Finite Group DatabasebetaFinite Group Databasebeta| order | 3960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | A4×C3⋊AGL(1,𝔽11) |
| Fitting, socle, derived | C22×C3×C11 ⋊ C2×C3×C5 |
| Hall | A4×D33 ⋊ C5 |
| Hall | C11⋊C5 ⋊ D3×A4 |
| Sylow | C11 ⋊ C5×D3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C3×C11 | C2×C3×C5 |
| LCS | G ▷ C22×C3×C11 | |
| UCS | C1 | |
104 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 132 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×A4×AGL(1,𝔽11), S4×C3⋊AGL(1,𝔽11), #72268710 |
| maximal normal subgroup of | D3×A4×AGL(1,𝔽11), S4×C3⋊AGL(1,𝔽11), #72268710 |
Past the SmallGroups library coverage — no SmallGroups id.