Finite Group DatabasebetaFinite Group Databasebeta| order | 20724 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊D157 |
| unambiguous semidirect product | D471⋊D11 |
| unambiguous semidirect product | D1727⋊D3 |
| Fitting, socle, derived, Hall | C3×C11×C157 ⋊ C22 |
| Hall | C11×C157 ⋊ C2×D3 |
| Hall | C3×C157 ⋊ C2×D11 |
| Sylow | C157 ⋊ D3×D11 |
| Hall | C3×C11 ⋊ C2×D157 |
| Sylow | C11 ⋊ D3×D157 |
| Sylow | C3 ⋊ D11×D157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C157 | C22 |
| LCS | G ▷ C3×C11×C157 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5181 |
Polycyclic presentation:
2^2,3,11,157|d^a=d^10,e^a=e^156,c^b=c^2,d^b=d^101425 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20724, 30);