Finite Group DatabasebetaFinite Group Databasebeta| order | 5740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C7×C41 ⋊ C22×C5 |
| Hall | C7×C41⋊C5 ⋊ C22 |
| Hall | D7×D41 ⋊ C5 |
| Hall | C41⋊C5 ⋊ C2×D7 |
| Sylow | C41 ⋊ C2×C5×D7 |
| Sylow | C7 ⋊ C2×D41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C41 | C22×C5 |
| LCS | G ▷ C7×C41 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
70 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×D41⋊C5, C3×D7×D41⋊C5, D21×D41⋊C5, … |
| maximal normal subgroup of | AGL(1,𝔽7)×D41⋊C5, C3×D7×D41⋊C5, C5×D7×D41⋊C5 |
| maximal quotient of | C3×D7×D41⋊C5, D21×D41⋊C5, D7×C3⋊(D41⋊C5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5740, 16);