Finite Group DatabasebetaFinite Group Databasebeta| order | 20724 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C11⋊#10597845 |
| unambiguous semidirect product | C11⋊(C3×#10597845) |
| Fitting, socle, Hall | C3×C11×C157 ⋊ C4 |
| derived, Hall | C11×C157 ⋊ C3×C4 |
| Hall | C3×C157 ⋊ Dic11 |
| Sylow | C157 ⋊ C3×Dic11 |
| Hall | C3×C11 ⋊ #10597845 |
| Sylow | C11 ⋊ C3×#10597845 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C11⋊#10597845 |
| commutator, hypocenter | C11×C157 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C157 | C4 |
| prime radical | C3×C11×D157 | C2 |
| cosocle | C11×D157 | C2×C3 |
| LCS | G ▷ C11×C157 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5181 |
1329 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20724, 21);