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) = C2 |
| direct product | C3×C5×#2183 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C5×C8 | C23 |
| commutator | C22 | C22×C3×C5×C8 |
| Frattini, cosocle | C2×C8 | C23×C3×C5 |
| socle, prime radical | C22×C3×C5 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5×C8 ◁ G | |
252 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 3 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,16)(12,14)(13,15)(17,18,20,24,21,19,26,27,22,25,29,32,30,28,23,31);(9,11,13,12)(10,14,15,16);(9,12,13,11)(10,14,15,16)(17,19,20,27,21,25,26,32,22,28,29,31,30,18,23,24)840 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 915);