Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #12609 |
444 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,c^2=e,f^2=g,g^2=h,b^a=bd,d^a=dh,c^b=cg,e^b=eh,i^b=i^2,f^c=fh126 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#12609, #72270184, #72270203, … |
| maximal normal subgroup of | D3×#12609, #72270184, #72270203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84642);