Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #12667 |
296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,c^2=de,e^2=g,g^2=h,b^a=bd,f^a=fh,c^b=cg,d^b=dh,i^b=i^2,f^c=fh144 conjugacy classes — view the full character table.
| maximal subgroup of | #72225834, #72226295, #72226299, … |
| maximal normal subgroup of | #72225834, #72226295, #72226299, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84942);