Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C32 |
No aliases for this group.
| Fitting | C3×Q8×H(3,𝔽3) ⋊ C2 |
| Sylow | C3×H(3,𝔽3) ⋊ #41 |
610 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 118 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:
2^3,3,2,3^3|b^2=e,c^2=e,c^a=ce,f^a=f^2,g^a=g^2,h^a=h^2,c^b=ce,g^d=gh105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2646);