Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#3290 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ G | |
908 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,20)(12,17)(13,30)(14,19)(15,23)(16,28)(18,31)(21,33)(22,39)(24,35)(25,34)(26,32)(27,37)(29,36)(38,40);(9,11)(10,15)(12,26)(13,24)(14,25)(16,33)(17,38)(18,34)(19,35)(20,30)(21,29)(22,27)(23,31)(28,40)(32,37)(36,39);(9,12)(10,16)(11,21)(13,27)(14,29)(15,32)(17,30)(18,36)(19,37)(20,39)(22,23)(24,40)(25,26)(28,31)(33,35)(34,38);(9,12)(10,17)(11,22)(13,28)(14,29)(15,33)(16,30)(18,37)(19,36)(20,39)(21,23)(24,26)(25,40)(27,31)(32,35)(34,38)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2022);