Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of A6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C3 |
| special orthogonal | SO−(4,𝔽3) |
| direct product | C2×A6 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2 | A6 |
| commutator, hypocenter | A6 | C2 |
| Frattini | C1 | G |
| LCS | G ▷ A6 | |
| UCS | C1 ◁ C2 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12 |
14 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 766);