Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C31 · Schur multiplier (H2) = C2 |
| direct product | C3×C31×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C31 | A5 |
| commutator, hypocenter | A5 | C3×C31 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C3×C31 | |
42 conjugacy classes of subgroups.
465 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×C31×A5, C3×A5×ΓL(1,𝔽32) |
| maximal normal subgroup of | C3×C5×C31×A5, C3×A5×ΓL(1,𝔽32) |
| maximal quotient of | C3×C5×C31×A5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 176);