Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D3×SU(3,𝔽2) |
| Fitting, Sylow | C3×H(3,𝔽3) ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D3×PSU(3,𝔽2) |
| commutator, cosocle | C3×#272 | C23 |
| Fitting, hypocenter | C3×H(3,𝔽3) | C2×Q8 |
| socle | C32 | C2×PSU(3,𝔽2) |
| prime radical | D3×#272 | C22 |
| LCS | G ▷ C3×#272 ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2911);