Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C34 |
No aliases for this group.
| Fitting | C31×#6895 ⋊ C3 |
| Sylow | C31 ⋊ #10624872 |
824 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 283 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=f,d^3=e,b^a=be,c^a=cf,g^c=g^5,g^d=g^25663 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 3347);