Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #360 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#2148 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | #102 |
| commutator | C8 | C22×C3×C4×C5 |
| Frattini, cosocle | C2×C8 | C23×C3×C5 |
| socle | C2×C3×C5 | C2×#102 |
| prime radical | C2×C3×C5×#135 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C22×C3×C4×C5 ◁ 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)(9,10,12,16,14,19,26,18)(11,20,23,34,24,37,21,36)(13,27,25,17,29,33,38,35)(15,28,31,22,32,39,30,40);(9,11)(10,15)(12,21)(13,28)(14,24)(16,30)(17,34)(18,31)(19,32)(20,33)(22,38)(23,26)(25,40)(27,37)(29,39)(35,36);(9,12,14,26)(10,16,19,18)(11,21,24,23)(13,25,29,38)(15,30,32,31)(17,33,35,27)(20,36,37,34)(22,28,40,39)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 880);