Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C3×C9 |
No aliases for this group.
| Sylow | C31 ⋊ #10624559 |
332 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 22599 |
Polycyclic presentation:
3^6,31|a^3=f,b^3=ef,c^3=d,b^a=bd,c^a=ce,g^b=g^25,g^c=g^51143 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 922);