Finite Group DatabasebetaFinite Group Databasebeta| order | 5616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | D32×AGL(1,𝔽13) |
| Fitting, socle, derived | C32×C13 ⋊ C22×C3×C4 |
| Hall | C32×C13⋊C3 ⋊ C22×C4 |
| Sylow | C13 ⋊ C3×C4×D32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C13 | C22×C3×C4 |
| prime radical | D32×D13⋊C3 | C2 |
| cosocle | C32×D13 | C23×C3 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 | |
540 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
117 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.