Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1714 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C4 |
| direct product | C3×C5×#1723 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C3×C5 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C3×C5 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G | |
352 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)(10,13)(11,15)(14,16)(17,18,21,24)(19,25,28,32)(20,29,26,23)(22,30,31,27);(9,10,11,13,12,14,15,16);(10,14)(13,16)(17,19,26,30,21,28,20,27)(18,22,29,32,24,31,23,25)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 455);