Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #87856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#87860 |
| Hall | C3×C52 ⋊ M16 |
| Sylow | C52 ⋊ C3×M16 |
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)(5,8)(9,11)(17,18,19,21,20);(4,5,6,9,7,8,10,11)(13,14,15,16)(18,19,20,21);(12,13,14,16,15)102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 714);