Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×PGL(2,𝔽9) |
| socle | C5×A6 ⋊ C2 |
| derived | A6 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C5 | PGL(2,𝔽9) |
| commutator, cosocle, hypocenter | A6 | C2×C5 |
| Frattini | C1 | G |
| socle | C5×A6 | C2 |
| LCS | G ▷ A6 | |
| UCS | C1 ◁ C5 | |
56 conjugacy classes of subgroups.
55 conjugacy classes — view the full character table.
| maximal quotient of | C5×#13088276 |
Past the SmallGroups library coverage — no SmallGroups id.