Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C9 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C3×C9×Dic3 |
| derived | C3 ⋊ C22×C3×C4×C9 |
| Sylow | C32×C9 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3×C9 | D3 |
| commutator, hypocenter | C3 | C22×C3×C4×C9 |
| Frattini | C2×C3 | C22×C32×D3 |
| Fitting | C23×C32×C9 | C2 |
| socle, prime radical | C23×C33 | C2×C3 |
| cosocle | C2×C32 | C23×C32 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C23×C3×C9 | |
780 conjugacy classes of subgroups; only the 430 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 430 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2588);