Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C2 |
| direct product | C3×C11×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C11 | A5 |
| commutator, hypocenter | A5 | C3×C11 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C3×C11 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 165 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C7×C11×A5, C11×ΓL(1,𝔽8)×A5, C3×A5×C121, … |
| maximal normal subgroup of | C3×C7×C11×A5, C3×A5×C121, C3×C112×A5, … |
| maximal quotient of | C3×C7×C11×A5, C11×ΓL(1,𝔽8)×A5, C3×A5×C121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 58);