Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#2912 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C22×D4 |
| commutator | C4 | C23×C3×C4×C5 |
| Frattini, cosocle | C2×C4 | C24×C3×C5 |
| prime radical | C2×C3×C5×#41 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C2×C3×C5×#41 ◁ G | |
952 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 28 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12)(14,18)(16,23)(19,24)(20,25)(22,27)(26,28);(13,14,16,18,17,20,23,25)(15,19,22,24,21,26,27,28);(13,15)(14,19)(16,22)(17,21)(18,24)(20,26)(23,27)(25,28);(15,21)(19,26)(22,27)(24,28)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1644);