Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C22×#66363 |
| Fitting | C24×H(3,𝔽3) ⋊ C3 |
| Sylow | C24 ⋊ AΣL(1,𝔽27) |
409 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 409 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1876);