Finite Group DatabasebetaFinite Group Databasebeta| order | 37479 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C961 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×C961 |
| unambiguous semidirect product | C13⋊(C3×C961) |
| Fitting, Hall | C13×C961 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C961 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C961 | C13⋊C3 |
| commutator, hypocenter | C13 | C3×C961 |
| Frattini | C31 | C31×C13⋊C3 |
| Fitting | C13×C961 | C3 |
| socle, cosocle | C13×C31 | C3×C31 |
| prime radical | C31×C13⋊C3 | C31 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C961 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12493 |
6727 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37479, 2);