Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#68342 |
| Fitting | C3×C5×#329 ⋊ C2 |
| Hall | C3×C5 ⋊ #1525 |
| Sylow | C3 ⋊ C5×#1525 |
540 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 126 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)(17,19,21,20)(18,22,23,24);(6,7,8)(10,13)(11,15)(17,18)(19,22)(20,24)(21,23);(9,10,11,14,12,13,15,16)(18,22,23,24)285 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 9671);