Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #564⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×#564⋊C5 |
| unambiguous semidirect product | (C2×C3×#564)⋊C5 |
| Fitting, Hall | C2×C3×#564 ⋊ C5 |
| derived | #564 ⋊ C2×C3×C5 |
| Sylow | C2×#564 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23×C3 | C24⋊C5 |
| commutator, cosocle, hypocenter | #564 | C2×C3×C5 |
| Frattini | C22 | C2×C3×C24⋊C5 |
| Fitting | C2×C3×#564 | C5 |
| LCS | G ▷ #564 | |
| UCS | C1 ◁ C23×C3 | |
244 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237196);