Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×C5×#1484 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C2×D4 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C42 | C23×C3×C5 |
| socle | C22×C3×C5 | C2×C22⋊C4 |
| prime radical | C3×C5×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ C2×C3×C42×C5 ◁ G | |
524 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,15)(12,14)(13,16)(17,18,21,24,22,19,20,23);(10,14)(11,12)(15,16)(17,19)(18,22)(20,24)(21,23);(9,11,13,12)(10,15,16,14)(17,20,22,21)(18,23,19,24)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 216);