Finite Group DatabasebetaFinite Group Databasebeta| order | 5439 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#11715912 |
| Fitting, socle, Hall | C72×C37 ⋊ C3 |
| derived | C7×C37 ⋊ C3×C7 |
| Sylow | C72 ⋊ C37⋊C3 |
| Sylow | C37 ⋊ C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #11715912 |
| commutator, hypocenter | C7×C37 | C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C37 | C3 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C7 | |
20 conjugacy classes of subgroups.
623 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#13095538, C7×#13095536, C7×#13095532, … |
| maximal normal subgroup of | C7×#13095538, C7×#13095536, C7×#13095532, … |
| maximal quotient of | C2×C7×#11715912, C7×#14556418, C3×C7×#11715912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5439, 10);