Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2212 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C3×C5×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ C3×C4×C5×C8 ◁ G | |
308 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)(11,19)(12,24)(13,28)(14,30)(15,20)(16,22)(17,21)(18,29)(23,37)(25,36)(26,40)(27,32)(31,33)(34,38)(35,39);(9,11,13,22,15,23,29,14)(10,16,18,19,20,30,28,37)(12,21,25,38,27,39,26,31)(17,32,33,36,35,24,34,40);(9,12)(10,17)(11,21)(13,25)(14,31)(15,27)(16,32)(18,33)(19,36)(20,35)(22,38)(23,39)(24,30)(26,29)(28,34)(37,40)345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 944);