Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C3×#1786 ⋊ C2 |
| Sylow | C3 ⋊ #24248 |
1940 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|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,c^b=cg,f^b=fh,g^b=gh,i^b=i^2,d^c=dh,f^c=fh,g^c=gh,i^c=i^2,i^d=i^284 conjugacy classes — view the full character table.
| maximal subgroup of | #72269938, #72269996, D3×#24248 |
| maximal normal subgroup of | #72269938, #72269996, D3×#24248 |
| maximal quotient of | #72271529 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 205056);