Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2230 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#2231 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | #476 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C3×C5×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ C3×C4×C5×C8 ◁ G | |
240 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)(9,10,15,20)(11,21,24,19)(12,25)(13,29,22,18)(14,16,31,33)(17,34)(23,37)(26,39)(27,38)(28,32)(30,35)(36,40);(9,11,22,31,15,24,13,14)(10,16,29,19,20,33,18,21)(12,23,27,40,28,34,26,30)(17,32,36,38,37,25,35,39);(9,12)(10,17)(11,23)(13,26)(14,30)(15,28)(16,32)(18,35)(19,38)(20,37)(21,39)(22,27)(24,34)(25,33)(29,36)(31,40)345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 963);