Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C26 |
| direct product | C3×C5×#3011 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| prime radical | C2×C3×C5×2−1+4 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C2×C3×C5×#41 ◁ G | |
1400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 44 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,12)(13,14,18,22)(15,23,26,36)(16,20,27,34)(17,29,31,21)(19,30,33,25)(24,37,38,44)(28,41,40,35)(32,42,43,39);(13,15,18,26)(14,19,22,33)(16,24,27,38)(17,30,31,25)(20,32,34,43)(21,36,29,23)(28,42,40,39)(35,44,41,37);(10,12)(13,16)(14,20)(15,24)(17,28)(18,27)(19,32)(21,35)(22,34)(23,37)(25,39)(26,38)(29,41)(30,42)(31,40)(33,43)(36,44);(16,27)(20,34)(24,38)(28,40)(32,43)(35,41)(37,44)(39,42)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1743);