Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C2×C42 |
| direct product | C3×C5×#2736 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| prime radical | C25×C3×C5 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
1120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,15)(12,13)(14,16)(17,18,21,22)(19,23,24,20)(25,26,28,30)(27,31,32,29);(10,13)(11,16)(18,22)(20,23)(25,26,28,30)(27,29,32,31);(9,11)(10,14)(12,16)(13,15)(17,19)(18,20)(21,24)(22,23)(25,26)(27,29)(28,30)(31,32);(9,10)(11,14)(12,13)(15,16)(17,20)(18,19)(21,23)(22,24)(25,27)(26,29)(28,32)(30,31)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1468);