Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C34 |
No aliases for this group.
| Fitting | C31×H(3,𝔽3)⋊C9 ⋊ C3 |
| Sylow | C31 ⋊ #10624698 |
512 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 94 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,b^a=bd,c^a=cf,d^a=df,d^b=df,g^c=g^25615 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 2045);