Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×C5×#405 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C5×C8 | C22 |
| commutator | C2 | C2×C3×C42×C5 |
| Frattini, cosocle | C2×C4 | C23×C3×C5 |
| socle | C22×C3×C5 | C22×C4 |
| prime radical | C23×C3×C5 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5×C8 ◁ G | |
260 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)(13,14,16,19,17,20,23,26)(15,18,22,25,21,24,27,28);(9,10,11,12)(13,15)(14,18)(16,22)(17,21)(19,25)(20,24)(23,27)(26,28);(15,21)(18,24)(22,27)(25,28)600 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5575);