Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| direct product | A5×C31⋊C3 |
| unambiguous semidirect product | C31⋊(C3×A5) |
| unambiguous semidirect product | (C31×A5)⋊C3 |
| Fitting, Sylow | C31 ⋊ C3×A5 |
| socle, derived | C31×A5 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C31×A5 | C3 |
| Fitting | C31 | C3×A5 |
| LCS | G ▷ C31×A5 | |
| UCS | C1 | |
42 conjugacy classes of subgroups.
65 conjugacy classes — view the full character table.
| maximal subgroup of | A5×(C31⋊C3)⋊C5, C5×A5×C31⋊C3 |
| maximal normal subgroup of | A5×(C31⋊C3)⋊C5, C5×A5×C31⋊C3 |
| maximal quotient of | C5×A5×C31⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 177);