Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1913 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#1915 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | #386 |
| commutator | C23 | C22×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| prime radical | C2×C3×C5×#41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
616 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)(9,10,13,18,14,17,19,32)(11,15,22,29,21,30,26,33)(12,23,25,34,24,16,27,31)(20,28,36,39,35,38,37,40);(9,11,19,22,14,21,13,26)(10,15,18,33,17,30,32,29)(12,20,25,37,24,35,27,36)(16,28,34,39,23,38,31,40);(9,12)(10,16)(11,20)(13,27)(14,24)(15,28)(17,23)(18,34)(19,25)(21,35)(22,37)(26,36)(29,40)(30,38)(31,32)(33,39)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 647);