Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×#733⋊C2)⋊C4 |
| Fitting | C2×C4×#733 ⋊ C2 |
| Sylow | #733 ⋊ C22⋊C4 |
221 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 221 conjugacy classes of subgroups — too many to draw. Only its 53 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:
2^4,3^4|b^2=c,e^3=h,f^3=h,b^a=bd,e^a=e^2h^2,f^a=f^2h^2,g^a=gh^2,h^a=h^2,f^e=fg,g^f=gh86 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 522);