Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C1 |
| direct product | C3×C27⋊C16 |
| derived | C27 ⋊ C3×C16 |
| Sylow | C3×C27 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C8 | D27 |
| commutator, hypocenter | C27 | C3×C16 |
| Frattini | C8×C9 | C3×D3 |
| Fitting | C3×C8×C27 | C2 |
| socle, prime radical | C2×C32 | C9⋊C8 |
| cosocle | C8×C27 | C2×C3 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C3×C8 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 432 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 32);