Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #10619734 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C9 |
| direct product | C3×#10619734 |
| Fitting, Sylow | C3×C92 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10619734 |
| commutator, cosocle | C9⋊D9 | C22×C3 |
| Frattini | C32 | C3×PSU(3,𝔽2) |
| Fitting | C3×C92 | Q8 |
| socle | C33 | PSU(3,𝔽2) |
| prime radical | C3×C9⋊D9 | C22 |
| hypocenter | C92 | C3×Q8 |
| LCS | G ▷ C9⋊D9 ▷ C92 | |
| UCS | C1 ◁ C3 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
45 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2328);