Finite Group DatabasebetaFinite Group Databasebeta| order | 5740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D7×D41 |
| Fitting, socle, Hall | C5×C7×C41 ⋊ C22 |
| derived, Hall | C7×C41 ⋊ C22×C5 |
| Hall | C5×C41 ⋊ C2×D7 |
| Sylow | C41 ⋊ C2×C5×D7 |
| Hall | C5×C7 ⋊ C2×D41 |
| Sylow | C7 ⋊ C2×C5×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D7×D41 |
| commutator, hypocenter | C7×C41 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C41 | C22 |
| LCS | G ▷ C7×C41 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
550 conjugacy classes — view the full character table.
| maximal subgroup of | C5×AGL(1,𝔽7)×D41, C3×C5×D7×D41, C5×D21×D41, … |
| maximal normal subgroup of | C5×AGL(1,𝔽7)×D41, C3×C5×D7×D41, D7×D41⋊C25, … |
| maximal quotient of | C3×C5×D7×D41, C5×D21×D41, C5×D7×D123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5740, 23);