Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C9⋊(C22⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C24×C32 |
| direct product | C3×C9⋊(C22⋊A4) |
| Fitting | C24×C3×C9 ⋊ C3 |
| Sylow | C24 ⋊ C3×3−1+2 |
466 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×3−1+2×C22⋊A4, #72259463 |
| maximal normal subgroup of | C3×3−1+2×C22⋊A4, #72259463 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3053);