Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#3292 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ G | |
952 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)(11,22)(12,18)(13,20)(14,19)(15,21)(16,23)(17,24);(9,11,15,17)(10,16,21,12)(13,18,14,23)(19,24,20,22);(9,12)(10,17)(11,21)(13,24)(14,22)(15,16)(18,19)(20,23);(9,12)(10,18)(11,20)(13,22)(14,24)(15,16)(17,19)(21,23)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2024);