Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C3×Q8×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ SD16 |
254 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^2,3,2^2,3^3|b^2=e,d^2=e,g^3=h,b^a=bd,d^a=de,f^a=f^2,g^a=g^2h^2,h^a=h^2,d^b=de,g^c=gh^296 conjugacy classes — view the full character table.
| maximal subgroup of | #72252958, #72252963, SD16×C3⋊AGL(1,ℤ/9), … |
| maximal normal subgroup of | SD16×C3⋊AGL(1,ℤ/9), #72254704, #72254757, … |
| maximal quotient of | #72254659, #72254699, #72268713, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1703);