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×#3225 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| prime radical | C3×C5×#449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C5×#117 ◁ G | |
752 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 960 |
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)(18,23)(19,26)(20,22)(24,31)(27,32)(28,30);(9,11,12,16)(10,13,14,15)(17,18)(19,27)(20,29)(21,23)(22,25)(24,28)(26,31)(30,32);(11,16)(13,15)(17,19)(18,24)(20,26)(21,28)(22,30)(23,27)(25,31)(29,32);(10,14)(13,15)(17,20,21,22)(18,25,23,29)(19,26,28,30)(24,31,27,32)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1957);