Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C33 |
| unambiguous semidirect product | (C3⋊S4)⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×(C3⋊S4)⋊C3)⋊C3 |
| Fitting | C22×C3×H(3,𝔽3) ⋊ D3 |
389 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 389 conjugacy classes of subgroups — too many to draw. Only its 34 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:
2,3^5,2^2|e^a=e^2,f^a=f^2,g^a=gh,c^b=cd,e^c=ef^2,g^e=h,h^e=gh75 conjugacy classes — view the full character table.
| maximal subgroup of | #72220526, #72222924, #72222951, … |
| maximal normal subgroup of | #72222924, #72222951, #72222965 |
| maximal quotient of | #72220526, #72276200 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2373);