Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C27 · Schur multiplier (H2) = C36 |
| direct product | C32×C27×C31⋊C3 |
| Fitting | C32×C27×C31 ⋊ C3 |
| derived, Sylow | C31 ⋊ C33×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C27 | C31⋊C3 |
| commutator, hypocenter | C31 | C33×C27 |
| Frattini | C9 | C33×C31⋊C3 |
| Fitting | C32×C27×C31 | C3 |
| socle | C33×C31 | C3×C9 |
| prime radical | C33×C31⋊C3 | C9 |
| cosocle | C9×C31 | C34 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C32×C27 | |
1160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7533 |
3159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 3884);