Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33×C4 |
| direct product | C32×C42⋊C9 |
| derived, Sylow | C42 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | C42⋊C3 |
| commutator, hypocenter | C42 | C32×C9 |
| Frattini | C22×C3 | C32×A4 |
| Fitting | C33×C42 | C3 |
| socle, prime radical | C22×C33 | A4 |
| cosocle | C3×C42 | C33 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C33 | |
262 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1504);