Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3×C5 · Schur multiplier (H2) = C29 |
| direct product | C3×C5×#585 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | C24 |
| commutator, Frattini, cosocle | C2 | C25×C3×C5 |
| socle | C2×C3×C5 | C25 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ G | |
1620 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 5 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,17)(12,16)(13,15)(14,18)(19,23)(20,22)(21,24);(9,11)(10,14)(12,19)(13,18)(15,17)(16,21)(20,24)(22,23);(11,18)(14,17)(19,24)(21,23);(10,15)(14,17)(16,22)(21,23);(9,12,13,20)(10,16,15,22)(11,19,18,24)(14,21,17,23)510 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11354);