Finite Group DatabasebetaFinite Group Databasebeta| order | 20631 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C529 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×C529 |
| unambiguous semidirect product | C13⋊(C3×C529) |
| unambiguous semidirect product | (C13×C529)⋊C3 |
| Fitting, Hall | C13×C529 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C529 | C13⋊C3 |
| commutator, hypocenter | C13 | C3×C529 |
| Frattini | C23 | C23×C13⋊C3 |
| Fitting | C13×C529 | C3 |
| socle, cosocle | C13×C23 | C3×C23 |
| prime radical | C23×C13⋊C3 | C23 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C529 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6877 |
3703 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20631, 2);