Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C9×#14578893 |
| Fitting | C9×H(3,𝔽3)×C31 ⋊ C3 |
| Sylow | C31 ⋊ C9×AΣL(1,𝔽27) |
472 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2511 |
1143 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 2141);