Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C9 · Schur multiplier (H2) = C37 |
| direct product | C3×#21419297 |
| Fitting | C3×C31×C32⋊C9 ⋊ C3 |
| Sylow | C31 ⋊ C3×C9×H(3,𝔽3) |
1688 conjugacy classes of subgroups; only the 508 normal subgroups are shown.
This group has 1688 conjugacy classes of subgroups — too many to draw. Only its 508 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7533 |
1287 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 3270);