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) = C23×C4 |
| direct product | C3×C5×#2642 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C3×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
832 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 4 generators on 36 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12)(15,19)(17,20)(22,26)(27,29)(28,34)(35,36);(9,10,11,12)(13,14,16,18)(15,17,19,20)(21,22)(23,29)(24,28)(25,26)(27,31)(30,36)(32,35)(33,34);(9,10)(11,12)(13,15)(14,17)(16,19)(18,20)(21,23,25,31)(22,27,26,29)(24,32,33,30)(28,36,34,35);(21,24,25,33)(22,28,26,34)(23,30,31,32)(27,35,29,36)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1374);