Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#3078 ⋊ C2 |
| Sylow | C3 ⋊ #24183 |
1002 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|b^2=h,c^2=h,d^2=e,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,g^a=gh,i^a=i^2,c^b=cg,f^b=fh,i^b=i^2,d^c=dh,f^c=fh72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 204296);