Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#1832 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3×C4×C5 | C23 |
| commutator | C23 | C22×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| socle, prime radical | C23×C3×C5 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C4×C5 ◁ G | |
432 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 3 generators on 36 points:
(1,2,3)(4,5,6,7,8)(10,11)(13,14)(15,18)(16,17)(19,20)(21,22,24,27,25,28,31,34)(23,26,30,33,29,32,35,36);(9,10,12,11)(14,17)(18,20)(21,23)(22,26)(24,30)(25,29)(27,33)(28,32)(31,35)(34,36);(9,11,12,10)(13,15,16,19)(14,18,17,20)(23,29)(26,32)(30,35)(33,36)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 564);