Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1685 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#1689 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C3×C5 |
| prime radical | C2×C3×C5×D4 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G | |
332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,13)(12,15)(14,16)(17,18,21,24)(19,25,27,32)(20,29,26,23)(22,30,31,28);(17,19,26,30,21,27,20,28)(18,22,29,32,24,31,23,25);(10,13)(11,16)(14,15)(19,27)(22,31)(25,32)(28,30)345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 421);