Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43 |
No aliases for this group.
| Fitting | C3×C4×#97 ⋊ C2 |
| Sylow | C3 ⋊ #20331 |
1470 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,c^2=g,e^2=h,c^a=ch,d^b=dh,i^d=i^2216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 166911);