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×#519 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C24 |
| commutator | C2 | C23×C3×C4×C5 |
| Frattini, cosocle | C22 | C24×C3×C5 |
| prime radical | C23×C3×C5 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 28 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12)(14,18)(16,24)(19,21)(22,28);(13,14,17,18)(15,21,23,19)(16,20,24,25)(22,27,28,26);(13,15,17,23)(14,19,18,21)(16,22,24,28)(20,26,25,27);(13,16)(14,20)(15,22)(17,24)(18,25)(19,26)(21,27)(23,28)510 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10803);