Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#10619899 |
| Sylow | C33×C9 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #66431 |
| commutator, cosocle | C2×C32×C9 | C22×C3 |
| Frattini | C2×C3 | C3×#1113 |
| Fitting | C2×C33×C9 | C22 |
| socle | C2×C34 | C2×D3 |
| hypocenter | C32×C9 | C3×D4 |
| LCS | G ▷ C2×C32×C9 ▷ C32×C9 | |
| UCS | C1 ◁ C2×C3 | |
558 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 558 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) = 72 |
189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3119);