Finite Group DatabasebetaFinite Group Databasebeta| order | 3168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D11×AΓL(1,𝔽9) |
| Fitting, socle, Hall | C32×C11 ⋊ C2×SD16 |
| Sylow | C11 ⋊ C2×AΓL(1,𝔽9) |
| Sylow | C32 ⋊ SD16×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C11×#157 | C23 |
| Fitting, socle, hypocenter | C32×C11 | C2×SD16 |
| prime radical | D11×GO+(4,𝔽2) | C2 |
| LCS | G ▷ C11×#157 ▷ C11×C3⋊D3 ▷ C32×C11 | |
| UCS | C1 | |
168 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 99 |
63 conjugacy classes — view the full character table.
| maximal subgroup of | D11×AGL(2,𝔽3), AGL(1,𝔽11)×AΓL(1,𝔽9) |
| maximal normal subgroup of | AGL(1,𝔽11)×AΓL(1,𝔽9) |
Past the SmallGroups library coverage — no SmallGroups id.