Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | #6859 ⋊ Q8 |
162 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 22 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|a^2=c,b^2=c,d^3=h,b^a=bc,e^a=e^2,f^a=f^2h,g^a=g^2,d^b=d^2h^2,f^b=f^2g,h^b=h^2,e^d=ef,f^d=fg,f^e=fh49 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 137);