Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C26 |
| direct product | C3×C5×#3018 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | #120 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| socle | C2×C3×C5 | C2×#120 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C22×C3×C4×C5 ◁ G | |
1448 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,18)(12,16)(13,21)(14,17)(15,19)(20,23)(22,24);(9,11)(10,15)(12,19)(13,22)(14,20)(16,23)(17,24)(18,21);(9,10)(11,15)(12,16)(13,21)(14,17)(18,22)(19,23)(20,24);(9,12,14,13)(10,16,17,21)(11,19,20,22)(15,23,24,18)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1750);