Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C26 |
| direct product | C5×#71570 |
| Fitting | C22×C3×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #1439 |
| Sylow | C3 ⋊ C5×#1439 |
1560 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)(14,16)(22,24);(6,7,8)(17,18,19,20)(21,22)(23,24);(9,10,11,12)(13,14)(15,16)(18,20)420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5746);