Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1284 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42×C5 · Schur multiplier (H2) = C4 |
| direct product | C3×C5×#1287 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #95 |
| commutator | C2×C4 | C3×C42×C5 |
| Frattini, cosocle | C2×C42 | C22×C3×C5 |
| prime radical | C23×C3×C5 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C2×C3×C42×C5 ◁ G | |
252 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 2 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,12,17,14,18,13,16)(11,19,20,15,22,23,21,24)(25,26)(27,33,35,39)(28,31)(29,32)(30,34,37,40)(36,38);(9,11,13,21,14,22,12,20)(10,15,17,23,18,24,16,19)(25,27)(26,30,32,37)(28,34)(29,35)(31,33,38,39)(36,40)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 19);