Finite Group DatabasebetaFinite Group Databasebeta| order | 5589 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C11×C81 (order 3564) · Inn(G) = C1 · Out(G) = C22×C11×C81 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C5589 |
| abelian | C23×C243 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C81 | C3×C23 |
| socle | C3×C23 | C81 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12 conjugacy classes of subgroups.
5589 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×C729, C3×C23×C243, C23×C243⋊C3, … |
| maximal normal subgroup of | C23×C729, C3×C23×C243, C23×C243⋊C3, … |
| maximal quotient of | C23×C729, C3×C23×C243, C2×C23×C243, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5589, 1);