Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#10708580 |
| Fitting | C2×C3×#3292 ⋊ C2 |
| Sylow | C3 ⋊ C2×#12310 |
2180 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2,3)(4,5);(2,3)(7,12)(8,16)(9,19)(11,15)(13,21)(14,20)(17,18);(2,3)(7,11,13,20,14,21,15,12);(6,7)(8,11)(9,13)(10,14)(12,16)(15,19)(17,20)(18,21)126 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)(4,5), (2,3)(7,12)(8,16)(9,19)(11,15)(13,21)(14,20)(17,18), (2,3)(7,11,13,20,14,21,15,12), (6,7)(8,11)(9,13)(10,14)(12,16)(15,19)(17,20)(18,21));