Finite Group DatabasebetaFinite Group Databasebeta| order | 5589 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C23×C27 · Schur multiplier (H2) = C3 |
| direct product | C23×C9⋊C27 |
| unambiguous semidirect product | C9⋊(C23×C27) |
| unambiguous semidirect product | (C9×C23)⋊C27 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C23 | C32 |
| commutator | C3 | C3×C23×C27 |
| Frattini | C3×C9 | C32×C23 |
| socle | C32×C23 | C3×C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C23 ◁ G | |
52 conjugacy classes of subgroups.
2277 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×#10624462, C3×C23×C9⋊C27, C23×#10624706, … |
| maximal normal subgroup of | C23×#10624462, C3×C23×C9⋊C27, C23×#10624706, … |
| maximal quotient of | C23×#10624462, C23×#10624463, C23×C9⋊C81, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5589, 21);