Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | Q8×(C2×D3)⋊AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ Q8×C22⋊C4 |
| Sylow | C5 ⋊ Q8×(C2×D3)⋊C4 |
| Sylow | C3 ⋊ Q8×C22⋊AGL(1,𝔽5) |
1640 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 51859);