Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D15×#400 |
| Fitting | C3×C5×#400 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×#400 |
| Sylow | C5 ⋊ D3×#400 |
| Sylow | C3 ⋊ D5×#400 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D15 |
| commutator, socle, cosocle | C23×C3×C5 | C24 |
| Fitting | C3×C5×#400 | C2 |
| prime radical | C23×D15 | C23 |
| hypercenter | #400 | D15 |
| hypocenter | C3×C5 | C2×#400 |
| LCS | G ▷ C23×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ #400 | |
1208 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 57722);