Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C31×C32⋊C27 ⋊ C3 |
| Sylow | C31 ⋊ C27⋊H(3,𝔽3) |
256 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 82 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=e,c^3=e,e^3=f,b^a=bd,c^a=cf,g^b=g^5,g^c=g^251143 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 2136);