Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#3068 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | C2×#121 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
932 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3)(4,5,6,7,8)(10,14)(11,17)(12,20)(16,22)(18,19)(21,24);(9,10,12,14,13,16,20,22)(11,15,18,21,19,23,17,24);(9,11)(10,15)(12,18)(13,19)(14,21)(16,23)(17,20)(22,24);(10,16)(14,22)(15,23)(21,24)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1800);