Finite Group DatabasebetaFinite Group Databasebeta| order | 20772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C577 ⋊ C4×C9 |
| Hall | #19104462 ⋊ C4 |
| Hall | Dic577 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19104462⋊C2 |
| commutator, hypocenter | C577 | C4×C9 |
| Fitting, socle | C2×C577 | C2×C9 |
| prime radical, cosocle | C2×C577⋊C3 | C2×C3 |
| LCS | G ▷ C577 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2308 |
Polycyclic presentation:
2,3^2,577,2|a^2=e,b^3=c,d^a=d^576,d^b=d^335,d^c=d^363100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20772, 20);