Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | Q8×C32⋊C9 ⋊ C3 |
| Sylow | Q8 ⋊ C9⋊H(3,𝔽3) |
272 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 67 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:
3^5,2^3|a^3=e,c^3=e,f^2=h,g^2=h,c^a=ce,f^a=fg,g^a=f,c^b=cd,g^f=gh135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1569);