Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C25×D24 |
| Fitting | C3×C8×C25 ⋊ C2 |
| Hall | C3×C25 ⋊ D8 |
| Sylow | C3 ⋊ D8×C25 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 600 |
A minimal faithful permutation representation — 2 generators on 36 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)(26,27,28,29,30,31,32,33)(34,35,36);(27,33)(28,32)(29,31)(35,36)375 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 52);