Finite Group DatabasebetaFinite Group Databasebeta| order | 20772 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#19104462 |
| Fitting, socle, derived, Hall | C22×C577 ⋊ C9 |
| Sylow | C577 ⋊ C22⋊C9 |
| Sylow | C22 ⋊ #19104462 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C577 | C9 |
| prime radical, cosocle | C22×C577⋊C3 | C3 |
| LCS | G ▷ C22×C577 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2308 |
Polycyclic presentation:
3^2,2^2,577|a^3=b,c^a=d,d^a=cd,e^a=e^335,e^b=e^363268 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20772, 37);