Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#349 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | C22⋊C4 |
| commutator | C22 | C2×C3×C5×C8 |
| Frattini, cosocle | C2×C8 | C22×C3×C5 |
| socle | C2×C3×C5 | C22⋊C8 |
| prime radical | C23×C3×C5 | C8 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C2×C3×C5×C8 ◁ G | |
116 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 116 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)(9,10,11,15,12,16,18,22,13,14,17,20,19,21,23,24);(10,14)(11,17)(16,21)(18,23)330 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 612);