Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#68195 |
| Fitting | C3×C5×D4⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #1629 |
| Sylow | C3 ⋊ C5×#1629 |
628 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(18,23)(19,20)(22,24);(7,8)(10,13)(11,16)(14,15)(18,22)(19,20)(23,24);(7,8)(9,10,12,15)(11,13,16,14)(17,18,21,24)(19,22,20,23)270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 15047);