Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2190 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#2191 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C3×C5×#575 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ C2×C3×C5×M16 ◁ G | |
432 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)(9,10,14,18)(11,19,21,37)(12,23,25,39)(13,28,26,17)(15,30,31,20)(16,33,35,27)(22,38,29,34)(24,36,40,32);(9,11)(10,15)(12,24)(13,29)(14,21)(16,34)(17,36)(18,31)(19,23)(20,27)(22,26)(25,40)(28,32)(30,33)(35,38)(37,39);(12,25)(16,35)(19,37)(20,30)(23,39)(24,40)(27,33)(34,38)300 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 923);