Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #66472 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C34×C4 |
| direct product | C4×#66472 |
| Fitting | C34×C4 ⋊ C4 |
| derived, Sylow | C34 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #66472 |
| commutator, hypocenter | C34 | C42 |
| Frattini | C2 | C2×#66472 |
| Fitting | C34×C4 | C4 |
| socle | C2×C34 | C2×C4 |
| prime radical, cosocle | C2×C3⋊(C3⋊(C3⋊D3)) | C22 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C4 | |
980 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10620198, C4×#10620206, AGL(1,𝔽5)×#66472 |
| maximal normal subgroup of | C4×#10620198, C4×#10620206 |
| maximal quotient of | AGL(1,𝔽5)×#66472 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3317);