Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #87809 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C5 |
| direct product | C3×#87811 |
| Fitting | C3×C52×Q8 ⋊ C2 |
| Hall | C3×C52 ⋊ SD16 |
| Sylow | C52 ⋊ C3×SD16 |
160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 600 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3)(4,5,7,9)(6,11,10,8)(17,18,20,21,19);(5,8)(6,10)(9,11)(13,14)(15,16)(18,19)(20,21);(12,13,15,16,14)201 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 414);