Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #6249⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#6249⋊C2 |
| unambiguous semidirect product | #6249⋊(C2×C3) |
| Fitting, Sylow | C3×H(3,𝔽3) ⋊ SD16 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
42 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2900);