Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#541 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C3×C5 |
| prime radical | C23×C3×C5 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
384 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 32 points:
(1,2,3)(4,5,6,7,8)(11,15)(13,16)(17,18,21,24)(19,22,27,25)(20,28,29,23)(26,31,32,30);(9,10,12,14)(11,13,15,16)(17,18)(19,25)(20,23)(21,24)(22,27)(26,31)(28,29)(30,32);(9,11)(10,13)(12,15)(14,16)(17,19)(18,22)(20,26)(21,27)(23,30)(24,25)(28,31)(29,32);(17,20,21,29)(18,23,24,28)(19,26,27,32)(22,30,25,31)330 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10825);