Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D4×A5⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×S5 |
| commutator | C2×A5 | C22×C4 |
| Fitting, hypercenter | C2×D4 | S5 |
| socle, cosocle | C22×A5 | C23 |
| prime radical | C2×D4×A5 | C2 |
| hypocenter | A5 | C4×D4 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
937 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 937 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | S4×A5⋊C4, SD16×A5⋊C4 |
| maximal normal subgroup of | SD16×A5⋊C4 |
| maximal quotient of | D4×GL(2,𝔽5), SD16×A5⋊C4, #72277090 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240497);