Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2155 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | #106 |
| commutator | C8 | C22×C3×C4×C5 |
| Frattini, cosocle | C2×C8 | C23×C3×C5 |
| socle | C2×C3×C5 | C2×#106 |
| prime radical | C23×C3×C5 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C22×C3×C4×C5 ◁ C22×C3×C5×C8 ◁ G | |
288 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)(11,20,23,34)(12,17)(13,26)(14,29)(15,19)(16,22,31,36)(18,27)(21,33,24,38)(25,32)(28,39)(30,35,40,37);(9,11,13,22,14,24,27,37,15,23,28,36,12,21,25,35)(10,16,18,20,17,30,26,33,19,31,32,34,29,40,39,38);(9,12,15,14)(10,17,19,29)(11,21,23,24)(13,25,28,27)(16,30,31,40)(18,26,32,39)(20,33,34,38)(22,35,36,37)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 887);