Finite Group DatabasebetaFinite Group Databasebeta| order | 7920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | C2×D32×AGL(1,𝔽11) |
| Fitting, socle | C2×C32×C11 ⋊ C23×C5 |
| derived, Hall | C32×C11 ⋊ C24×C5 |
| Hall | C2×D32×D11 ⋊ C5 |
| Hall | C32×C11⋊C5 ⋊ C24 |
| Hall | C11⋊C5 ⋊ C22×D32 |
| Sylow | C11 ⋊ C22×C5×D32 |
| Sylow | C32 ⋊ C23×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D32×AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C32×C11 | C24×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C11 | C23×C5 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C2 | |
1136 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 1136 conjugacy classes of subgroups — too many to draw. Only its 236 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, D33×AGL(1,𝔽11) |
| maximal normal subgroup of | AGL(1,𝔽11)×#3811 |
| maximal quotient of | AGL(1,𝔽11)×#3811, D33×AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.