Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#560 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C3×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
504 conjugacy classes of subgroups; only the 284 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 284 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,18)(12,17)(13,15)(14,20)(16,22)(19,23)(21,24);(9,11)(10,14)(12,20)(13,21)(15,23)(16,24)(17,18)(19,22);(10,15)(11,19)(14,18)(16,17)(20,21)(23,24);(10,16)(11,20)(14,23)(15,17)(18,24)(19,21)285 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10844);