Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#3054 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| socle | C22×C3×C5 | C22×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ C23×C3×C4×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)(9,10)(11,12)(13,14)(15,22)(16,20)(17,26)(18,21)(19,25)(23,28)(24,27);(13,15,17,25,18,23,16,24)(14,19,20,22,21,27,26,28);(10,12)(15,23)(19,27)(22,28)(24,25);(13,16,18,17)(14,20,21,26)(15,24,23,25)(19,22,27,28)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1786);