Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | #731 ⋊ #41 |
216 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^4,3^4|b^2=d,f^3=h,c^a=cd,e^a=e^2,g^a=g^2h,f^b=f^2h^2,g^b=g^2,h^b=h^2,f^e=fg,g^e=gh47 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 919);