Finite Group DatabasebetaFinite Group Databasebeta| order | 20631 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C13⋊(C232⋊C3) |
| unambiguous semidirect product | C232⋊(C13⋊C3) |
| Fitting, socle, derived, Hall | C13×C232 ⋊ C3 |
| Sylow | C232 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ C232⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C232 | C3 |
| LCS | G ▷ C13×C232 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 897 |
Polycyclic presentation:
3,13,23^2|b^a=b^3,c^a=c^7d^4,d^a=c^3d^152295 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20631, 5);