Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | #733 ⋊ C22⋊C4 |
221 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^4,3^4|a^2=d,e^3=h,f^3=h,b^a=bc,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, 557);