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×#6729 | C2 |
| hypocenter | SL(2,𝔽5) | D4 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
121 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 121 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) = 160 |
Permutation generators:
(1,4,2,3)(5,27,35,13,21,7,26,34,15,23,6,28,36,14,22,8,25,33,16,24)(9,11,10,12)(17,38,46,41,51,19,40,48,43,50,18,37,45,42,52,20,39,47,44,49)(29,31,30,32);(1,2)(5,49,9,38,6,50,10,37)(7,51,11,40,8,52,12,39)(13,43,15,42,14,44,16,41)(17,22,31,25,18,21,32,26)(19,24,30,27,20,23,29,28)(33,47,36,45,34,48,35,46)33 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11751511, #14515123, #14515124, … |
| maximal normal subgroup of | C2×#11751511, #14515123, #14515124, … |
| maximal quotient of | #14514938, #14514939, #14514959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5706);