Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D5×A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| direct product | D5×A5 |
| unambiguous semidirect product | C5⋊(C2×A5) |
| Fitting | C5 ⋊ C2×A5 |
| socle, derived | C5×A5 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C5×A5 | C2 |
| Fitting, cosocle | C5 | C2×A5 |
| LCS | G ▷ C5×A5 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25 |
20 conjugacy classes — view the full character table.
| maximal subgroup of | A5⋊AGL(1,𝔽5), AGL(1,𝔽5)×A5, D5×S5, … |
| maximal normal subgroup of | A5⋊AGL(1,𝔽5), AGL(1,𝔽5)×A5, D5×S5, … |
| maximal quotient of | Dic5×A5, D5×SL(2,𝔽5), C5⋊#6732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 146);