Finite Group DatabasebetaFinite Group Databasebeta| order | 1560 |
| isoclinism | isoclinic class of Dic26 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×C22⋊D13 |
| Fitting | C22×C3×C5×C13 ⋊ C2 |
| Hall | C3×C5×C13 ⋊ D4 |
| Hall | C5×C13 ⋊ C3×D4 |
| Hall | C3×C13 ⋊ C5×D4 |
| Sylow | C13 ⋊ C3×C5×D4 |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 780 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3)(4,5,6,7,8)(9,10,12,14,16,18,20,21,19,17,15,13,11)(23,25);(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)435 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1560, 112);