Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C9 · Schur multiplier (H2) = C36 |
| direct product | C32×C9×SL(2,𝔽3) |
| Fitting | C32×Q8×C9 ⋊ C3 |
| derived, Sylow | Q8 ⋊ C33×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C9 | A4 |
| commutator, hypocenter | Q8 | C33×C9 |
| Frattini | C2×C3 | C33×A4 |
| Fitting | C32×Q8×C9 | C3 |
| socle | C2×C33 | C3×A4 |
| prime radical | C33×SL(2,𝔽3) | C3 |
| cosocle | C3×Q8 | C34 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C32×C9 | |
1238 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
567 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3251);