Finite Group DatabasebetaFinite Group Databasebeta| order | 3744 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | S4×AGL(1,𝔽13) |
| Fitting, socle | C22×C13 ⋊ C3×C4×D3 |
| derived | A4×C13 ⋊ C2×C3×C4 |
| Sylow | C13 ⋊ C3×C4×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | A4×C13 | C2×C3×C4 |
| Fitting, socle | C22×C13 | C3×C4×D3 |
| prime radical | S4×D13⋊C3 | C2 |
| cosocle | A4×D13 | C22×C3 |
| LCS | G ▷ A4×C13 | |
| UCS | C1 | |
236 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 236 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.
65 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.