Finite Group DatabasebetaFinite Group Databasebeta| order | 1140 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C19 · Schur multiplier (H2) = C2 |
| direct product | C19×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C19 | A5 |
| commutator, hypocenter | A5 | C19 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C19 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 95 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24);(20,21,22)95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1140, 13);