Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C31×#6866 ⋊ C3 |
| Sylow | C31 ⋊ AΣL(1,𝔽27)⋊C9 |
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2511 |
Polycyclic presentation:
3^6,31|a^3=e,c^3=e,b^a=bd,d^a=df,c^b=cf,g^c=g^5615 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 2165);