Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#464 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C3×C5 |
| prime radical | C2×C3×C5×D4 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G | |
224 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,6,7,8)(10,12)(13,14)(15,21)(16,18)(17,25)(19,23)(20,24)(22,28)(26,27);(9,10,11,12)(14,18)(19,27)(20,25)(21,28);(13,15,16,22)(14,19,18,27)(17,26,24,23)(20,28,25,21)285 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5634);