Finite Group DatabasebetaFinite Group Databasebeta| order | 9660 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C23 · Schur multiplier (H2) = C2 |
| direct product | C7×C23×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C7×C23 | A5 |
| commutator, hypocenter | A5 | C7×C23 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C7×C23 | |
36 conjugacy classes of subgroups.
805 conjugacy classes — view the full character table.
| socle of | ΓL(1,𝔽8)×C23×A5 |
| maximal subgroup of | C3×C7×C23×A5, ΓL(1,𝔽8)×C23×A5 |
| maximal normal subgroup of | C3×C7×C23×A5, ΓL(1,𝔽8)×C23×A5 |
| maximal quotient of | C3×C7×C23×A5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9660, 105);