Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C8 |
No aliases for this group.
| Fitting | C3×#1957 ⋊ C2 |
| Sylow | C3 ⋊ #9837 |
710 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=dfg,c^2=e,d^2=g,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,c^b=ch,i^c=i^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#9837, #72226002, #72226005 |
| maximal normal subgroup of | D3×#9837, #72226002, #72226005 |
| maximal quotient of | #72258820, #72258861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 69404);