Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#73135 |
| Fitting | C22×C5×Q16 ⋊ D3 |
204 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 36 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) = 240 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4,5)(6,7,9)(10,11,14,17)(12,19,21,25)(13,22,20,16)(15,23,24,18);(7,8)(11,15)(12,18)(13,20)(16,25)(17,24)(19,22)(21,23)145 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236557);