Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (C3⋊(C3⋊#157))⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | (C3⋊(C3⋊#622))⋊C3 |
| derived | C34 ⋊ C3×C8 |
| Sylow | C32×H(3,𝔽3) ⋊ C8 |
326 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 27 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=ef,f^a=ef^2,g^a=g^2,h^a=h^2,g^b=gh,e^c=e^2,f^c=f^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2986);