Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#2227 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C3×C5 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ C3×C4×C5×C8 ◁ G | |
260 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 3 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10,12,14)(11,15,16,13)(18,22)(19,25)(21,28)(23,31)(24,27)(26,32)(29,30);(9,11,12,16)(10,13,14,15)(17,18,20,22)(19,23,26,30)(21,24,27,28)(25,29,32,31);(17,19,20,26)(18,23,22,30)(21,29,27,31)(24,32,28,25)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 959);