Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #6858⋊Q8 |
| Sylow | #6858 ⋊ Q8 |
180 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^2=c,d^3=h,e^3=h,b^a=bc,d^a=d^2h^2,e^a=e^2h^2,f^a=fg^2h^2,g^a=g^2,h^a=h^2,e^d=ef,f^d=fh,f^e=fg79 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 495);