Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2×C3 |
| direct product | #157×A5 |
| Fitting | C32 ⋊ C4×A5 |
| socle, derived | C32×A5 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C32×A5 | C4 |
| Fitting | C32 | C4×A5 |
| prime radical | C3⋊D3×A5 | C2 |
| cosocle | C3⋊D3 | C2×A5 |
| LCS | G ▷ C32×A5 | |
| UCS | C1 | |
126 conjugacy classes of subgroups.
30 conjugacy classes — view the full character table.
| maximal subgroup of | A5×A6 |
| maximal quotient of | A5×#622, #157×SL(2,𝔽5), #72228180, … |
Past the SmallGroups library coverage — no SmallGroups id.