Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C3×D4×D8 ⋊ C2 |
| Sylow | C3 ⋊ #61480 |
2010 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|e^2=fh,g^2=h,b^a=bf,c^a=cg,g^a=gh,i^a=i^2,d^b=df,e^b=eh,g^c=gh,i^d=i^2,i^e=i^293 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1052139);