Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of D92 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D92 |
| Fitting, Sylow | C3×C92 ⋊ C22 |
| derived | C92 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D92 |
| commutator, cosocle, hypocenter | C92 | C22×C3 |
| Frattini | C32 | C3×D32 |
| Fitting | C3×C92 | C22 |
| socle | C33 | D32 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C3 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#66343⋊C2, #14517923, D3×D92, … |
| maximal normal subgroup of | C3×#66343⋊C2, #14517923, D3×D92, … |
| maximal quotient of | C3×D9×Dic9, C3×#10619528, C3×#10619529, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 418);