Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(#4184⋊C3) |
| unambiguous semidirect product | (C4⋊#4184)⋊C3 |
| Fitting | C4×#6910 ⋊ C2 |
| Sylow | #6910 ⋊ D4 |
362 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 57 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|b^2=d,f^3=h^2,b^a=bd,e^a=e^2,f^a=f^2h,h^a=h^2,f^c=fh,f^e=fg,g^e=gh,g^f=gh^297 conjugacy classes — view the full character table.
| maximal subgroup of | #72228541, D4×#4184⋊C3, #72259694, … |
| maximal normal subgroup of | D4×#4184⋊C3, #72259694, #72259725 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2012);