Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×C5×#428 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3×C5 | C2×D4 |
| commutator | C4 | C23×C3×C4×C5 |
| Frattini, cosocle | C2×C4 | C24×C3×C5 |
| prime radical | C24×C3×C5 | D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ C23×C3×C4×C5 ◁ G | |
1072 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 22 points:
(1,2)(15,16,17)(18,19,20,21,22);(3,4,5,6)(8,11)(9,13)(12,14);(7,8,9,11,10,12,13,14);(8,12)(11,14)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1642);