Finite Group DatabasebetaFinite Group Databasebeta| order | 1520 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#686 |
| Fitting | C5×D4×C19 ⋊ C2 |
| Hall | C5×C19 ⋊ D8 |
| Sylow | C5 ⋊ D8×C19 |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 760 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,24,22)(26,29)(27,32)(30,31);(21,22)(23,24)(25,26)(27,29)(28,31)(30,32)323 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1520, 59);