Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | D4×S5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×S5 |
| commutator, socle, cosocle | C2×A5 | C23 |
| Fitting, hypercenter | D4 | S5 |
| hypocenter | A5 | C2×D4 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ D4 | |
399 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 399 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 20 |
35 conjugacy classes — view the full character table.
| maximal subgroup of | D8×S5, SD16×S5, #14514882, … |
| maximal normal subgroup of | D8×S5, SD16×S5, #14514882, … |
| maximal quotient of | C22⋊C4×S5, C4⋊C4×S5, D4×A5⋊C4, … |
| automorphism group of | C4⋊S5, A5⋊Q8, #91871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10871);