Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#2399 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3×C4×C5 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| socle, prime radical | C23×C3×C5 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C4×C5 ◁ G | |
1008 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 4 generators on 28 points:
(1,2,3)(4,5,6,7,8)(13,14,17,20)(15,19,16,18)(21,22,25,28)(23,27,24,26);(9,10)(11,12)(13,15,17,16)(14,18,20,19)(21,23,25,24)(22,26,28,27);(10,12)(13,15,17,16)(14,19,20,18)(21,24,25,23)(22,27,28,26);(13,16,17,15)(14,18,20,19)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1131);