Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of (C3⋊S4)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×(C3⋊SL(2,ℤ/4))⋊C3 |
| unambiguous semidirect product | (C3⋊SL(2,ℤ/4))⋊C32 |
| unambiguous semidirect product | (C3×C3⋊SL(2,ℤ/4))⋊C3 |
| derived | C3×A4 ⋊ C32×C4 |
308 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 308 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) = 36 |
114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2095);