Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#2253 |
| 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 | |
232 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)(19,27,29,41)(21,34,32,47)(22,35,33,26)(24,38,36,30)(25,40,37,28)(31,46,45,43)(39,44,42,48);(9,11,12,16)(10,13,14,15)(18,23)(24,36)(25,37)(26,35)(27,41)(34,47)(39,42)(43,46);(17,19,28,44,22,31,32,38,20,29,40,48,33,45,21,30)(18,24,34,43,26,39,37,41,23,36,47,46,35,42,25,27)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 985);