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, Frattini, socle | C22 | C2×S5 |
| commutator, cosocle | C2×SL(2,𝔽5) | C22 |
| Fitting, hypercenter | C2×C4 | S5 |
| prime radical | C2×#6732 | C2 |
| hypocenter | SL(2,𝔽5) | D4 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
131 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 131 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Permutation generators:
(1,3,2,4)(5,52,14,46,19,23,6,51,13,45,20,24)(7,44,21,33,30,39,8,43,22,34,29,40)(9,37,28,36,17,42,10,38,27,35,18,41)(11,47,15,50,31,25,12,48,16,49,32,26);(1,3)(2,4)(5,17,44,50,6,18,43,49)(7,41,45,12,8,42,46,11)(9,32,24,39,10,31,23,40)(13,29,16,27,14,30,15,28)(19,26,36,21,20,25,35,22)(33,51,38,47,34,52,37,48)33 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11751513, #14515097, #14515099, … |
| maximal normal subgroup of | C2×#11751513, #14515097, #14515099, … |
| maximal quotient of | #14514929, #14514938, #14514968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5708);