Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2081 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | #397 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3×C5 |
| prime radical | C22×C3×C5×D4 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10,13,15,14,18,12,17)(11,19,21,24,20,23,22,16);(10,15)(11,20)(12,13)(16,23)(17,18)(19,24);(9,11,12,21,14,20,13,22)(10,16,17,19,18,24,15,23)345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 813);