Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #66343 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C9 |
| direct product | C3×#66343 |
| Fitting, Sylow | C3×C92 ⋊ C4 |
| derived | C92 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #66343 |
| commutator, hypocenter | C92 | C3×C4 |
| Frattini | C32 | C3×#157 |
| Fitting | C3×C92 | C4 |
| socle | C33 | #157 |
| prime radical | C3×C9⋊D9 | C2 |
| cosocle | C9⋊D9 | C2×C3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C3 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10619732, C3⋊#10619732, D3×#66343, … |
| maximal normal subgroup of | C3×#10619732, C3⋊#10619732, D3×#66343, … |
| maximal quotient of | C3×#10619526, C2×C3×#66343 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 404);