Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#71485 |
| Fitting | C2×C3×C5×SD32 ⋊ C2 |
| Hall | C3×C5 ⋊ #2187 |
| Sylow | C3 ⋊ C5×#2187 |
512 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 512 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) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3,4,5)(7,8)(10,12);(6,7,8)(14,18)(15,22)(16,23)(19,20)(21,27)(24,28)(25,26);(9,10)(11,12)(13,14,17,21)(15,18,24,27)(16,25,23,20)(19,28,26,22)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 41855);