Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C26 |
| direct product | C3×C5×#3021 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | C2×#120 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
1472 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)(10,15)(12,13)(16,23)(17,20)(18,21)(22,24);(9,10)(11,16)(12,15)(13,20)(14,17)(18,22)(19,24)(21,23);(9,11)(10,16)(12,18)(13,21)(14,19)(15,22)(17,24)(20,23);(9,12,14,13)(10,15,17,20)(11,18,19,21)(16,22,24,23)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1753);