Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C36 |
| direct product | C31⋊C3×C9⋊H(3,𝔽3) |
| Fitting | C31×C9⋊H(3,𝔽3) ⋊ C3 |
| Sylow | C31 ⋊ C3×C9⋊H(3,𝔽3) |
1328 conjugacy classes of subgroups; only the 313 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 313 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2511 |
663 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 3309);