Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C39 |
| direct product | C3×#21419308 |
| Fitting | C35×C31 ⋊ C3 |
| Sylow | C31 ⋊ C3×C32⋊H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center | C33 | C32×C31⋊C3 |
| commutator, cosocle | C32×C31 | C34 |
| Frattini | C32 | C33×C31⋊C3 |
| Fitting | C35×C31 | C3 |
| socle | C33×C31 | C33 |
| hypercenter | C35 | C31⋊C3 |
| hypocenter | C31 | C3×C32⋊H(3,𝔽3) |
| LCS | G ▷ C32×C31 ▷ C31 | |
| UCS | C1 ◁ C33 ◁ C35 | |
3824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2511 |
2583 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 3303);