Finite Group DatabasebetaFinite Group Databasebeta| order | 5700 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C19 · Schur multiplier (H2) = C2 |
| direct product | C5×C19×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C5×C19 | A5 |
| commutator, hypocenter | A5 | C5×C19 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C5×C19 | |
40 conjugacy classes of subgroups.
475 conjugacy classes — view the full character table.
| socle of | C5×C19⋊C3×A5 |
| maximal subgroup of | C3×C5×C19×A5, C5×C19⋊C3×A5 |
| maximal normal subgroup of | C3×C5×C19×A5, C5×C19⋊C3×A5 |
| maximal quotient of | C3×C5×C19×A5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5700, 165);