Finite Group DatabasebetaFinite Group Databasebeta| order | 8820 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2×C7 |
| direct product | A5×#3862 |
| Fitting, Sylow | C72 ⋊ C3×A5 |
| socle, derived | C72×A5 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C72×A5 | C3 |
| Fitting | C72 | C3×A5 |
| LCS | G ▷ C72×A5 | |
| UCS | C1 | |
102 conjugacy classes of subgroups.
95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8820, 672);