Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #3667⋊C9 |
| Sylow | C9⋊C9 ⋊ M16 |
122 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3,2,3,2,3^2|a^2=d,c^3=e,d^2=f,g^3=h,b^a=bf,g^a=g^2h^2,h^a=h^2,g^c=gh^2186 conjugacy classes — view the full character table.
| maximal subgroup of | #72219867, #72219908, #72219959, … |
| maximal normal subgroup of | #72219867, #72219908, #72219959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 322);