Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | C4⋊(C9⋊#272) |
| Fitting | C4×C9×H(3,𝔽3) ⋊ C2 |
| Sylow | C9×H(3,𝔽3) ⋊ D4 |
678 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3^5|b^2=c,d^3=h,b^a=bc,d^a=d^2h^2,e^a=e^2,f^a=f^2,h^a=h^2,f^e=fg207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2121);