Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#73114 |
252 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 52 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)(10,12,13,21,15,22,14,23)(11,16,17,20,19,24,18,25);(7,8)(10,11,14,18,15,19,13,17)(12,20,21,24,22,25,23,16)190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236536);