Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C9 |
No aliases for this group.
| Sylow | C92 ⋊ M16 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^4,3^4|a^2=c,c^2=d,e^3=h,f^3=g,b^a=bd,e^a=efg^2,f^a=ef^2g^2,g^a=g^2h,h^a=gh,e^c=e^2h^2,f^c=f^2g^2,g^c=g^2,h^c=h^290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 789);