Finite Group DatabasebetaFinite Group Databasebeta| order | 2688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | ΓL(1,𝔽8)×#2002 |
| Fitting, Hall | C7×#2002 ⋊ C3 |
| Sylow | C7 ⋊ C3×#2002 |
956 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3,4)(5,7,6)(12,13,14,17,15,16,18,19);(1,2,4,6,3,5,7)(8,9)(10,11)(13,16)(14,18);(9,11)(13,17)(14,18)(16,19)130 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((2,3,4)(5,7,6)(12,13,14,17,15,16,18,19), (1,2,4,6,3,5,7)(8,9)(10,11)(13,16)(14,18), (9,11)(13,17)(14,18)(16,19));