Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2221 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2221 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | #466 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ C3×C5×#131 ◁ G | |
296 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)(10,16)(11,22)(12,17)(13,14)(18,33)(19,30)(20,29)(21,31)(23,37)(24,27)(25,26)(28,34)(35,40)(36,39);(9,10,17,30,14,20,26,31,15,21,25,29,13,19,12,16)(11,18,32,33,22,34,37,39,24,35,38,40,27,36,23,28);(9,11)(10,18)(12,23)(13,27)(14,22)(15,24)(16,28)(17,32)(19,36)(20,34)(21,35)(25,38)(26,37)(29,40)(30,33)(31,39)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 953);