Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#3263 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| prime radical | C3×C5×#469 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C5×#117 ◁ G | |
692 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)(10,13)(11,15)(17,18,20,24)(19,26,27,22)(21,23,29,25)(28,30,32,31);(9,10)(11,14)(12,13)(15,16)(17,19,20,27)(18,22,24,26)(21,28,29,32)(23,31,25,30);(10,13)(14,16)(18,23)(19,27)(21,29)(22,30)(24,25)(26,31);(9,11,12,15)(10,14,13,16)(18,24)(19,27)(23,25)(28,32)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1995);