Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C169 · Schur multiplier (H2) = C2 |
| direct product | A5×C169 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C169 | A5 |
| commutator, hypocenter | A5 | C169 |
| Frattini, cosocle | C13 | C13×A5 |
| socle, prime radical | C13×A5 | C13 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C169 | |
27 conjugacy classes of subgroups.
845 conjugacy classes — view the full character table.
| derived subgroup of | A5×C169⋊C3 |
| maximal subgroup of | C3×A5×C169, A5×C169⋊C3 |
| maximal normal subgroup of | C3×A5×C169, A5×C169⋊C3 |
| maximal quotient of | C3×A5×C169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 273);