Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| isoclinism | isoclinic class of C11⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C11⋊(A4⋊C8) |
| unambiguous semidirect product | A4⋊(C11⋊C8) |
| derived | C11×A4 ⋊ C8 |
| Sylow | C11 ⋊ A4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | C11⋊S4 |
| commutator, hypocenter | C11×A4 | C8 |
| Fitting | C22×C4×C11 | D3 |
| socle | C23×C11 | Dic3 |
| prime radical | C2×C11×A4 | C4 |
| cosocle | C4×C11×A4 | C2 |
| LCS | G ▷ C11×A4 | |
| UCS | C1 ◁ C4 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^3,3,11,2^2|a^2=b,b^2=c,d^a=d^2,e^a=e^10,f^a=fg,f^d=g,g^d=fg100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 220);