Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#328 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C22⋊C4 |
| commutator | C2×C4 | C2×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C22×C3×C5 |
| prime radical | C23×C3×C5 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
160 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 68 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 — 2 generators on 24 points:
(1,2,3)(4,5,6,7,8)(10,14,15,23)(11,18)(16,24,17,19)(20,22);(9,10,12,16)(11,19,18,23)(13,17,21,15)(14,22,24,20)285 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 591);