Finite Group DatabasebetaFinite Group Databasebeta| order | 5589 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 21384 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3 |
| abelian | C3×C23×C81 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C27 | C32×C23 |
| socle | C32×C23 | C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
36 conjugacy classes of subgroups.
5589 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C23×C81, C23×#10624499, C23×C32⋊C81, … |
| maximal normal subgroup of | C9×C23×C81, C23×#10624499, C23×C32⋊C81, … |
| maximal quotient of | C9×C23×C81, C23×C32⋊C81, C23×C9⋊C81, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5589, 23);