Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊GU(2,𝔽3) |
| derived | C11×SL(2,𝔽3) ⋊ C4 |
| Sylow | C11 ⋊ GU(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | C11⋊S4 |
| commutator, hypocenter | C11×SL(2,𝔽3) | C4 |
| Fitting | C11×#41 | D3 |
| socle | C2×C11 | SL(2,ℤ/4) |
| prime radical, cosocle | C11×#41⋊C3 | C2 |
| LCS | G ▷ C11×SL(2,𝔽3) | |
| UCS | C1 ◁ C4 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^2,3,11,2^3|a^2=b,b^2=g,e^2=g,f^2=g,c^a=c^2,d^a=d^10,e^a=ef,f^a=fg,e^c=f,f^c=efg,f^e=fg86 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 222);