Finite Group DatabasebetaFinite Group Databasebeta| order | 7920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C3⋊D3×AGL(1,𝔽11) |
| Fitting, socle | C22×C32×C11 ⋊ C22×C5 |
| derived, Hall | C32×C11 ⋊ C24×C5 |
| Hall | C22×C3⋊D3×D11 ⋊ C5 |
| Hall | C32×C11⋊C5 ⋊ C24 |
| Hall | C11⋊C5 ⋊ C23×C3⋊D3 |
| Sylow | C11 ⋊ C23×C5×C3⋊D3 |
| Sylow | C32 ⋊ C23×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊D3×AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C32×C11 | C24×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C11 | C22×C5 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C22 | |
1608 conjugacy classes of subgroups; only the 335 normal subgroups are shown.
This group has 1608 conjugacy classes of subgroups — too many to draw. Only its 335 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 396 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,𝔽11)×#3811 |
| maximal normal subgroup of | AGL(1,𝔽11)×#3811 |
Past the SmallGroups library coverage — no SmallGroups id.