Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D5×#564⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C24 |
| direct product | D5×#564⋊C3 |
| unambiguous semidirect product | C5⋊(C2×#564⋊C3) |
| unambiguous semidirect product | (D5×#564)⋊C3 |
| Fitting, derived | C5×#564 ⋊ C2×C3 |
| Hall | D5×#564 ⋊ C3 |
| Sylow | C5 ⋊ C2×#564⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×#564 | C2×C3 |
| Frattini | C22 | D5×C22⋊A4 |
| socle | C22×C5 | C2×C22⋊A4 |
| LCS | G ▷ C5×#564 | |
| UCS | C1 | |
352 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
36 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239958);