Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C2×C35 |
| direct product | C3×#66436 |
| Fitting | C22×C32×C9 ⋊ C3 |
| Sylow | C22 ⋊ C3×#737 |
530 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10620044, C3×#10620045, C3⋊#10620044, … |
| maximal normal subgroup of | C3×#10620044, C3×#10620045, C3⋊#10620044, … |
| maximal quotient of | C3×#10619912, C2×C3×#66436 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 822);