Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D3×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | C32×Dic3×A4 |
| unambiguous semidirect product | C3⋊(C32×C4×A4) |
| unambiguous semidirect product | (C22×Dic3)⋊C33 |
| unambiguous semidirect product | (C22×C3×Dic3)⋊C32 |
| derived | C22×C3 ⋊ C33×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D3×A4 |
| commutator, hypocenter | C22×C3 | C33×C4 |
| Frattini | C2 | C32×D3×A4 |
| Fitting, socle | C23×C33 | C2×C3 |
| prime radical | C2×C33×A4 | C2 |
| cosocle | C23×C3 | C2×C33 |
| LCS | G ▷ C22×C3 | |
| UCS | C1 ◁ C2×C32 | |
764 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3287);