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 | C2×C3×C5×#453 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #120 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
1688 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);(4,7)(5,9)(8,10);(3,4)(5,10)(6,8)(7,9);(5,9)(7,10)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1746);