Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | H(3,𝔽3)⋊(C31⋊C27) |
| Sylow | C31 ⋊ H(3,𝔽3)⋊C27 |
144 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7533 |
Polycyclic presentation:
3^6,31|a^3=d,d^3=f,b^a=bc,c^a=ce,g^a=g^25,c^b=ce1143 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 517);