Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C8 |
| direct product | C5×#68050 |
| Fitting | C3×C5×C82 ⋊ C2 |
| Hall | C3×C5 ⋊ #1455 |
| Sylow | C3 ⋊ C5×#1455 |
428 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 226 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) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(7,8)(10,13)(14,16)(18,21)(22,24);(6,7,8)(17,18,19,22,20,21,23,24);(9,10,11,14,12,13,15,16)600 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 6401);