Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#2009 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | #392 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3×C5 |
| prime radical | C3×C5×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
696 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)(11,21)(12,25)(13,19)(14,18)(15,20)(16,23)(17,27)(22,30)(24,35)(26,34)(28,33)(29,31)(32,38)(36,37)(39,40);(9,11)(10,16)(12,22)(13,29)(14,23)(15,24)(17,32)(18,35)(19,21)(20,31)(25,36)(26,39)(27,37)(28,38)(30,34)(33,40);(9,12,15,28)(10,17,20,34)(11,22,24,38)(13,27,14,26)(16,30,31,32)(18,25,19,33)(21,36,35,40)(23,39,29,37)345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 741);