Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D5×A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
| direct product | Dic5×A5 |
| derived | C5×A5 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×A5 |
| commutator, hypocenter | C5×A5 | C4 |
| Fitting, cosocle | C2×C5 | C2×A5 |
| socle, prime radical | C2×C5×A5 | C2 |
| LCS | G ▷ C5×A5 | |
| UCS | C1 ◁ C2 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
40 conjugacy classes — view the full character table.
| maximal subgroup of | A5×SL(2,𝔽5), A5×SL(2,𝔽9), Dic5×A6 |
| maximal quotient of | Dic5×SL(2,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 479);