Finite Group DatabasebetaFinite Group Databasebeta| order | 2688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C2×#121×AGL(1,𝔽7) |
| Fitting | C2×C7×#121 ⋊ C2×C3 |
| Hall | C2×D7×#121 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C22×#121 |
| Sylow | C7 ⋊ C22×C3×#121 |
5056 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 5 generators on 17 points:
(1,2)(11,12,17)(13,14,16);(8,10);(4,6)(7,8)(9,10);(12,13)(14,16)(15,17);(3,4,5,6)196 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2)(11,12,17)(13,14,16), (8,10), (4,6)(7,8)(9,10), (12,13)(14,16)(15,17), (3,4,5,6));