Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of C3⋊D3×C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C34 |
| direct product | C3⋊D3×C3⋊(C3⋊D3) |
| Fitting, socle, derived, Sylow | C35 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C35 | C22 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
3336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 891);