Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24×C3 |
| direct product | D4×A4⋊AGL(1,ℤ/9) |
| Fitting | C22×D4×3−1+2 ⋊ D3 |
2014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 108 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,4,3,2)(10,16,17,12,13,14)(11,15);(6,8)(9,17,16,11,10,12,15,13,14);(2,3,4)(5,6,7,8)155 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((1,4,3,2)(10,16,17,12,13,14)(11,15), (6,8)(9,17,16,11,10,12,15,13,14), (2,3,4)(5,6,7,8));