Finite Group DatabasebetaFinite Group Databasebeta| order | 20724 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(#10597845⋊C3) |
| unambiguous semidirect product | (C11⋊#10597845)⋊C3 |
| Fitting, socle, derived, Hall | C11×C157 ⋊ C3×C4 |
| Hall | C11⋊#10597845 ⋊ C3 |
| Hall | C11×C157⋊C3 ⋊ C4 |
| Hall | C157⋊C3 ⋊ Dic11 |
| Sylow | C157 ⋊ C3×Dic11 |
| Sylow | C11 ⋊ #10597845⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C157 | C3×C4 |
| prime radical | C11×D157⋊C3 | C2 |
| cosocle | C11×D157 | C2×C3 |
| LCS | G ▷ C11×C157 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1727 |
Polycyclic presentation:
2,3,2,11,157|a^2=c,d^a=d^10,e^a=e^28,e^b=e^12,e^c=e^156185 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20724, 15);