Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C3 |
| direct product | D5×A6 |
| Fitting | C5 ⋊ C2×A6 |
| socle, derived | C5×A6 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C5×A6 | C2 |
| Fitting, cosocle | C5 | C2×A6 |
| LCS | G ▷ C5×A6 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
28 conjugacy classes — view the full character table.
| maximal subgroup of | A5×A6 |
| maximal quotient of | D5×SL(2,𝔽9), Dic5×A6, #72228177, … |
Past the SmallGroups library coverage — no SmallGroups id.