Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D12×#713 |
| Fitting | C3×C4×C5×Q8 ⋊ C22 |
| Hall | C3×C5 ⋊ D4×#41 |
| Sylow | C5 ⋊ #41×D12 |
| Sylow | C3 ⋊ D4×#713 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C25 |
| Fitting | C3×C4×C5×Q8 | C22 |
| hypercenter | C4×Q8 | D3×D5 |
| hypocenter | C3×C5 | D4×#41 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
3296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 208915);