Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C36 |
| direct product | C32×#14578893 |
| Fitting | C32×H(3,𝔽3)×C31 ⋊ C3 |
| Sylow | C31 ⋊ C32×AΣL(1,𝔽27) |
2672 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 2672 conjugacy classes of subgroups — too many to draw. Only its 328 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, 3899);