Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C4⋊#92211 |
| Fitting | C4×H(3,𝔽3)⋊C9 ⋊ C2 |
| Sylow | H(3,𝔽3)⋊C9 ⋊ D4 |
337 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 337 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2^3,3^5|b^2=c,e^3=g,b^a=bc,d^a=d^2,e^a=e^2g^2,g^a=g^2,h^a=h^2,e^d=ef,f^d=fh,f^e=fh^2111 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 530);