Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C4×Dic3×Dic5 |
| derived, Hall | C3×C5 ⋊ C2×C43 |
| Sylow | C5 ⋊ C2×C42×Dic3 |
| Sylow | C3 ⋊ C2×C42×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D3×D5 |
| commutator, hypocenter | C3×C5 | C2×C43 |
| Frattini | C23 | C22×D3×D5 |
| Fitting | C23×C3×C4×C5 | C22 |
| socle, prime radical | C24×C3×C5 | C23 |
| cosocle | C23×C3×C5 | C24 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C23×C4 | |
2544 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1920 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 45026);