Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #6249 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#6249 |
| Fitting, Sylow | C9×H(3,𝔽3) ⋊ C8 |
| derived | H(3,𝔽3) ⋊ C8×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #6249 |
| commutator, hypocenter | H(3,𝔽3) | C8×C9 |
| Frattini, socle | C32 | C3×AGL(1,𝔽9) |
| Fitting | C9×H(3,𝔽3) | C8 |
| prime radical | C3×#272 | C3×C4 |
| cosocle | C3×#1088 | C2×C3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C9 | |
68 conjugacy classes of subgroups.
| 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, 2297);