Finite Group DatabasebetaFinite Group Databasebeta| order | 7920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | GO+(4,𝔽2)×AGL(1,𝔽11) |
| Fitting, socle, Hall | C32×C11 ⋊ C2×C5×D4 |
| Hall | D11×GO+(4,𝔽2) ⋊ C5 |
| Hall | C32×C11⋊C5 ⋊ C2×D4 |
| Hall | C11⋊C5 ⋊ C2×GO+(4,𝔽2) |
| Sylow | C11 ⋊ C2×C5×GO+(4,𝔽2) |
| Sylow | C32 ⋊ D4×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C11×C3⋊D3 | C23×C5 |
| Fitting, socle, hypocenter | C32×C11 | C2×C5×D4 |
| LCS | G ▷ C11×C3⋊D3 ▷ C32×C11 | |
| UCS | C1 | |
344 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 66 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×AΓL(1,𝔽9) |
| maximal normal subgroup of | AGL(1,𝔽11)×AΓL(1,𝔽9) |
Past the SmallGroups library coverage — no SmallGroups id.