Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4 ⋊ S5 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×S5 |
| commutator, socle, cosocle | C2×A5 | C23 |
| Frattini | C2 | C22×S5 |
| Fitting, hypercenter | C2×C4 | S5 |
| hypocenter | A5 | #41 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
291 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 291 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) = 40 |
Permutation generators:
(1,7)(2,8)(3,6)(4,5)(12,13);(1,4,2,3)(5,8,6,7)(9,10,11,13,12);(1,7,2,8)(3,6,4,5)(9,13)(10,11,12)38 conjugacy classes — view the full character table.
| maximal subgroup of | #14514857, #14514858, #14514873, … |
| maximal normal subgroup of | #14514857, #14514858, #14514873, … |
| maximal quotient of | #14514792, #14514793, C4×C4⋊S5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10864);