Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C33 |
| direct product | C3×#10619977 |
| Fitting | C22×C32×H(3,𝔽3) ⋊ C2 |
| Sylow | C32×H(3,𝔽3) ⋊ D4 |
1521 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 1521 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | #72229150, C3×#67×(C3⋊D3)⋊C3, C3×#13048733, … |
| maximal normal subgroup of | C3×#67×(C3⋊D3)⋊C3, C3×#13048733, #72259996, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3347);