Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2010 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2098 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | #127 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3×C5 |
| socle | C2×C3×C5 | #399 |
| prime radical | C2×C3×C5×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C22×C3×C4×C5 ◁ G | |
420 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)(9,10,13,18,14,19,15,29)(11,20,22,32,24,36,23,16)(12,25,27,35,28,17,30,34)(21,37,26,40,38,33,39,31);(9,11,15,22,14,24,13,23)(10,16,29,20,19,32,18,36)(12,26,30,38,28,39,27,21)(17,33,35,31,25,37,34,40);(9,12)(10,17)(11,21)(13,27)(14,28)(15,30)(16,31)(18,34)(19,25)(20,37)(22,26)(23,39)(24,38)(29,35)(32,40)(33,36)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 830);