Finite Group DatabasebetaFinite Group Databasebeta| order | 1520 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×D40 |
| Fitting | C5×C8×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)(20,21,22,23,24,25,26,27)(28,29,30,31,32);(21,27)(22,26)(23,25)(29,32)(30,31)437 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1520, 51);