Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C5×#68647 |
| Fitting | C3×C5×#336 ⋊ C2 |
| Hall | C3×C5 ⋊ C8×C22⋊C4 |
| Sylow | C3 ⋊ C5×C8×C22⋊C4 |
768 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)(17,19,20,24,21,18,22,23);(6,7,8)(9,10,11,12)(14,16);(13,14)(15,16)(17,18,20,23,21,19,22,24)600 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 20837);