Finite Group DatabasebetaFinite Group Databasebeta| order | 5616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33×C4 · Schur multiplier (H2) = C23×C33 |
| direct product | C22×C32×AGL(1,𝔽13) |
| Fitting, socle | C22×C32×C13 ⋊ C3×C4 |
| derived, Sylow | C13 ⋊ C22×C33×C4 |
| Hall | C32×C13⋊C3 ⋊ C22×C4 |
| Hall | C22×#261 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | AGL(1,𝔽13) |
| commutator, hypocenter | C13 | C22×C33×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C13 | C3×C4 |
| prime radical | C22×C32×D13⋊C3 | C2 |
| cosocle | D13 | C23×C33 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C32 | |
1512 conjugacy classes of subgroups; only the 786 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 786 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 468 |
468 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C3⋊D3×AGL(1,𝔽13), C3×#67×AGL(1,𝔽13) |
| maximal normal subgroup of | C22×C3⋊D3×AGL(1,𝔽13), C3×#67×AGL(1,𝔽13) |
Past the SmallGroups library coverage — no SmallGroups id.