Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #560⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C2×C5×#560⋊C3 |
| unambiguous semidirect product | (#126⋊C3)⋊(C22×C5) |
| unambiguous semidirect product | (C2×#560)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×#560)⋊C3 |
| Fitting, Hall | C2×C5×#560 ⋊ C3 |
| derived | C42 ⋊ C23×C3×C5 |
| Sylow | C2×#560 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #560⋊C3 |
| commutator, cosocle, hypocenter | C42 | C23×C3×C5 |
| Frattini | C22 | C23×C5×A4 |
| Fitting | C2×C5×#560 | C3 |
| socle | C23×C5 | C22×A4 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C2×C5 | |
608 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237058);