Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of S5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×A5⋊C8 |
| derived | A5 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C42 | S5 |
| commutator, hypocenter | A5 | C4×C8 |
| Frattini | C2×C4 | C2×S5 |
| socle, prime radical | C22×A5 | C2×C4 |
| cosocle | C2×C4×A5 | C22 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C42 | |
351 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 351 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240421);