Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #66472 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C34 |
| direct product | C3×#66472 |
| Fitting, socle, Sylow | C35 ⋊ C4 |
| derived | C34 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #66472 |
| commutator, hypocenter | C34 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C35 | C4 |
| prime radical | C3×C3⋊(C3⋊(C3⋊D3)) | C2 |
| cosocle | C3⋊(C3⋊(C3⋊D3)) | C2×C3 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C3 | |
1032 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10620192, C3×#10620193, C3⋊#10620192, … |
| maximal normal subgroup of | C3×#10620192, C3×#10620193, C3⋊#10620192, … |
| maximal quotient of | C3×#10620126, C2×C3×#66472 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 882);