Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×C5×#1979 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #121 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| prime radical | C23×C3×C5 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 44 points:
(1,2,3)(4,5,6,7,8)(10,12)(13,14,18,23,19,22,17,31)(15,20,26,35,25,36,32,34)(16,27,29,37,30,41,28,21)(24,38,40,33,39,43,42,44);(9,10,11,12)(13,15,17,26,19,25,18,32)(14,20,23,34,22,36,31,35)(16,24,28,40,30,39,29,42)(21,33,27,38,37,44,41,43);(13,16,18,29,19,30,17,28)(14,21,31,41,22,37,23,27)(15,24,32,42,25,39,26,40)(20,33,35,43,36,44,34,38)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 711);