Finite Group DatabasebetaFinite Group Databasebeta| order | 8540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D305 |
| unambiguous semidirect product | (C5×D7)⋊D61 |
| unambiguous semidirect product | (D7×C61)⋊D5 |
| Fitting, socle, derived, Hall | C5×C7×C61 ⋊ C22 |
| Hall | C7×C61 ⋊ C2×D5 |
| Hall | C5×C61 ⋊ C2×D7 |
| Sylow | C61 ⋊ D5×D7 |
| Hall | C5×C7 ⋊ C2×D61 |
| Sylow | C7 ⋊ C2×D305 |
| Sylow | C5 ⋊ D7×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C61 | C22 |
| LCS | G ▷ C5×C7×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | #14579425⋊D5, #14579424⋊D5, AGL(1,𝔽7)×D305, … |
| maximal normal subgroup of | #14579425⋊D5, #14579424⋊D5, AGL(1,𝔽7)×D305, … |
| maximal quotient of | C3×D7×D305, D7×D915, D21×D305, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8540, 37);