Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C3×C4×2−1+4 ⋊ C2 |
| Sylow | C3 ⋊ #62653 |
10930 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=h,c^2=g,d^2=g,b^a=bg,f^a=fg,e^b=eg,d^c=dg,i^f=i^2198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076188);