Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D3×D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | Dic3×Dic27 |
| derived, Sylow | C3×C27 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D27 |
| commutator, hypocenter | C3×C27 | C42 |
| Frattini | C22×C9 | D32 |
| Fitting, cosocle | C22×C3×C27 | C22 |
| socle, prime radical | C22×C32 | C2×D9 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C22 | |
144 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 191);