Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2214 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C3×C5×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ C3×C4×C5×C8 ◁ G | |
300 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)(9,10,16,22)(11,20,25,31)(12,26,28,39)(13,21,15,19)(14,17,24,32)(18,33,35,23)(27,40,30,36)(29,37,38,34);(9,11,15,24,16,25,13,14)(10,17,21,31,22,32,19,20)(12,23,30,38,28,33,27,29)(18,26,37,40,35,39,34,36);(9,12)(10,18)(11,23)(13,27)(14,29)(15,30)(16,28)(17,26)(19,34)(20,36)(21,37)(22,35)(24,38)(25,33)(31,40)(32,39)345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 946);