Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| general unitary | GU(2,𝔽9) |
| direct product | C5×#13088276 |
| derived | SL(2,𝔽9) ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C2×C5 | PGL(2,𝔽9) |
| commutator, cosocle, hypocenter | SL(2,𝔽9) | C2×C5 |
| Frattini | C2 | C5×PGL(2,𝔽9) |
| LCS | G ▷ SL(2,𝔽9) | |
| UCS | C1 ◁ C2×C5 | |
76 conjugacy classes of subgroups.
100 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.