Finite Group DatabasebetaFinite Group Databasebeta| order | 5940 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×C3⋊AGL(1,𝔽11) |
| Fitting, socle, Hall | C33×C11 ⋊ C22×C5 |
| derived | C32×C11 ⋊ C22×C3×C5 |
| Hall | C33×C11⋊C5 ⋊ C22 |
| Hall | C3×D3×D33 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C3×D32 |
| Sylow | C33 ⋊ C2×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C3×C5×D32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×C3⋊AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C32×C11 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C33×C11 | C22×C5 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C3 | |
216 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 132 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D32×AGL(1,𝔽11), D32×C3⋊AGL(1,𝔽11), D3×(C3⋊D3)⋊AGL(1,𝔽11) |
| maximal normal subgroup of | C3×D32×AGL(1,𝔽11), D32×C3⋊AGL(1,𝔽11), D3×(C3⋊D3)⋊AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.