Finite Group DatabasebetaFinite Group Databasebeta| order | 20724 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(Dic157⋊C3) |
| unambiguous semidirect product | Dic1727⋊C3 |
| derived, Hall | C11×C157 ⋊ C3×C4 |
| Hall | Dic1727 ⋊ C3 |
| Hall | C11×C157⋊C3 ⋊ C4 |
| Hall | C157⋊C3 ⋊ Dic11 |
| Sylow | C157 ⋊ C3×Dic11 |
| Sylow | C11 ⋊ Dic157⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊(D157⋊C3) |
| commutator, hypocenter | C11×C157 | C3×C4 |
| Fitting, socle, cosocle | C2×C11×C157 | C2×C3 |
| prime radical | C2×C11×C157⋊C3 | C2 |
| LCS | G ▷ C11×C157 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6908 |
Polycyclic presentation:
2,3,11,157,2|a^2=e,c^a=c^10,d^a=d^156,d^b=d^12614 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20724, 12);