Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C2×C3×#585 ⋊ C2 |
| Sylow | C3 ⋊ #60387 |
4764 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|e^2=h,f^2=h,b^a=bf,c^a=cg,d^a=dh,f^a=fh,i^a=i^2,f^b=fh,g^b=gh,f^c=fh126 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#60387, #72253896, #72253911 |
| maximal normal subgroup of | D3×#60387, #72253896, #72253911 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036239);