Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#68239 |
| Fitting | C3×C5×Q8⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #1491 |
| Sylow | C3 ⋊ C5×#1491 |
504 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(7,8)(10,13)(14,16)(17,20,22,21)(18,23,19,24);(6,7,8)(17,19,22,18)(20,23,21,24);(9,10,11,14,12,13,15,16)(17,18,21,23,22,19,20,24)330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 8017);