Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C26 |
| direct product | C3×C5×#3010 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C2×C3×C5×#41 ◁ G | |
1464 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 28 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,12)(14,18)(16,23)(19,25)(20,24)(22,27)(26,28);(13,14,17,20)(15,19,21,26)(16,24,23,18)(22,28,27,25);(10,12)(13,15)(14,19)(16,22)(17,21)(18,25)(20,26)(23,27)(24,28);(15,21)(19,26)(22,27)(25,28)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1742);