Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C2×C35 |
| direct product | C3×#66440 |
| Fitting | C22×C3×3−1+2 ⋊ C3 |
| Sylow | C22 ⋊ C3×#737 |
518 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#66440⋊C2, C3⋊(#66440⋊C2), D3×#66440, … |
| maximal normal subgroup of | C3×#66440⋊C2, C3⋊(#66440⋊C2), D3×#66440, … |
| maximal quotient of | C3×#10619916, C2×C3×#66440 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 828);