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) = C25 |
| direct product | C3×C5×#1442 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C3×C5 | C23 |
| commutator | C23 | C22×C3×C4×C5 |
| Frattini, cosocle | C24 | C23×C3×C5 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C3×C5 ◁ G | |
1040 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,6,7,8)(13,14,16,15)(18,19)(21,22,23,24);(10,12)(14,15)(17,18,20,19);(9,10)(11,12)(13,15,16,14)(17,19,20,18)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 174);