Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#2005 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3×C5 |
| prime radical | C2×C3×C5×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
724 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,12)(13,14)(15,23)(16,20)(17,26)(18,22)(19,24)(21,27)(25,28);(13,15,18,16)(14,19,22,28)(17,25,27,24)(20,26,23,21);(10,12)(13,16,18,15)(14,20,22,23)(17,24,27,25)(19,21,28,26)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 737);