Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C81 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C22⋊C81 |
| unambiguous semidirect product | (C22×C3)⋊C81 |
| derived, Sylow | C22 ⋊ C3×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C27 | A4 |
| commutator, hypocenter | C22 | C3×C81 |
| Frattini | C27 | C3×A4 |
| Fitting | C22×C3×C27 | C3 |
| socle, prime radical | C22×C32 | C27 |
| cosocle | C22×C27 | C32 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C27 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 486 |
324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 146);