Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#3307 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C4×C5×D4 ◁ G | |
788 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)(9,10,12,14)(11,15,16,13)(17,18)(19,26)(20,24)(21,29)(22,25)(23,28)(27,32)(30,31);(9,11)(10,13)(12,16)(14,15)(19,27)(23,31)(26,32)(28,30);(17,19)(18,23)(20,28)(21,30)(22,27)(24,32)(25,31)(26,29);(11,16)(13,15)(17,20,22,21)(18,24,25,29)(19,28,27,30)(23,32,31,26)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2039);