Finite Group DatabasebetaFinite Group Databasebeta| order | 20724 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#10597845⋊C3 |
| unambiguous semidirect product | #10597845⋊(C3×C11) |
| unambiguous semidirect product | (C11×#10597845)⋊C3 |
| Fitting, socle, Hall | C11×C157 ⋊ C3×C4 |
| derived, Sylow | C157 ⋊ C3×C4×C11 |
| Hall | C11×#10597845 ⋊ C3 |
| Hall | C11×C157⋊C3 ⋊ C4 |
| Hall | #10597845 ⋊ C3×C11 |
| Hall | C157⋊C3 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #10597845⋊C3 |
| commutator, hypocenter | C157 | C3×C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C157 | C3×C4 |
| prime radical | C11×D157⋊C3 | C2 |
| cosocle | D157 | C2×C3×C11 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1727 |
275 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20724, 14);