Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C9⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C9⋊#157 |
| Fitting | C22×C32×C9 ⋊ C4 |
| derived, Sylow | C32×C9 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C9⋊#157 |
| commutator, hypocenter | C32×C9 | C22×C4 |
| Frattini | C3 | C22×C3⋊#157 |
| Fitting | C22×C32×C9 | C4 |
| socle | C22×C33 | Dic3 |
| prime radical | C22×C3×C3⋊D3 | D3 |
| cosocle | C9×C3⋊D3 | C23 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C22 | |
298 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3028);