Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#2852⋊C3 |
| unambiguous semidirect product | #2852⋊(C3×C5) |
| unambiguous semidirect product | (C5×#2852)⋊C3 |
| Fitting, Hall | C5×#2852 ⋊ C3 |
| Sylow | #2852 ⋊ C3×C5 |
274 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4,5)(7,9)(10,15,12)(13,25,17)(14,18,20)(16,24,19)(21,23,22);(6,7)(8,9)(10,23,11,25)(12,20,15,24)(13,17,16,14)(18,22,21,19)140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236639);