Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×(C2×D11)⋊C8 |
| unambiguous semidirect product | (C2×D11)⋊(C3×C8) |
| Fitting | C2×C3×C8×C11 ⋊ C2 |
| Hall | C3×C11 ⋊ C22⋊C8 |
| Sylow | C11 ⋊ C3×C22⋊C8 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 528 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3)(4,5,7,9,11,13,14,12,10,8,6)(16,18)(19,20,21,23,22,24,25,26);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 95);