Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×#2273 ⋊ C2 |
| Sylow | C3 ⋊ #10938 |
1234 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,c^2=ef,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^2,d^b=dh,e^b=eh,f^b=fh,d^c=dh126 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10938, #72258672, #72258756 |
| maximal normal subgroup of | D3×#10938, #72258672, #72258756 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 75898);