Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #88414⋊C3 |
| Sylow | C3×3−1+2 ⋊ M16 |
178 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 47 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:
2^2,3,2^2,3^3|a^2=d,b^2=d,d^2=e,g^3=h,b^a=be,g^a=g^2h^2,h^a=h^2,f^b=f^2,g^c=gh^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #72219868, #72219893, #72219914, … |
| maximal normal subgroup of | #72219893, #72219914, #72219917 |
| maximal quotient of | #72219868 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1303);