Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×C32⋊C9 ⋊ C22 |
| Sylow | C32⋊C9 ⋊ C2×D4 |
345 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^4,3^4|c^2=d,e^3=g,e^a=e^2g^2,g^a=g^2,h^a=h^2,c^b=cd,f^b=f^2,h^b=h^2,f^e=fh63 conjugacy classes — view the full character table.
| maximal subgroup of | D4×((C3⋊D3)⋊C9)⋊C2, #72259319 |
| maximal normal subgroup of | D4×((C3⋊D3)⋊C9)⋊C2, #72259319 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 811);