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) = C22 |
| direct product | C3×C5×#2209 |
| 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 | |
308 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 3 generators on 44 points:
(1,2,3)(4,5,6,7,8)(10,12)(13,14,18,22)(15,23,26,42)(16,27,31,41)(17,32,29,21)(19,34,36,24)(20,37,39,30)(25,43,33,38)(28,40,44,35);(9,10,11,12);(13,15,18,26)(14,19,22,36)(16,28,31,44)(17,33,29,25)(20,38,39,43)(21,40,32,35)(23,41,42,27)(24,37,34,30)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 941);