Finite Group DatabasebetaFinite Group Databasebeta| order | 5439 |
| isoclinism | isoclinic class of C49⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×C49⋊C3 |
| unambiguous semidirect product | C49⋊(C3×C37) |
| Fitting, Hall | C37×C49 ⋊ C3 |
| derived, Sylow | C49 ⋊ C3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C49⋊C3 |
| commutator, hypocenter | C49 | C3×C37 |
| Frattini | C7 | ΓL(1,𝔽8)×C37 |
| Fitting | C37×C49 | C3 |
| socle | C7×C37 | ΓL(1,𝔽8) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C37 | |
12 conjugacy classes of subgroups.
703 conjugacy classes — view the full character table.
| maximal subgroup of | D37×C49⋊C3, C37×D49⋊C3, (C49⋊C3)⋊D37, … |
| maximal normal subgroup of | D37×C49⋊C3, C37×D49⋊C3, (C49⋊C3)⋊D37, … |
| maximal quotient of | C2×C37×C49⋊C3, C37×C49⋊C9, C3×C37×C49⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5439, 2);