Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#1679 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C3×C5 |
| prime radical | C2×C3×C5×D4 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G | |
332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10,13,15)(11,16,14,12)(17,18)(19,21)(20,22)(23,24);(9,11,12,10,13,14,16,15)(18,21)(22,23);(18,22)(20,24)(21,23)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 411);