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) = C2 |
| direct product | C3×C5×#2237 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C23×C3×C5 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ C22×C3×C5×C8 ◁ G | |
264 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 48 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,14)(12,13)(15,16)(17,18,22,27)(19,23,30,38)(20,24,33,40)(21,34,32,26)(25,41,39,31)(28,35,44,47)(29,45,43,37)(36,48,46,42);(10,13)(14,16)(17,19,22,30)(18,23,27,38)(20,28,33,44)(21,29,32,43)(24,35,40,47)(25,36,39,46)(26,37,34,45)(31,42,41,48);(9,11,12,15)(10,14,13,16)(18,24)(20,31)(21,32)(23,35)(25,26)(27,40)(28,42)(29,43)(33,41)(34,39)(36,37)(38,47)(44,48)(45,46)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 969);