Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5×C8 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#2117 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C5×C8 | C2×D4 |
| commutator | C4 | C22×C3×C5×C8 |
| Frattini, cosocle | C2×C8 | C23×C3×C5 |
| socle | C2×C3×C5 | C2×C22⋊C8 |
| prime radical | C2×C3×C5×#41 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C5×C8 ◁ C22×C3×C5×C8 ◁ G | |
440 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)(9,10,13,19,14,20,28,37,15,17,29,33,12,18,26,35)(11,21,23,38,22,31,39,36,24,34,27,40,25,16,30,32);(9,11)(10,16)(12,25)(13,27)(14,22)(15,24)(17,31)(18,34)(19,36)(20,21)(23,29)(26,39)(28,30)(32,33)(35,38)(37,40);(10,17)(16,31)(18,20)(19,33)(21,34)(32,36)(35,37)(38,40)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 849);