Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D3×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C3⋊D3×C3⋊C8 |
| derived | C33 ⋊ C2×C3×C8 |
| Sylow | C34 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | D3×C3⋊D3 |
| commutator, hypocenter | C33 | C2×C3×C8 |
| Frattini | C4 | C3×D3×C3⋊D3 |
| Fitting | C34×C4 | C22 |
| socle | C2×C34 | C2×C4 |
| prime radical | C2×C32×C3⋊D3 | C4 |
| cosocle | C33×C4 | C22×C3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C3×C4 | |
524 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2727);