Finite Group DatabasebetaFinite Group Databasebeta| order | 5589 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C23 · Schur multiplier (H2) = C32 |
| direct product | C23×H(3,𝔽3)⋊C9 |
| unambiguous semidirect product | H(3,𝔽3)⋊(C9×C23) |
| unambiguous semidirect product | (C23×H(3,𝔽3))⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C23 | H(3,𝔽3) |
| commutator | C32 | C3×C9×C23 |
| Frattini | C33 | C32×C23 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C23 ◁ C33×C23 ◁ G | |
94 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, 17);