Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C32 |
No aliases for this group.
| derived | C3×H(3,𝔽3) ⋊ C3×C8 |
| Sylow | C32⋊H(3,𝔽3) ⋊ C8 |
446 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2,3,2^2,3^4|a^2=c,c^2=d,e^a=e^2,f^a=f^2,g^a=g^2,f^b=fg,f^e=fh156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 727);