Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 82575360 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210 |
| abelian | C24×C3×C4×C5 |
| multiplicative | (ℤ/3080)ˣ, (ℤ/3432)ˣ, (ℤ/3696)ˣ, (ℤ/3720)ˣ, (ℤ/3960)ˣ, (ℤ/4200)ˣ, (ℤ/4620)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C25×C3×C5 |
| socle, prime radical | C25×C3×C5 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2724 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 5 generators on 20 points:
(1,2,3,4)(13,14,15)(16,17,18,19,20);(5,6);(7,8);(9,10);(11,12)960 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11348);