Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | C4⋊#92300 |
| Fitting | C4×C32⋊H(3,𝔽3) ⋊ C2 |
| Sylow | C32⋊H(3,𝔽3) ⋊ D4 |
706 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 706 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,b^a=bd,e^a=e^2,f^a=f^2,g^a=g^2,f^c=fg,f^e=fh129 conjugacy classes — view the full character table.
| maximal subgroup of | #72228541, D4×#92300, #72259923, … |
| maximal normal subgroup of | D4×#92300, #72259923, #72259937 |
| maximal quotient of | #72229206 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1917);