Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Sylow | C32×H(3,𝔽3) ⋊ Q8 |
693 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 693 conjugacy classes of subgroups — too many to draw. Only its 88 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:
2^2,3,2,3^4|a^2=d,b^2=d,b^a=bd,g^a=g^2,e^b=e^2,f^b=f^2,h^b=h^2,f^c=fh117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3060);