Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#92302 |
| Fitting | C4×#6891 ⋊ C2 |
| Sylow | #6891 ⋊ D4 |
553 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 553 conjugacy classes of subgroups — too many to draw. Only its 69 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:
2^2,3,2,3^4|b^2=d,f^3=h,b^a=bd,e^a=e^2,f^a=f^2h^2,h^a=h^2,f^c=fh^2,f^e=fg129 conjugacy classes — view the full character table.
| maximal subgroup of | #72228541, D4×#92302, #72259315, … |
| maximal normal subgroup of | D4×#92302, #72259315, #72259319 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1922);