Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2161 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | C2×D8 |
| commutator | C8 | C22×C3×C4×C5 |
| Frattini, cosocle | C2×C8 | C23×C3×C5 |
| socle | C2×C3×C5 | C2×#107 |
| prime radical | C23×C3×C5 | Q16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C22×C3×C4×C5 ◁ C22×C3×C5×C8 ◁ G | |
280 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)(9,10,13,18,15,19,14,29)(11,20,24,36,22,34,25,39)(12,26,27,33,28,40,21,17)(16,30,32,38,31,37,35,23);(9,11,21,37,14,25,28,38,15,22,27,30,13,24,12,23)(10,16,26,36,18,32,33,34,19,31,40,39,29,35,17,20);(11,22)(16,31)(20,34)(23,38)(24,25)(30,37)(32,35)(36,39)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 893);