Finite Group DatabasebetaFinite Group Databasebeta| order | 5589 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AΣL(1,𝔽27) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C23 · Schur multiplier (H2) = C33 |
| direct product | C3×C23×#731 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C23 | H(3,𝔽3) |
| commutator, Frattini | C32 | C33×C23 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C23 ◁ C33×C23 ◁ G | |
144 conjugacy classes of subgroups.
1173 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C23×#731, C23×#731⋊C9, C23×#10624731, … |
| maximal normal subgroup of | C9×C23×#731, C23×#731⋊C9, C23×#10624731, … |
| maximal quotient of | C3×C23×#6857, C3×C23×#6858, C3×C23×#6859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5589, 52);