Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C34 |
No aliases for this group.
| Sylow | C34 ⋊ M16 |
920 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^4,3^4|a^2=c,b^2=d,c^2=d,b^a=bd,e^a=ef,f^a=ef^2,g^a=gh,h^a=gh^2,e^c=e^2,f^c=f^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, 3316);