Finite Group DatabasebetaFinite Group Databasebeta| order | 7260 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C121 · Schur multiplier (H2) = C2 |
| direct product | A5×C121 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C121 | A5 |
| commutator, hypocenter | A5 | C121 |
| Frattini | C11 | C11×A5 |
| socle | C11×A5 | C11 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C121 | |
27 conjugacy classes of subgroups.
605 conjugacy classes — view the full character table.
| derived subgroup of | A5×C121⋊C5 |
| maximal subgroup of | C3×A5×C121, C5×A5×C121, A5×C121⋊C5 |
| maximal normal subgroup of | C3×A5×C121, C5×A5×C121, A5×C121⋊C5 |
| maximal quotient of | C3×A5×C121, C5×A5×C121 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7260, 232);