Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#2580 ⋊ C2 |
| Sylow | C3 ⋊ #24338 |
1296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=e,d^2=e,f^2=h,g^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,g^b=gh,i^b=i^2,d^c=dh,f^c=fh,g^c=gh84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#24338, #72269965, #72270054 |
| maximal normal subgroup of | D3×#24338, #72269965, #72270054 |
| maximal quotient of | #72271578 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 206089);