Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of S5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×S5 |
| derived | A5 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C8 | S5 |
| commutator, hypocenter | A5 | C2×C8 |
| Frattini | C4 | C2×S5 |
| socle | C2×A5 | C2×C4 |
| prime radical | C2×S5 | C4 |
| cosocle | C4×A5 | C22 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C8 | |
139 conjugacy classes of subgroups; only the 15 normal subgroups are shown.
This group has 139 conjugacy classes of subgroups — too many to draw. Only its 15 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | C16×S5, #14514769, C2×C8×S5, … |
| maximal normal subgroup of | C16×S5, #14514769, C2×C8×S5, … |
| maximal quotient of | C8×A5⋊C4, (C2×S5)⋊C8, (A5⋊C4)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5681);