3×S4×AGL(1,𝔽11) |
| maximal normal subgroup of | D3×S4×AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.