Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C3×#390 ⋊ C2 |
| Sylow | C3 ⋊ #13970 |
3058 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=h,b^2=eh,d^2=e,b^a=be,c^a=cf,d^a=de,i^a=i^2,c^b=cg,i^b=i^2,i^c=i^2132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#13970, #72271048, #72271069, … |
| maximal normal subgroup of | D3×#13970, #72271048, #72271069, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 92376);