Finite Group DatabasebetaFinite Group Databasebeta| order | 5589 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6909 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C23 · Schur multiplier (H2) = C34 |
| direct product | C23×#6911 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C23 | C3×H(3,𝔽3) |
| commutator, Frattini | C32 | C33×C23 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C23 ◁ C33×C23 ◁ G | |
160 conjugacy classes of subgroups.
805 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5589, 58);