Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#1946 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C2×D4 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| socle | C22×C3×C5 | C4×D4 |
| prime radical | C23×C3×C5 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ C22×C3×C5×C8 ◁ G | |
400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,12)(13,14,17,22,18,23,27,21)(15,19,16,25,24,20,26,28);(10,12)(13,15,17,16,18,24,27,26)(14,19,22,25,23,20,21,28);(13,16,17,24,18,26,27,15)(14,20,21,25,23,19,22,28)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 678);