Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C27 · Schur multiplier (H2) = C33 |
| direct product | C3×SL(2,𝔽3)×C27 |
| Fitting | C3×Q8×C27 ⋊ C3 |
| derived, Sylow | Q8 ⋊ C32×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C27 | A4 |
| commutator, hypocenter | Q8 | C32×C27 |
| Frattini | C2×C9 | C32×A4 |
| Fitting | C3×Q8×C27 | C3 |
| socle | C2×C32 | C9×A4 |
| prime radical | C32×SL(2,𝔽3) | C9 |
| cosocle | Q8×C9 | C33 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C3×C27 | |
230 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, 1594);