Finite Group DatabasebetaFinite Group Databasebeta| order | 20988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D99⋊D53 |
| unambiguous semidirect product | D477⋊D11 |
| unambiguous semidirect product | D583⋊D9 |
| Fitting, derived, Hall | C9×C11×C53 ⋊ C22 |
| Hall | C11×C53 ⋊ C2×D9 |
| Hall | C9×C53 ⋊ C2×D11 |
| Hall | C9×C11 ⋊ C2×D53 |
| Sylow | C53 ⋊ D9×D11 |
| Sylow | C11 ⋊ D9×D53 |
| Sylow | C9 ⋊ D11×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C11×C53 | C22 |
| Frattini | C3 | D33⋊D53 |
| socle | C3×C11×C53 | C2×D3 |
| LCS | G ▷ C9×C11×C53 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5247 |
Polycyclic presentation:
2^2,3,11,53,3|c^3=f^2,d^a=d^10,e^a=e^52,c^b=c^2f,d^b=d^10,f^b=f^21368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20988, 20);