Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#3508 ⋊ C2 |
| Sylow | C3 ⋊ #23998 |
1266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|b^2=e,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,g^a=gh,c^b=cg,g^b=gh,e^c=eh,f^c=fh,i^c=i^2,f^d=fh84 conjugacy classes — view the full character table.
| maximal subgroup of | #72257991, D3×#23998, #72271917, … |
| maximal normal subgroup of | #72257991, D3×#23998, #72271917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 202153);