Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#347 ⋊ C2 |
| Sylow | C3 ⋊ #33329 |
716 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,e^2=g,g^2=h,b^a=bg,f^a=fh,e^b=eh,d^c=dh,i^d=i^2126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10947846, #72222739, #72222773, … |
| maximal normal subgroup of | C3×#10947846, D3×#33329, #72228227, … |
| maximal quotient of | C3×#10947846, #72222739, #72222773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322227);