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×#88907 |
| Sylow | C24 ⋊ C3×3−1+2 |
826 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #72220143, #72220148, C3×3−1+2×C22⋊A4, … |
| maximal normal subgroup of | #72220143, #72220148, C3×3−1+2×C22⋊A4, … |
| maximal quotient of | C2×C3×#88907, C3×#11722589, A4×#88907, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3060);