Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #4177 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C3 |
| direct product | C23×#4177 |
| Fitting | C23×#731 ⋊ C2 |
| derived | C3×C9 ⋊ C24×C3 |
| Sylow | #731 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #4177 |
| commutator, cosocle, hypocenter | C3×C9 | C24×C3 |
| Frattini | C32 | C23×C3×D3 |
| Fitting | C23×#731 | C2 |
| socle | C23×C3 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C23 | |
702 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1911);