Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C23×C4 |
| direct product | C3×C5×#3222 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| prime radical | C3×C5×#535 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C5×#117 ◁ G | |
792 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,15)(12,14)(13,16)(17,18,21,25)(19,22,26,30)(20,23,28,24)(27,29,32,31);(9,11,12,16)(10,13,14,15)(17,19)(18,22)(20,27)(21,26)(23,29)(24,31)(25,30)(28,32);(11,16)(13,15)(18,23)(20,28)(22,29)(24,25)(27,32)(30,31);(10,14)(13,15)(19,26)(22,30)(27,32)(29,31)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1954);