Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C33 |
| direct product | C3⋊D3×C22⋊H(3,𝔽3) |
| unambiguous semidirect product | C3⋊(D3×C22⋊H(3,𝔽3)) |
| Fitting | C22×C34 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×A4×C3⋊D3 |
| commutator, socle, cosocle | C22×C33 | C2×C32 |
| Fitting | C22×C34 | C2×C3 |
| hypercenter | C32 | A4×C3⋊D3 |
| hypocenter | C22×C32 | C2×H(3,𝔽3) |
| LCS | G ▷ C22×C33 ▷ C22×C32 | |
| UCS | C1 ◁ C3 ◁ C32 | |
880 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3661);