Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×C5×#1977 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #121 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| prime radical | C22×C3×C5×D4 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
592 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)(10,12)(13,14,18,22,19,21,17,15)(16,24,26,28,27,23,25,20);(9,10,11,12)(13,15,18,21,19,22,17,14)(16,23,26,28,27,24,25,20);(13,16,17,25,19,27,18,26)(14,20,22,24,21,28,15,23)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 709);