Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11751509 |
| derived | SL(2,𝔽5) ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×S5 |
| commutator, hypocenter | SL(2,𝔽5) | C22×C4 |
| Frattini | C22 | C22×S5 |
| Fitting, hypercenter | C22×C4 | S5 |
| prime radical | C22×#6729 | C2 |
| cosocle | C2×SL(2,𝔽5) | C23 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
574 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240763);