Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C243 · Schur multiplier (H2) = C3 |
| direct product | C3×C31⋊C243 |
| unambiguous semidirect product | (C3×C31)⋊C243 |
| derived, Sylow | C31 ⋊ C3×C243 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C81 | C31⋊C3 |
| commutator, hypocenter | C31 | C3×C243 |
| Frattini | C81 | C3×C31⋊C3 |
| Fitting | C3×C31×C81 | C3 |
| socle, prime radical | C32×C31 | C81 |
| cosocle | C31×C81 | C32 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C81 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22599 |
3159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 828);