Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C27 |
| direct product | C2×C3×C5×B(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #120 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C24×C3×C5 ◁ G | |
2036 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 18 points:
(1,2)(11,12,13)(14,15,16,17,18);(7,10);(3,4)(5,7)(6,8)(9,10);(3,5)(4,7)(6,9)(8,10)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1755);