Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | C3×#10619585 |
| Fitting | C34×Q8 ⋊ C3 |
| Sylow | Q8 ⋊ C3×AΣL(1,𝔽27) |
590 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
183 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1666);