Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| isoclinism | isoclinic class of C11⋊#857 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C11⋊#857 |
| Fitting | C42×C11 ⋊ D3 |
| derived | C11×C42⋊C3 ⋊ C2 |
| Sylow | C11 ⋊ #857 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C11×C42⋊C3 | C2 |
| Frattini | C22 | C11⋊S4 |
| Fitting | C42×C11 | D3 |
| socle | C22×C11 | S4 |
| LCS | G ▷ C11×C42⋊C3 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 132 |
Polycyclic presentation:
2,3,11,2^4|d^2=f,e^2=g,b^a=b^2,c^a=c^10,d^a=deg,e^a=eg,f^a=fg,d^b=ef,e^b=de,f^b=g,g^b=fg50 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 219);