Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | C32⋊C9 ⋊ C3×C8 |
| Sylow | #6891 ⋊ C8 |
329 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 329 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2,3,2^2,3^4|a^2=c,c^2=d,f^3=h,e^a=e^2,f^a=f^2h^2,h^a=h^2,f^b=fh^2,f^e=fg156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 729);