Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×D5×2−1+4⋊C3 |
| unambiguous semidirect product | (C2×D5×2−1+4)⋊C3 |
| Fitting | C2×C5×2−1+4 ⋊ C2×C3 |
| Hall | C2×D5×2−1+4 ⋊ C3 |
| Sylow | C5 ⋊ C22×2−1+4⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D5×A4 |
| commutator, cosocle, hypocenter | C5×Q8 | C24×C3 |
| Frattini | C2 | C23×D5×A4 |
| Fitting | C2×C5×2−1+4 | C2×C3 |
| socle | C22×C5 | C23×A4 |
| hypercenter | C2×D4 | D5×A4 |
| LCS | G ▷ C5×Q8 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
2574 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240364);