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, socle | C2 | C4⋊S5 |
| commutator, cosocle | #6732 | C22 |
| Frattini | C4 | C2×S5 |
| Fitting, hypercenter | C8 | S5 |
| prime radical | #91872 | C2 |
| hypocenter | SL(2,𝔽5) | D4 |
| LCS | G ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
109 conjugacy classes of subgroups; only the 10 normal subgroups are shown.
This group has 109 conjugacy classes of subgroups — too many to draw. Only its 10 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 80 points:
(1,73,68,14,9,74,67,12)(2,78,19,13,4,77,11,18)(3,37,51,34,8,33,49,36)(5,20,17,32,10,15,16,31)(6,35,63,50,7,38,64,52)(21,62,40,80,29,57,42,79)(22,26,39,45,24,27,47,44)(23,72,43,75,28,70,48,76)(25,61,41,71,30,53,46,69)(54,66,58,55,56,65,59,60);(1,21,12,79,68,55,7,28,15,65,49,61,37,30,3,70,16,58,50,76,9,29,14,80,67,60,6,23,20,66,51,53,33,25,8,72,17,59,52,75)(2,48,18,71,32,44,34,22,5,41,19,56,77,42,35,26,74,47,63,62,4,43,13,69,31,45,36,24,10,46,11,54,78,40,38,27,73,39,64,57)27 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11751493, #14515135, #14515136, … |
| maximal normal subgroup of | C2×#11751493, #14515135, #14515136, … |
| maximal quotient of | #14514947, #14514948, #14514962, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5688);