Finite Group DatabasebetaFinite Group Databasebeta| order | 16536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C2 |
| direct product | D3×AGL(1,𝔽53) |
| Fitting, socle, derived, Hall | C3×C53 ⋊ C2×C4×C13 |
| Hall | C3×C53⋊C13 ⋊ C2×C4 |
| Hall | D3×#6157 ⋊ C13 |
| Hall | C53⋊C13 ⋊ C4×D3 |
| Sylow | C53 ⋊ C4×D3×C13 |
| Sylow | C3 ⋊ C2×AGL(1,𝔽53) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C53 | C2×C4×C13 |
| prime radical | D3×D53⋊C13 | C2 |
| cosocle | C3×D53 | C22×C13 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 159 |
159 conjugacy classes — view the full character table.
| holomorph of | C3×C53 |
Past the SmallGroups library coverage — no SmallGroups id.