Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×Dic14 |
| unambiguous semidirect product | C7⋊(C52×Q8) |
| Hall | C52×C7 ⋊ Q8 |
| Sylow | C7 ⋊ C52×Q8 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 1400 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4,5)(11,12,13,14)(15,18,17,16)(19,20,21,22,23,24,25);(6,7,8,9,10)(11,15,13,17)(12,16,14,18)(20,25)(21,24)(22,23)425 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 86);