Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#359 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | D8 |
| commutator | C8 | C2×C3×C4×C5 |
| Frattini, cosocle | C2×C8 | C22×C3×C5 |
| socle | C2×C3×C5 | #102 |
| prime radical | C3×C5×#135 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C2×C3×C4×C5 ◁ C2×C3×C5×C8 ◁ G | |
112 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,13,18,15,19,14,29)(11,20,22,36,23,37,30,34)(12,24,26,35,28,39,27,17)(16,25,31,38,33,40,32,21);(9,11)(10,16)(12,25)(13,22)(14,30)(15,23)(17,34)(18,31)(19,33)(20,24)(21,27)(26,38)(28,40)(29,32)(35,36)(37,39)330 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 622);