Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×#364 ⋊ C2 |
| Sylow | C3 ⋊ #12823 |
430 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=d,d^2=h,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,i^a=i^2,e^c=egh,f^c=fh,g^c=gh,i^c=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#12823, #72226156, #72226194, … |
| maximal normal subgroup of | D3×#12823, #72226156, #72226194, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 85670);