Finite Group DatabasebetaFinite Group Databasebeta| order | 5280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C210 |
| direct product | C23×D3×AGL(1,𝔽11) |
| Fitting, socle | C23×C3×C11 ⋊ C22×C5 |
| derived, Hall | C3×C11 ⋊ C25×C5 |
| Hall | C23×D3×D11 ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ C25 |
| Hall | C11⋊C5 ⋊ C24×D3 |
| Sylow | C11 ⋊ C24×C5×D3 |
| Sylow | C3 ⋊ C24×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C3×C11 | C25×C5 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C11 | C22×C5 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C23 | |
2992 conjugacy classes of subgroups; only the 965 normal subgroups are shown.
This group has 2992 conjugacy classes of subgroups — too many to draw. Only its 965 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
264 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.