Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×S5)⋊C4 |
| Fitting | C2×C4 ⋊ S5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×S5 |
| commutator | C2×A5 | C2×C4 |
| Fitting, hypercenter | C2×C4 | S5 |
| socle, cosocle | C22×A5 | C22 |
| prime radical | C22×S5 | C2 |
| hypocenter | A5 | C22⋊C4 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
247 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 247 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Permutation generators:
(1,4,2,3)(5,8,6,7)(9,10,12,13,11);(1,2)(3,5)(4,6)(7,8)(11,13)38 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×S5)⋊C4, C22⋊C4×S5, #14514793, … |
| maximal normal subgroup of | C2×(C2×S5)⋊C4, C22⋊C4×S5, #14514793, … |
| maximal quotient of | A5⋊#95, (C2×S5)⋊C8, #14514733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5702);