Finite Group DatabasebetaFinite Group Databasebeta| order | 5616 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | C3×A4×AGL(1,𝔽13) |
| Fitting, socle | C22×C3×C13 ⋊ C32×C4 |
| derived | C22×C13 ⋊ C33×C4 |
| Hall | C22×#261 ⋊ C33 |
| Sylow | C13 ⋊ C32×C4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4×AGL(1,𝔽13) |
| commutator, hypocenter | C22×C13 | C33×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C13 | C32×C4 |
| prime radical | C3×A4×D13⋊C3 | C2 |
| cosocle | C22×D13 | C2×C33 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 ◁ C3 | |
420 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 156 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | A42×AGL(1,𝔽13), D3×A4×AGL(1,𝔽13), C3×S4×AGL(1,𝔽13), … |
| maximal normal subgroup of | D3×A4×AGL(1,𝔽13), C3×S4×AGL(1,𝔽13), C3⋊S4×AGL(1,𝔽13) |
| maximal quotient of | A42×AGL(1,𝔽13) |
Past the SmallGroups library coverage — no SmallGroups id.