Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | (C2×D3)⋊#338 |
| Fitting | C2×C3×#338 ⋊ C2 |
| Sylow | C3 ⋊ C22⋊#338 |
1294 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,d^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,g^a=gh,f^b=fh,i^c=i^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #72248313, #72248339, #72248342, … |
| maximal normal subgroup of | #72248313, #72248339, #72248342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 74805);