Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#2103 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | #124 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3×C5 |
| socle | C2×C3×C5 | #400 |
| prime radical | C23×C3×C5 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C22×C3×C4×C5 ◁ G | |
296 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)(9,10,13,18,14,19,15,30)(11,20,22,32,24,35,23,16)(12,25,27,39,28,17,29,34)(21,33,36,40,37,38,26,31);(9,11,15,22,14,24,13,23)(10,16,30,20,19,32,18,35)(12,26,29,21,28,36,27,37)(17,33,39,40,25,38,34,31);(9,12,13,27,14,28,15,29)(10,17,18,34,19,25,30,39)(11,21,22,36,24,37,23,26)(16,31,20,33,32,40,35,38)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 835);