Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C4 · Schur multiplier (H2) = C2×C34 |
| direct product | C3×C4×C22⋊H(3,𝔽3) |
| unambiguous semidirect product | (C22×C3×C4)⋊H(3,𝔽3) |
| Fitting | C22×C33×C4 ⋊ C3 |
| Sylow | C22×C4 ⋊ C3×H(3,𝔽3) |
532 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2532);