Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#10619679 |
| Fitting | C22×C3×AΣL(1,𝔽27) ⋊ C2 |
| Sylow | C3×AΣL(1,𝔽27) ⋊ D4 |
634 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
129 conjugacy classes — view the full character table.
| maximal subgroup of | #72228545, C3×D4×#4183, C3×A4⋊#4183, … |
| maximal normal subgroup of | C3×D4×#4183, C2×C3×#10619679 |
| maximal quotient of | C2×C3×#10619679 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2086);