Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×C11⋊GL(2,𝔽3) |
| unambiguous semidirect product | C11⋊(C3×GL(2,𝔽3)) |
| Fitting | C3×Q8×C11 ⋊ D3 |
| derived | C11×SL(2,𝔽3) ⋊ C2×C3 |
| Sylow | C11 ⋊ C3×GL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C11⋊S4 |
| commutator, cosocle, hypocenter | C11×SL(2,𝔽3) | C2×C3 |
| Frattini | C2 | C3×C11⋊S4 |
| Fitting | C3×Q8×C11 | D3 |
| socle | C2×C3×C11 | S4 |
| LCS | G ▷ C11×SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
129 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 447);