Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C2×#11751518 |
| Fitting | C2×D4 ⋊ S5 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊S5 |
| commutator, cosocle | C4×A5 | C23 |
| Frattini | C4 | C22×S5 |
| Fitting, hypercenter | C2×D4 | S5 |
| socle | C22×A5 | D4 |
| hypocenter | A5 | C2×D8 |
| LCS | G ▷ C4×A5 ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D4 | |
661 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 661 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
52 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240558);