Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #60335⋊C3 |
| Fitting, Sylow | #60335 ⋊ C3 |
446 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 128 |
Polycyclic presentation:
3,2^8|b^2=h,c^2=g,d^2=g,f^2=h,h^2=i,c^a=dei,d^a=cdegh,c^b=cg,e^b=eg,f^b=fi,d^c=dgi104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084693);