Finite Group DatabasebetaFinite Group Databasebeta| order | 20724 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C22×C11×C157 ⋊ C3 |
| derived, Hall | C22×C157 ⋊ C3×C11 |
| Hall | C11×C157 ⋊ A4 |
| Sylow | C157 ⋊ C11×A4 |
| Hall | C22×C11 ⋊ C157⋊C3 |
| Sylow | C22 ⋊ C11×C157⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C22⋊(C157⋊C3) |
| commutator, cosocle, hypocenter | C22×C157 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C22×C11×C157 | C3 |
| LCS | G ▷ C22×C157 | |
| UCS | C1 ◁ C11 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6908 |
2332 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20724, 32);