Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #32928⋊C3 |
| Fitting, Sylow | #32928 ⋊ C3 |
358 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 32 |
Polycyclic presentation:
3,2^8|c^2=fi,b^a=bghi,d^a=defi,e^a=di,g^a=ghi,h^a=gi,c^b=cf,d^b=dg,e^b=eh,h^d=hi,g^e=gi43 conjugacy classes — view the full character table.
| maximal subgroup of | #72344081, #72344082, #72344087, … |
| maximal normal subgroup of | #72344081, #72344082, #72344087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083990);