Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| isoclinism | isoclinic class of #4323 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#66871 |
| Hall | C3×C11 ⋊ #107 |
| Sylow | C11 ⋊ C3×#107 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 1056 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3)(4,5,7,9,11,13,14,12,10,8,6)(15,16,17,18)(20,23)(21,26)(24,25);(5,6)(7,8)(9,10)(11,12)(13,14)(19,20,21,24,22,25,26,23)192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 83);