Finite Group DatabasebetaFinite Group Databasebeta| order | 8540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C7×C61 ⋊ C22×C5 |
| Hall | C7×C61⋊C5 ⋊ C22 |
| Hall | D7×D61 ⋊ C5 |
| Hall | C61⋊C5 ⋊ C2×D7 |
| Sylow | C61 ⋊ C2×C5×D7 |
| Sylow | C7 ⋊ C2×D61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C61 | C22×C5 |
| LCS | G ▷ C7×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8540, 16);