Finite Group DatabasebetaFinite Group Databasebeta| order | 2640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | C22×D3×AGL(1,𝔽11) |
| Fitting, socle | C22×C3×C11 ⋊ C22×C5 |
| derived, Hall | C3×C11 ⋊ C24×C5 |
| Hall | C22×D3×D11 ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ C24 |
| Hall | C11⋊C5 ⋊ C23×D3 |
| Sylow | C11 ⋊ C23×C5×D3 |
| Sylow | C3 ⋊ C23×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C3×C11 | C24×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C11 | C22×C5 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C22 | |
536 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
132 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.