Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #66343 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C9 |
| direct product | C3×#10619526 |
| derived | C92 ⋊ C3×C8 |
| Sylow | C3×C92 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #66343 |
| commutator, hypocenter | C92 | C3×C8 |
| Frattini | C2×C32 | C3×#157 |
| Fitting | C2×C3×C92 | C4 |
| socle, prime radical | C2×C33 | #157 |
| cosocle | C9⋊Dic9 | C2×C3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C2×C3 | |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1116);