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×#2229 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C3×C5 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ C3×C4×C5×C8 ◁ G | |
248 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 3 generators on 48 points:
(1,2,3)(4,5,6,7,8)(9,10,12,14)(11,15,16,13)(17,18,20,23)(19,27,28,45)(21,33,31,46)(22,36,32,26)(24,40,38,29)(25,42,39,35)(30,47,37,43)(34,44,48,41);(9,11,12,16)(10,13,14,15)(18,23)(24,38)(25,39)(26,36)(27,45)(33,46)(41,44)(43,47);(17,19,20,28)(18,24,23,38)(21,34,31,48)(22,37,32,30)(25,43,39,47)(26,44,36,41)(27,46,45,33)(29,42,40,35)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 961);