Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | Q16×A5 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×A5 |
| commutator | C4×A5 | C22 |
| Frattini, cosocle | C4 | C22×A5 |
| Fitting, hypercenter | Q16 | A5 |
| socle, prime radical | C2×A5 | D4 |
| hypocenter | A5 | Q16 |
| LCS | G ▷ C4×A5 ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
133 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
35 conjugacy classes — view the full character table.
| maximal subgroup of | #14514774, SD32×A5, #14514778, … |
| maximal normal subgroup of | #14514774, SD32×A5, #14514778, … |
| maximal quotient of | #103×A5, #107×A5, C2×Q16×A5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5743);