Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #4185 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C3×C4 |
| direct product | C4×#66332 |
| derived, Sylow | #732 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #4185 |
| commutator, hypocenter | #732 | C42 |
| Frattini | C22×C32 | C2×C3⋊D3 |
| Fitting | C2×C4×#732 | C2 |
| socle | C22×C3 | C2×#272 |
| prime radical, cosocle | C22×#732 | C22 |
| LCS | G ▷ #732 | |
| UCS | C1 ◁ C2×C4 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 513);