Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#2071 ⋊ C2 |
| Sylow | C3 ⋊ #23628 |
1226 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,c^2=e,g^2=h,b^a=be,c^a=cf,c^b=cg,g^b=gh,d^c=dh,g^c=gh,i^d=i^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 198329);