Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C34 |
| direct product | SL(2,𝔽3)×C32⋊C9 |
| Fitting | Q8×C32⋊C9 ⋊ C3 |
| Sylow | Q8 ⋊ C3×C32⋊C9 |
455 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 455 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1577);