Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×Q8×M16 ⋊ C2 |
| Sylow | C3 ⋊ #22515 |
1014 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=eh,d^2=e,g^2=h,b^a=be,c^a=cf,f^a=fh,d^b=de,g^c=gh,i^c=i^2105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 186132);