Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of S5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×C4×A5⋊C4 |
| unambiguous semidirect product | (C2×A5)⋊C42 |
| derived | A5 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C22×C4 | S5 |
| commutator, hypocenter | A5 | C2×C42 |
| Frattini | C22 | C22×S5 |
| socle, prime radical | C23×A5 | C22 |
| cosocle | C22×A5 | C23 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C22×C4 | |
1077 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 1077 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240479);