Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×#1088 |
| Fitting | C22×C3×H(3,𝔽3) ⋊ C4 |
| derived | H(3,𝔽3) ⋊ C22×C3×C4 |
| Sylow | C3×H(3,𝔽3) ⋊ C22×C4 |
438 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3026);