Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×#204 |
| Fitting | C3×C52×C8 ⋊ C2 |
| Hall | C3×C52 ⋊ SD16 |
| Sylow | C3 ⋊ C52×SD16 |
160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 600 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(11,12,13)(14,15,16,18,17,19,20,21);(6,7,8,9,10)(12,13)(15,18)(16,20)(19,21)375 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 419);