Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | D8×A5 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×A5 |
| commutator | C4×A5 | C22 |
| Frattini, cosocle | C4 | C22×A5 |
| Fitting, hypercenter | D8 | A5 |
| socle | C2×A5 | D4 |
| hypocenter | A5 | D8 |
| LCS | G ▷ C4×A5 ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
169 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 169 conjugacy classes of subgroups — too many to draw. Only its 14 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
35 conjugacy classes — view the full character table.
| maximal subgroup of | #14514771, D16×A5, #14514775, … |
| maximal normal subgroup of | #14514771, D16×A5, #14514775, … |
| maximal quotient of | #102×A5, #107×A5, D16×A5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5739);