Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C25×C22⋊D7 |
| unambiguous semidirect product | C22⋊(D7×C25) |
| Fitting | C22×C7×C25 ⋊ C2 |
| Hall | C7×C25 ⋊ D4 |
| Sylow | C7 ⋊ D4×C25 |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 700 |
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)(26,27,29,31,32,30,28)(34,36);(27,28)(29,30)(31,32)(33,34)(35,36)425 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 18);