Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of S5 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | C24×S5 |
| unambiguous semidirect product | A5⋊C25 |
| unambiguous semidirect product | (C2×A5)⋊C24 |
| socle | C24×A5 ⋊ C2 |
| derived | A5 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C24 | S5 |
| commutator, cosocle, hypocenter | A5 | C25 |
| Frattini | C1 | G |
| socle | C24×A5 | C2 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C24 | |
8633 conjugacy classes of subgroups; only the 441 normal subgroups are shown.
This group has 8633 conjugacy classes of subgroups — too many to draw. Only its 441 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240610);