Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8 ⋊ S5 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C4⋊S5 |
| commutator, cosocle | C4×A5 | C22 |
| Frattini | C4 | C2×S5 |
| Fitting, hypercenter | C8 | S5 |
| socle | C2×A5 | D4 |
| prime radical | C4⋊S5 | C2 |
| hypocenter | A5 | SD16 |
| LCS | G ▷ C4×A5 ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
124 conjugacy classes of subgroups; only the 11 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 11 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,5,3,7,2,6,4,8)(9,13,11);(1,3)(2,4)(5,6)(10,11,12,13)29 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11751488, SD16×S5, #14514874, … |
| maximal normal subgroup of | C2×#11751488, SD16×S5, #14514874, … |
| maximal quotient of | #14514743, #14514747, #14514756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5683);