Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×C3⋊#168 |
| derived, Hall | C3×C5 ⋊ C42×C8 |
| Sylow | C5 ⋊ C42×C3⋊C8 |
| Sylow | C3 ⋊ C42×#168 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D15 |
| commutator, hypocenter | C3×C5 | C42×C8 |
| Frattini | C22×C4 | C22×D15 |
| Fitting | C3×C43×C5 | C2 |
| socle, prime radical | C23×C3×C5 | C22×C4 |
| cosocle | C22×C3×C4×C5 | C23 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C43 | |
816 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, 19885);