Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#69497 |
| Hall | C3×C5 ⋊ #2029 |
| Sylow | C3 ⋊ C5×#2029 |
932 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(21,24);(9,11,12,16)(10,13,14,15)(17,19)(18,21)(20,23)(22,24);(7,8)(9,10,12,14)(11,15,16,13)(17,18)(19,21)(20,22)(23,24)270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 34678);