Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2168 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C5×C8 | C23 |
| commutator | C22 | C22×C3×C5×C8 |
| Frattini, cosocle | C2×C8 | C23×C3×C5 |
| socle | C22×C3×C5 | C22×C8 |
| prime radical | C2×C3×C5×D4 | C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5×C8 ◁ G | |
328 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,12)(13,14,16,20,17,15,22,23,18,21,25,28,26,24,19,27);(10,12);(13,15,16,23,17,21,22,28,18,24,25,27,26,14,19,20)840 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 900);