Finite Group DatabasebetaFinite Group Databasebeta| order | 4680 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D3×AGL(1,𝔽13) |
| Fitting, socle | C3×C5×C13 ⋊ C2×C3×C4 |
| derived | C3×C13 ⋊ C2×C3×C4×C5 |
| Hall | C3×C5×C13⋊C3 ⋊ C2×C4 |
| Hall | C3×C13⋊C3 ⋊ C2×C4×C5 |
| Hall | C5×C13 ⋊ C3×C4×D3 |
| Sylow | C13 ⋊ C3×C4×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×AGL(1,𝔽13) |
| commutator, hypocenter | C3×C13 | C2×C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13 | C2×C3×C4 |
| prime radical | C5×D3×D13⋊C3 | C2 |
| cosocle | C3×D13 | C22×C3×C5 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C5 | |
140 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 195 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D5×AGL(1,𝔽13) |
| maximal normal subgroup of | D3×D5×AGL(1,𝔽13) |
Past the SmallGroups library coverage — no SmallGroups id.