Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#520 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C24 |
| commutator | C2 | C23×C3×C4×C5 |
| Frattini, cosocle | C22 | C24×C3×C5 |
| prime radical | C2×C3×C5×#41 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
588 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12)(13,14)(15,19)(16,17)(18,20);(14,17)(18,19);(13,14)(15,18)(16,17)(19,20);(13,15,16,20)(14,18,17,19)510 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10804);