Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C26 |
| direct product | C3×C5×#2614 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| prime radical | C22×C3×C5×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
1564 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 32 points:
(1,2,3)(4,5,6,7,8)(14,16)(17,18,21,24)(19,25,27,22)(20,23,29,28)(26,31,32,30);(10,12)(14,16)(17,19,21,27)(18,22,24,25)(20,26,29,32)(23,30,28,31);(9,10)(11,12)(13,14)(15,16)(17,18)(19,25)(20,28)(21,24)(22,27)(23,29)(26,30)(31,32);(17,20)(18,23)(19,26)(21,29)(22,30)(24,28)(25,31)(27,32)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1346);