Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8 ⋊ S5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×S5 |
| commutator, socle | C2×A5 | C2×C4 |
| Fitting, hypercenter | C8 | S5 |
| prime radical | C2×S5 | C4 |
| cosocle | C4×A5 | C22 |
| hypocenter | A5 | M16 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C4 ◁ C8 | |
126 conjugacy classes of subgroups; only the 13 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 13 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:
(1,8,3,5,2,7,4,6)(9,13)(10,12,11);(1,7,4,5,2,8,3,6)(9,12,11)38 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11751491, M16×S5, #14514857, … |
| maximal normal subgroup of | C2×#11751491, M16×S5, #14514857, … |
| maximal quotient of | #14514727, (C2×S5)⋊C8, (A5⋊C4)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5686);