Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×SL(2,𝔽5)⋊C8 |
| derived | SL(2,𝔽5) ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C22×C4 | S5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C8 |
| Frattini | C2×C4 | C2×S5 |
| socle | C23 | A5⋊C4 |
| prime radical | C22×SL(2,𝔽5) | C4 |
| cosocle | C4×SL(2,𝔽5) | C22 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22×C4 | |
274 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240674);