Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3×C5 · Schur multiplier (H2) = C28 |
| direct product | C3×C5×#3529 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C3×C5 |
| socle | C22×C3×C5 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ G | |
2116 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 5 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,13)(12,14)(15,16)(17,18)(19,25)(20,24)(21,23)(22,26)(27,31)(28,30)(29,32);(9,11)(10,13)(12,15)(14,16)(17,19)(18,22)(20,27)(21,26)(23,25)(24,29)(28,32)(30,31);(10,14)(11,15)(19,26)(22,25)(27,32)(29,31);(10,14)(13,16)(18,23)(19,26)(24,30)(27,32);(17,20,21,28)(18,24,23,30)(19,27,26,32)(22,29,25,31)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2261);