Finite Group DatabasebetaFinite Group Databasebeta| order | 5589 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C23 · Schur multiplier (H2) = C3 |
| direct product | C23×#6872 |
| subgroup | G/H | |
|---|---|---|
| center | C9×C23 | H(3,𝔽3) |
| commutator | C32 | C3×C9×C23 |
| Frattini | C3×C9 | C32×C23 |
| socle | C3×C23 | C32⋊C9 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9×C23 ◁ C3×C9×C23 ◁ G | |
52 conjugacy classes of subgroups.
1173 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5589, 19);