Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| isoclinism | isoclinic class of #4314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#66869 |
| Fitting | C3×C42×C11 ⋊ C2 |
| Hall | C3×C11 ⋊ #104 |
| Sylow | C11 ⋊ C3×#104 |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 264 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,2,3)(4,5,7,9,11,13,14,12,10,8,6)(16,19,20,21);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,19)(18,20)(21,22)282 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 81);