Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3003 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#3040 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| prime radical | C2×C3×C5×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C2×C3×C42×C5 ◁ G | |
1000 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 28 points:
(1,2,3)(4,5,6,7,8)(10,12)(13,14)(15,23)(16,22)(17,19)(18,21)(20,24)(25,28)(26,27);(9,10,11,12)(14,19)(20,27)(21,22)(23,28);(13,15)(14,20)(16,24)(17,25)(18,26)(19,27)(21,23)(22,28);(13,16,17,18)(14,21,19,22)(15,24,25,26)(20,23,27,28)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1772);