Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C3⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C3×C4 |
| direct product | C3×C4×C3⋊#157 |
| Fitting | C34×C4 ⋊ C4 |
| derived | C33 ⋊ C3×C42 |
| Sylow | C34 ⋊ C42 |
364 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3303);