Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#69153 |
| Fitting | C3×C5×#354 ⋊ C2 |
| Hall | C3×C5 ⋊ #2197 |
| Sylow | C3 ⋊ C5×#2197 |
516 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 82 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)(9,17)(15,21)(22,23);(6,8,10,16)(7,11,13,18)(9,15,17,21)(12,14,19,20)(23,24);(6,7)(8,14)(9,12)(10,13)(11,15)(16,20)(17,19)(18,21)(23,24)165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 42383);