Finite Group DatabasebetaFinite Group Databasebeta| order | 20772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C577 ⋊ C4×C9 |
| Hall | #19104462 ⋊ C4 |
| Hall | #14556313 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C577 | C4×C9 |
| prime radical, cosocle | D577⋊C3 | C2×C3 |
| LCS | G ▷ C577 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 577 |
Polycyclic presentation:
2,3,2,3,577|a^2=c,b^3=d,e^a=e^553,e^b=e^335,e^c=e^576,e^d=e^36352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20772, 32);