Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#2395 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3×C4×C5 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| socle | C23×C3×C5 | C24 |
| prime radical | C22×C3×C5×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C4×C5 ◁ G | |
1120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 28 points:
(1,2,3)(4,5,6,7,8)(13,14)(15,18)(16,17)(19,20)(21,22)(23,25)(24,26)(27,28);(9,10)(11,12)(14,17)(18,20)(21,23,24,27)(22,25,26,28);(10,12)(22,26)(25,28);(13,15,16,19)(14,18,17,20)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1127);