Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C11⋊GL(2,𝔽3)) |
| unambiguous semidirect product | C11⋊(C3⋊GL(2,𝔽3)) |
| Fitting | C3×Q8×C11 ⋊ D3 |
| derived | C3×C11×SL(2,𝔽3) ⋊ C2 |
| Sylow | C11 ⋊ C3⋊GL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C11⋊S4) |
| commutator, cosocle, hypocenter | C3×C11×SL(2,𝔽3) | C2 |
| Fitting | C3×Q8×C11 | D3 |
| socle | C2×C3×C11 | S4 |
| LCS | G ▷ C3×C11×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2,3^2,11,2^3|e^2=g,f^2=g,b^a=b^2,c^a=c^2,d^a=d^10,e^a=ef,f^a=fg,e^b=f,f^b=efg,f^e=fg120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 453);