Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1462 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#1822 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C2×C22⋊C4 |
| commutator | C23 | C22×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| prime radical | C24×C3×C5 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C23×C3×C4×C5 ◁ G | |
544 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,14)(12,13)(15,16)(17,18,20,24,21,23,27,30)(19,22,25,29,26,28,31,32);(10,13)(14,16)(17,19,21,26)(18,22,23,28)(20,25,27,31)(24,29,30,32);(9,11,12,15)(10,14,13,16)(18,23)(20,27)(22,28)(25,31)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 554);