Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C42×Dic15 |
| derived, Hall | C3×C5 ⋊ C2×C43 |
| Sylow | C5 ⋊ C2×C42×Dic3 |
| Sylow | C3 ⋊ C2×C42×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | D15 |
| commutator, hypocenter | C3×C5 | C2×C43 |
| Frattini | C23 | C23×D15 |
| Fitting | C22×C3×C42×C5 | C2 |
| socle, prime radical | C24×C3×C5 | C23 |
| cosocle | C23×C3×C5 | C24 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C22×C42 | |
2544 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1920 |
576 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 45020);