Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#2879 ⋊ C2 |
| Sylow | C3 ⋊ #23531 |
1454 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|c^2=e,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,g^a=gh,c^b=cg,e^b=eh,f^b=fh,i^b=i^2,d^c=dh,g^c=gh,i^c=i^290 conjugacy classes — view the full character table.
| maximal subgroup of | #72254835, #72254888, #72254923, … |
| maximal normal subgroup of | #72254835, #72254888, #72254923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 197459);