Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #88989 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C4⋊(C3⋊#157) |
| unambiguous semidirect product | C4⋊(C3×C3⋊#157) |
| Fitting | C34×C4 ⋊ C4 |
| Sylow | C34 ⋊ C4⋊C4 |
348 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3304);