Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| isoclinism | isoclinic class of SL(2,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C3 |
| direct product | C5×SL(2,𝔽9) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C2×C5 | A6 |
| commutator, hypocenter | SL(2,𝔽9) | C5 |
| Frattini, cosocle | C2 | C5×A6 |
| LCS | G ▷ SL(2,𝔽9) | |
| UCS | C1 ◁ C2×C5 | |
58 conjugacy classes of subgroups.
65 conjugacy classes — view the full character table.
| derived subgroup of | D5×SL(2,𝔽9), #72228177 |
| maximal subgroup of | C5×#13088276, D5×SL(2,𝔽9), #72228177 |
| maximal normal subgroup of | C5×#13088276, D5×SL(2,𝔽9), #72228177 |
Past the SmallGroups library coverage — no SmallGroups id.