Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | H(3,𝔽3)⋊C9 ⋊ Q8 |
201 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 31 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,e^3=f,b^a=bc,e^a=e^2f^2,f^a=f^2,g^a=g^2,h^a=h^2,d^b=d^2,g^b=g^2h,e^d=eg,g^d=gh75 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 191);