Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×#73104 |
214 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 60 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)(11,15)(16,21)(17,22)(23,25);(7,8)(10,11,12,16,13,17,18,23,14,15,19,21,20,22,24,25)280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236526);