Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×Dic10 |
| unambiguous semidirect product | C5⋊(C5×C7×Q8) |
| Hall | C52×C7 ⋊ Q8 |
| Sylow | C52 ⋊ C7×Q8 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
455 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 91);