Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2218 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2219 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C23×C3×C5 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ C22×C3×C5×C8 ◁ G | |
300 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)(9,10)(11,12)(13,14,18,22)(15,23,25,37)(16,28,30,43)(17,31,29,21)(19,32,33,26)(20,35,36,24)(27,42,41,39)(34,40,38,44);(13,15,24,40,17,27,30,32,18,25,35,44,29,41,16,26)(14,19,28,39,21,34,36,37,22,33,43,42,31,38,20,23);(10,12)(15,25)(19,33)(23,37)(26,32)(27,41)(34,38)(39,42)(40,44)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 951);