Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2×C5 | A5 |
| commutator, hypocenter | A5 | C2×C5 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C2×C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 50 |
50 conjugacy classes — view the full character table.
| socle of | C5×A5⋊C4, A5⋊Dic5, Dic5×A5, … |
| maximal subgroup of | C5×A5⋊C4, A5⋊Dic5, Dic5×A5, … |
| maximal normal subgroup of | C5×A5⋊C4, A5⋊Dic5, Dic5×A5, … |
| maximal quotient of | C4×C5×A5, C5×#6732, C2×C5×SL(2,𝔽5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 147);