Finite Group DatabasebetaFinite Group Databasebeta| order | 5740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D287 |
| unambiguous semidirect product | (C7×D5)⋊D41 |
| unambiguous semidirect product | (D5×C41)⋊D7 |
| Fitting, socle, derived, Hall | C5×C7×C41 ⋊ C22 |
| Hall | C7×C41 ⋊ C2×D5 |
| Hall | C5×C41 ⋊ C2×D7 |
| Sylow | C41 ⋊ D5×D7 |
| Hall | C5×C7 ⋊ C2×D41 |
| Sylow | C7 ⋊ D5×D41 |
| Sylow | C5 ⋊ C2×D287 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C41 | C22 |
| LCS | G ▷ C5×C7×C41 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
580 conjugacy classes — view the full character table.
| maximal subgroup of | D5×ΓL(1,𝔽8)⋊D41, C3×D5×D287, D15×D287, … |
| maximal normal subgroup of | D5×ΓL(1,𝔽8)⋊D41, C3×D5×D287, D5×C7⋊(D41⋊C5), … |
| maximal quotient of | C3×D5×D287, D15×D287, D5×D861, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5740, 38);