Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | D5×A4×#41 |
| Fitting | C22×C5×#41 ⋊ C2×C3 |
| Hall | C22×D5×#41 ⋊ C3 |
| Sylow | C5 ⋊ C2×A4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D5×A4 |
| commutator, socle, cosocle | C23×C5 | C24×C3 |
| Frattini | C2 | C23×D5×A4 |
| Fitting | C22×C5×#41 | C2×C3 |
| hypercenter | #41 | D5×A4 |
| hypocenter | C22×C5 | C2×C3×#41 |
| LCS | G ▷ C23×C5 ▷ C22×C5 | |
| UCS | C1 ◁ C4 ◁ #41 | |
2720 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240357);