Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#1757 ⋊ C2 |
| Sylow | C3 ⋊ #23834 |
608 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=e,d^2=ef,f^2=h,g^2=h,b^a=be,c^a=cf,g^a=gh,i^a=i^2,c^b=cg,d^b=dh,i^b=i^2,e^c=eh,f^c=fh,g^c=gh90 conjugacy classes — view the full character table.
| maximal subgroup of | #72271494 |
| maximal normal subgroup of | #72271494 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 200465);