Finite Group DatabasebetaFinite Group Databasebeta| order | 7920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | #624×AGL(1,𝔽11) |
| derived, Hall | C32×C11 ⋊ C22×C4×C5 |
| Hall | D11×#624 ⋊ C5 |
| Hall | C32×C11⋊C5 ⋊ C22×C4 |
| Hall | C11⋊C5 ⋊ C2×#624 |
| Sylow | C11 ⋊ C2×C5×#624 |
| Sylow | C32 ⋊ C2×C4×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D32×AGL(1,𝔽11) |
| commutator, hypocenter | C32×C11 | C22×C4×C5 |
| Fitting, socle, cosocle | C2×C32×C11 | C23×C5 |
| prime radical | C2×C3⋊D3×AGL(1,𝔽11) | C2 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C2 | |
496 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 132 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×#3811 |
| maximal normal subgroup of | AGL(1,𝔽11)×#3811 |
Past the SmallGroups library coverage — no SmallGroups id.