Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C3⋊(#41⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×C3⋊(#41⋊C9) |
| unambiguous semidirect product | C3⋊(C3×#41⋊C9) |
| unambiguous semidirect product | (C3×#239)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D3×A4 |
| commutator, hypocenter | C3×Q8 | C2×C3×C9 |
| Frattini | C2×C3 | C3×D3×A4 |
| Fitting | C33×Q8 | C2×C3 |
| socle | C2×C33 | C2×A4 |
| prime radical | C32×#239 | C3 |
| cosocle | C32×Q8 | C2×C32 |
| LCS | G ▷ C3×Q8 | |
| UCS | C1 ◁ C2×C32 | |
213 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2162);