Finite Group DatabasebetaFinite Group Databasebeta| order | 5589 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #6878 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C23 · Schur multiplier (H2) = C3×C9 |
| direct product | C23×#6879 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C23 | #732 |
| commutator, Frattini | C3×C9 | C32×C23 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C23 ◁ C32×C23 ◁ C3×C9×C23 ◁ G | |
48 conjugacy classes of subgroups.
805 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5589, 26);