Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#2189 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C2×C3×C5×#135 | C2 |
| LCS | G ▷ C2×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)(13,14,19,23)(15,24,27,42)(16,21,18,33)(17,29,32,43)(20,35,38,26)(22,28,40,31)(25,41,34,39)(30,36,44,37);(13,15)(14,20)(16,25)(17,30)(18,34)(19,27)(21,36)(22,39)(23,38)(24,29)(26,31)(28,35)(32,44)(33,37)(40,41)(42,43);(10,12)(13,16,19,18)(14,21,23,33)(15,25,27,34)(17,28,32,31)(20,36,38,37)(22,29,40,43)(24,41,42,39)(26,30,35,44)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 921);