Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#2141 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C2×D8 |
| commutator | C8 | C22×C3×C4×C5 |
| Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C23×C3×C5 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ C22×C3×C5×C8 ◁ G | |
440 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 44 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12)(13,14)(15,24)(16,21)(17,30)(18,34)(19,23)(20,26)(22,32)(25,38)(27,44)(28,41)(29,39)(31,37)(33,40)(35,42)(36,43);(13,15,19,28)(14,20,23,36)(16,27,18,25)(17,31,33,42)(21,37,34,35)(22,38,39,44)(24,40,41,30)(26,29,43,32);(13,16,19,18)(14,21,23,34)(15,25,28,27)(17,29,33,32)(20,35,36,37)(22,30,39,40)(24,38,41,44)(26,42,43,31)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 873);