Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2 |
| direct product | C22⋊C9×#272 |
| derived | C22×H(3,𝔽3) ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | A4×C3⋊D3 |
| commutator, hypocenter | C22×H(3,𝔽3) | C2×C9 |
| Fitting, cosocle | C22×C3×H(3,𝔽3) | C2×C3 |
| socle | C22×C32 | C3×C3⋊D3 |
| prime radical | C22×C3×#272 | C3 |
| LCS | G ▷ C22×H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
400 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2652);