Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D3×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C27 · Schur multiplier (H2) = C2 |
| direct product | Dic3×C22⋊C27 |
| unambiguous semidirect product | C3⋊(C4×C22⋊C27) |
| unambiguous semidirect product | (C22×Dic3)⋊C27 |
| derived | C22×C3 ⋊ C4×C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C9 | D3×A4 |
| commutator, hypocenter | C22×C3 | C4×C27 |
| Fitting, cosocle | C23×C3×C9 | C2×C3 |
| socle, prime radical | C23×C32 | C2×C9 |
| LCS | G ▷ C22×C3 | |
| UCS | C1 ◁ C2×C9 | |
110 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 38 |
| 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, 769);