Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #634⋊C27 |
| Sylow | C32⋊C27 ⋊ Q8 |
120 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^2,3,2,3^4|a^2=d,b^2=d,c^3=e,e^3=f,b^a=bd,g^a=g^2,h^a=h^2,g^c=gh279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 330);