Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C23×#4208 |
| Fitting | C23×#737 ⋊ C2 |
| Sylow | #737 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C9 | C3⋊D3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C24×C3 |
| Frattini | C3 | C23×C3×C3⋊D3 |
| Fitting | C23×#737 | C2 |
| socle | C23×C3 | C3×C3⋊D3 |
| prime radical | C23×#272 | C3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C23×C9 | |
1267 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3074);