Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C4⋊S5 |
| commutator, cosocle | C4×A5 | C22 |
| Frattini | C4 | C2×S5 |
| Fitting, hypercenter | C8 | S5 |
| socle, prime radical | C2×A5 | D4 |
| hypocenter | A5 | Q16 |
| LCS | G ▷ C4×A5 ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
113 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Permutation generators:
(1,4,5,2)(6,19,7,18)(8,20,9,21)(10,15,11,14)(12,16,13,17);(1,3,4)(6,11,9,12,7,10,8,13)(14,19,17,20,15,18,16,21)29 conjugacy classes — view the full character table.
| maximal subgroup of | #14514775, #14514776, #14514778, … |
| maximal normal subgroup of | #14514775, #14514776, #14514778, … |
| maximal quotient of | #14514747, #14514759, C2×#11751489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5684);