Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | C32⋊(C22⋊C9) ⋊ C4 |
238 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^2,3^4,2^2|a^2=b,c^3=f,c^a=c^2f^2,d^a=d^2,f^a=f^2,g^a=gh,d^c=de,g^c=h,h^c=gh78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 743);