Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2104 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#2104 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | #401 |
| commutator, Frattini, cosocle | C24 | C23×C3×C5 |
| prime radical | C24×C3×C5 | C23 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C24×C3×C5 ◁ G | |
356 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,17,19,14)(12,15,21,24)(13,16)(18,23)(20,22);(9,11)(10,14)(12,20,21,18)(13,19)(15,23,24,22)(16,17);(9,12)(10,15,16,24)(11,18)(13,21)(14,22,17,23)(19,20)345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 836);