Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| Fitting | C22×C3×AΣL(1,𝔽27) ⋊ C2 |
| Sylow | C3×AΣL(1,𝔽27) ⋊ D4 |
832 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3,2,3^4|b^a=bd,e^a=e^2,f^a=f^2,g^a=g^2,h^a=h^2,f^c=fg,g^c=gh111 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2088);