Finite Group DatabasebetaFinite Group Databasebeta| order | 14760 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×#4223⋊C5 |
| Fitting, socle, Hall | C32×C41 ⋊ C2×C4×C5 |
| derived | C3×C41 ⋊ C2×C3×C4×C5 |
| Hall | C3×D3×#4223 ⋊ C5 |
| Hall | C32×C41⋊C5 ⋊ C2×C4 |
| Hall | C41⋊C5 ⋊ C3×C4×D3 |
| Sylow | C41 ⋊ C3×C4×C5×D3 |
| Sylow | C32 ⋊ C2×#4223⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×#4223⋊C5 |
| commutator, hypocenter | C3×C41 | C2×C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C41 | C2×C4×C5 |
| prime radical | C3×D3×D41⋊C5 | C2 |
| cosocle | C3×D41 | C22×C3×C5 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C3 | |
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) = 246 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#4223⋊C5, C3×D3×AGL(1,𝔽41), D3×#72230820 |
| maximal normal subgroup of | D32×#4223⋊C5, C3×D3×AGL(1,𝔽41), D3×#72230820 |
Past the SmallGroups library coverage — no SmallGroups id.