Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C4×C5×C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3×C4×C5 | C23 |
| commutator | C22 | C23×C3×C4×C5 |
| Frattini, cosocle | C23 | C24×C3×C5 |
| socle, prime radical | C23×C3×C5 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C4×C5 ◁ G | |
1176 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3)(4,5,6,7)(20,21,22,23,24);(9,11)(12,13,16,19)(14,18,15,17);(12,14,16,15)(13,17,19,18);(8,9,10,11)(12,15,16,14)(13,18,19,17)840 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1039);