Finite Group DatabasebetaFinite Group Databasebeta| order | 5589 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C23 · Schur multiplier (H2) = C37 |
| direct product | C32×C23×H(3,𝔽3) |
| unambiguous semidirect product | C32⋊(C33×C23) |
| unambiguous semidirect product | (C32×C23)⋊C33 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C23 | C32 |
| commutator, Frattini | C3 | C34×C23 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C33×C23 ◁ G | |
900 conjugacy classes of subgroups.
2277 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5589, 62);