Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C22 |
| direct product | C22×C5×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C22×C5 | A5 |
| commutator, hypocenter | A5 | C22×C5 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C22×C5 | |
152 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, 945);