Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | C4⋊(#4179⋊C3) |
| unambiguous semidirect product | (C4⋊#4179)⋊C3 |
| Fitting | C4×#6911 ⋊ C2 |
| Sylow | #6911 ⋊ D4 |
302 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 63 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:
2^2,3^2,2,3^3|b^2=e,f^3=h,b^a=be,f^a=f^2h^2,g^a=g^2,h^a=h^2,f^c=fh^2,f^d=fg,g^d=gh^297 conjugacy classes — view the full character table.
| maximal subgroup of | #72229211, #72259376, D4×#4179⋊C3, … |
| maximal normal subgroup of | #72229211, #72259376, D4×#4179⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1790);