Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2151 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C5×C8 | C23 |
| commutator | C22 | C22×C3×C5×C8 |
| Frattini, cosocle | C2×C8 | C23×C3×C5 |
| socle | C22×C3×C5 | C22×C8 |
| prime radical | C23×C3×C5 | C2×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5×C8 ◁ G | |
320 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 44 points:
(1,2,3)(4,5,6,7,8)(10,12)(13,14,16,20,17,21,26,32,18,22,27,33,28,34,38,42)(15,19,24,30,25,31,37,41,23,29,35,39,36,40,43,44);(9,10,11,12)(13,15)(14,19)(16,24)(17,25)(18,23)(20,30)(21,31)(22,29)(26,37)(27,35)(28,36)(32,41)(33,39)(34,40)(38,43)(42,44);(15,23)(19,29)(24,35)(25,36)(30,39)(31,40)(37,43)(41,44)840 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 883);