Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3×H(3,𝔽3) ⋊ C2×Q8 |
382 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^4,3^4|a^2=d,b^2=d,c^2=d,b^a=bd,c^a=cd,g^a=g^2,h^a=h^2,c^b=cd,e^b=e^2,h^b=h^2,f^c=f^2,g^e=gh51 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2041);