Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C3×#2923 ⋊ C2 |
| Sylow | C3 ⋊ #60129 |
2038 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,c^2=f,g^2=h,b^a=bf,i^a=i^2,c^b=ch,i^b=i^2,e^d=eh,i^e=i^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033395);