Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22×#6864 ⋊ C2 |
| Sylow | #6864 ⋊ D4 |
141 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 141 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3,2,3^4|c^3=e,f^3=g,g^3=h,b^a=bd,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,f^c=fh225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 433);