Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of C5⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C42×C5⋊S4 |
| Fitting | C22×C42×C5 ⋊ D3 |
| derived | C5×A4 ⋊ C2×C42 |
| Sylow | C5 ⋊ C42×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | C5⋊S4 |
| commutator, hypocenter | C5×A4 | C2×C42 |
| Frattini | C22 | C22×C5⋊S4 |
| Fitting | C22×C42×C5 | D3 |
| socle | C24×C5 | C22×D3 |
| prime radical | C22×C5⋊S4 | C22 |
| cosocle | C22×C5×A4 | C23 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C42 | |
994 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239386);