Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C22 | C2×S5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C4 |
| Fitting, hypercenter | C2×C4 | S5 |
| prime radical, cosocle | C2×SL(2,𝔽5) | C22 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
117 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 117 conjugacy classes of subgroups — too many to draw. Only its 14 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Permutation generators:
(5,40,13,30,34,51,6,39,14,29,33,52)(7,37,15,32,36,50,8,38,16,31,35,49)(9,47,23,18,27,41,10,48,24,17,28,42)(11,46,22,20,26,43,12,45,21,19,25,44);(1,3,2,4)(5,31,36,44,28,51,6,32,35,43,27,52)(7,30,33,41,25,50,8,29,34,42,26,49)(9,47,16,40,22,19,10,48,15,39,21,20)(11,46,13,37,24,18,12,45,14,38,23,17)36 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11751510, #14515067, C4×#91877, … |
| maximal normal subgroup of | C2×#11751510, #14515067, C4×#91877, … |
| maximal quotient of | #14514921, #14514938, #14514968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5705);