Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C4⋊#92392 |
| Fitting | C4×H(5,𝔽3) ⋊ C2 |
| Sylow | H(5,𝔽3) ⋊ D4 |
836 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 129 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:
2^2,3^2,2,3^3|b^2=e,b^a=be,f^a=f^2,g^a=g^2,d^c=dh,g^f=gh199 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3333);