Finite Group DatabasebetaFinite Group Databasebeta| order | 7439 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C173⋊C43 |
| Fitting, socle, derived, Sylow | C173 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C173 | C43 |
| LCS | G ▷ C173 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
43,173|b^a=b^1647 conjugacy classes — view the full character table.
| maximal subgroup of | D173⋊C43, C2×C173⋊C43, C3×C173⋊C43, … |
| maximal normal subgroup of | D173⋊C43, C2×C173⋊C43, C3×C173⋊C43, … |
| maximal quotient of | C2×C173⋊C43, C3×C173⋊C43, C5×C173⋊C43 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7439, 1);