Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C9 · Schur multiplier (H2) = C2×C33 |
| direct product | C32×C4×C22⋊C9 |
| derived | C22 ⋊ C32×C4×C9 |
| Sylow | C22×C4 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33×C4 | A4 |
| commutator, hypocenter | C22 | C32×C4×C9 |
| Frattini | C2×C3 | C2×C32×A4 |
| Fitting | C22×C33×C4 | C3 |
| socle, prime radical | C23×C33 | C2×C3 |
| cosocle | C23×C3 | C2×C33 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C33×C4 | |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
432 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2530);