Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | D4 ⋊ S5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×S5 |
| commutator, socle, cosocle | C2×A5 | C23 |
| Fitting, hypercenter | D4 | S5 |
| hypocenter | A5 | #41 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ D4 | |
302 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Permutation generators:
(1,2)(4,6)(9,10)(12,13);(1,3)(2,5)(4,7)(6,8)(9,13,10,12,11);(1,6,2,4)(3,8,5,7)(9,10)35 conjugacy classes — view the full character table.
| maximal subgroup of | #14514875, #14514876, #14514882, … |
| maximal normal subgroup of | #14514875, #14514876, #14514882, … |
| maximal quotient of | #14514794, #14514795, D4×A5⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10874);