Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Sylow | C34 ⋊ M16 |
436 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^4,3^4|a^2=c,c^2=d,b^a=bd,e^a=ef,f^a=ef^2,g^a=g^2,h^a=h^2,e^c=e^2,f^c=f^2114 conjugacy classes — view the full character table.
| maximal subgroup of | #72220216, #72220277 |
| maximal normal subgroup of | #72220216, #72220277 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3313);