Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1304 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#1305 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #95 |
| commutator | C23 | C3×C42×C5 |
| Frattini, cosocle | C23×C4 | C22×C3×C5 |
| prime radical | C24×C3×C5 | C2×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C23×C3×C4×C5 ◁ G | |
400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10,11,14,12,13,15,16)(17,18)(19,23)(20,22)(21,24);(10,13)(11,15)(17,19)(18,21,22,23)(20,24)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 37);