Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C31×#6881 ⋊ C3 |
| Sylow | C31 ⋊ #10624852 |
188 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 837 |
Polycyclic presentation:
3^6,31|a^3=f,b^3=e^2,d^3=f^2,b^a=bd,d^a=de,e^a=ef,g^a=g^25,c^b=ce,g^b=g^5,d^c=df^2,g^c=g^5231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 3209);