Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5×C8 · Schur multiplier (H2) = C4 |
| direct product | C3×C5×#322 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C42×C5 | C22 |
| commutator | C2 | C3×C4×C5×C8 |
| Frattini, cosocle | C42 | C22×C3×C5 |
| socle, prime radical | C22×C3×C5 | C42 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C42×C5 ◁ G | |
132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10,11,14,12,13,15,16);(10,13)(14,16)(17,18,19,21,20,22,23,24)600 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 585);