Finite Group DatabasebetaFinite Group Databasebeta| order | 8540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#11927414 |
| Fitting, socle, Hall | C5×C7×C61 ⋊ C4 |
| derived, Hall | C5×C61 ⋊ C4×C7 |
| Hall | C7×C61 ⋊ AGL(1,𝔽5) |
| Sylow | C61 ⋊ C7×AGL(1,𝔽5) |
| Hall | C5×C7 ⋊ Dic61 |
| Sylow | C5 ⋊ C7×Dic61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #11927414 |
| commutator, hypocenter | C5×C61 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C61 | C4 |
| LCS | G ▷ C5×C61 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
875 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#11927414⋊C3, #38785078, #38785079, … |
| maximal normal subgroup of | C7×#11927414⋊C3, #38785078, #38785079, … |
| maximal quotient of | C3×C7×#11927414, C7×C3⋊#11927414 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8540, 27);