Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C4⋊(A5⋊C4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×S5 |
| commutator | C2×A5 | C2×C4 |
| Fitting, hypercenter | C2×C4 | S5 |
| socle, prime radical, cosocle | C22×A5 | C22 |
| hypocenter | A5 | C4⋊C4 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
201 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Permutation generators:
(1,2)(3,4)(5,8,6,7)(9,12,11);(1,3,2,4)(5,6)(9,13,11,10)38 conjugacy classes — view the full character table.
| maximal subgroup of | #14514741, #14514743, #14514745, … |
| maximal normal subgroup of | #14514741, #14514743, #14514745, … |
| maximal quotient of | A5⋊#95, C4⋊(A5⋊C8), #14514756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5697);