Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1595 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#1617 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3×C5 |
| prime radical | C23×C3×C5 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
404 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,15,30)(11,20,22,37)(12,25,31,27)(13,18,14,19)(16,32,33,21)(17,29,40,28)(23,36,24,38)(26,34,39,35);(9,11,13,23)(10,16,18,34)(12,26,28,21)(14,24,15,22)(17,36,25,20)(19,35,30,33)(27,37,40,38)(29,32,31,39);(9,10,14,19)(11,16,24,35)(12,27,29,17)(13,18,15,30)(20,21,38,39)(22,33,23,34)(25,28,40,31)(26,37,32,36)345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 349);