Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#215 |
| Fitting | C3×Q8×C25 ⋊ C2 |
| Hall | C3×C25 ⋊ SD16 |
| Sylow | C3 ⋊ SD16×C25 |
60 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)(29,30,32,34)(31,36,35,33);(27,28)(30,33)(31,35)(34,36)300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 62);