Finite Group DatabasebetaFinite Group Databasebeta| order | 4680 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | D3×#63121⋊C3 |
| Fitting, socle, derived | C3×C5×C13 ⋊ C2×C3×C4 |
| Hall | C3×C5×C13⋊C3 ⋊ C2×C4 |
| Hall | C3×C13⋊C3 ⋊ C2×AGL(1,𝔽5) |
| Hall | C5×C13 ⋊ C3×C4×D3 |
| Sylow | C13 ⋊ C3×D3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ D3×AGL(1,𝔽13) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C13 | C2×C3×C4 |
| prime radical | D3×C5⋊(D13⋊C3) | C2 |
| cosocle | C3×D65 | C22×C3 |
| LCS | G ▷ C3×C5×C13 | |
| UCS | C1 | |
140 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 195 |
60 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.