Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#68112 |
| Fitting | C3×C5×#323 ⋊ C2 |
| Hall | C3×C5 ⋊ #1613 |
| Sylow | C3 ⋊ C5×#1613 |
576 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(19,23)(21,24);(7,8)(10,13)(11,16)(14,15)(17,18)(19,24)(20,22)(21,23);(7,8)(9,10,12,15)(11,13,16,14)(18,21)(19,23)(22,24)225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 14231);