Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×Dic3×Dic5 |
| derived, Hall | C3×C5 ⋊ C23×C42 |
| Sylow | C5 ⋊ C23×C4×Dic3 |
| Sylow | C3 ⋊ C23×C4×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D3×D5 |
| commutator, hypocenter | C3×C5 | C23×C42 |
| Frattini | C22 | C23×D3×D5 |
| Fitting, socle, prime radical | C25×C3×C5 | C22 |
| cosocle | C22×C3×C5 | C25 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C25 | |
6000 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, 204372);