Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×C3⋊#6258 |
| unambiguous semidirect product | C3⋊(C3×#6258) |
| Fitting | C22×C34 ⋊ D3 |
| derived | C3×C22⋊H(3,𝔽3) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊(C3⋊S4) |
| commutator, cosocle, hypocenter | C3×C22⋊H(3,𝔽3) | C2×C3 |
| Frattini | C3 | C3×C3⋊(C3⋊S4) |
| Fitting | C22×C34 | D3 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C3×C22⋊H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
1030 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3619);