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) = C24 |
| direct product | C3×C5×#3203 |
| 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 ◁ C2×C3×C5×#41 ◁ G | |
804 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)(17,18)(19,28)(20,27)(21,26)(22,25)(23,30)(24,29)(31,32);(9,11)(10,13)(12,16)(14,15)(17,19,21,30)(18,23,26,28)(20,31,22,29)(24,25,32,27);(11,16)(13,15)(17,19)(18,24)(20,29)(21,30)(22,31)(23,27)(25,28)(26,32);(10,14)(13,15)(17,20,21,22)(18,25,26,27)(19,29,30,31)(23,24,28,32)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1935);