Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#3177 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| prime radical | C23×C3×C5 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C5×#117 ◁ G | |
676 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 48 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,14)(12,13)(15,16)(17,18,22,26)(19,23,28,36)(20,30,33,45)(21,34,31,25)(24,38,39,32)(27,40,42,48)(29,44,41,37)(35,46,47,43);(10,13)(14,16)(17,19,22,28)(18,23,26,36)(20,27,33,42)(21,29,31,41)(24,35,39,47)(25,37,34,44)(30,40,45,48)(32,43,38,46);(17,20,31,38,22,33,21,32)(18,24,34,45,26,39,25,30)(19,27,41,46,28,42,29,43)(23,35,44,48,36,47,37,40);(9,11,12,15)(10,14,13,16)(19,28)(23,36)(27,42)(29,41)(35,47)(37,44)(40,48)(43,46)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1909);