Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C9 · Schur multiplier (H2) = C35 |
No aliases for this group.
| Fitting | C9×H(3,𝔽3)×C31 ⋊ C3 |
| Sylow | C31 ⋊ #10624862 |
1178 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 454 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,b^a=be,d^a=de,c^b=ce,g^d=g^251239 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 3286);