Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C11⋊C32) |
| unambiguous semidirect product | C11⋊(C3⋊C32) |
| derived, Hall | C3×C11 ⋊ C32 |
| Sylow | C11 ⋊ C3⋊C32 |
| Sylow | C3 ⋊ C11⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D33 |
| commutator, hypocenter | C3×C11 | C32 |
| Fitting, cosocle | C3×C11×C16 | C2 |
| socle, prime radical | C2×C3×C11 | C16 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C16 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 1056 |
Polycyclic presentation:
2^5,3,11|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^2,g^a=g^10288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 3);