Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C4×C5×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C4×C5 | A5 |
| commutator, hypocenter | A5 | C4×C5 |
| Frattini, cosocle | C2 | C2×C5×A5 |
| socle, prime radical | C2×C5×A5 | C2 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C4×C5 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 482);