Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×D3×#3292 |
| Fitting | C2×C3×#3292 ⋊ C2 |
| Sylow | C3 ⋊ C22×#3292 |
21460 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 6 generators on 21 points:
(1,2,3)(6,8,9,17,10,18,19,16)(7,13,12,20,14,21,11,15);(7,12,14,11)(13,20,21,15);(4,5);(2,3);(7,11)(8,16)(9,19)(12,14)(13,21)(17,18);(6,7)(8,15)(9,11)(10,14)(12,19)(13,16)(17,21)(18,20)174 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((1,2,3)(6,8,9,17,10,18,19,16)(7,13,12,20,14,21,11,15), (7,12,14,11)(13,20,21,15), (4,5), (2,3), (7,11)(8,16)(9,19)(12,14)(13,21)(17,18), (6,7)(8,15)(9,11)(10,14)(12,19)(13,16)(17,21)(18,20));