Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#1390 ⋊ C2 |
| Sylow | C3 ⋊ #13424 |
612 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=h,c^2=d,e^2=h,b^a=bd,c^a=ce,e^a=eh,f^a=fgh,i^a=i^2,c^b=cf,e^b=eg,i^b=i^2,e^c=eh,g^c=gh,i^c=i^2,f^e=fh57 conjugacy classes — view the full character table.
| maximal subgroup of | #72255114, #72255119, #72255121, … |
| maximal normal subgroup of | #72255114, #72255119, #72255121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 89018);