Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92303 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C32 |
No aliases for this group.
| derived | C32×C9 ⋊ C3×C8 |
| Sylow | C9⋊H(3,𝔽3) ⋊ C8 |
237 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 71 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:
2,3,2^2,3^4|a^2=c,c^2=d,e^3=h,e^a=e^2h^2,f^a=f^2,g^a=g^2,h^a=h^2,e^b=eh^2,f^b=fg120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 730);