Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C3×#417 ⋊ C2 |
| Sylow | C3 ⋊ #20618 |
3690 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,d^2=h,e^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,e^b=eh,f^b=fh,e^c=eh,i^c=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#20618, #72248210, #72248220, … |
| maximal normal subgroup of | D3×#20618, #72248210, #72248220, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 168881);