Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C3×#1883 ⋊ C2 |
| Sylow | C3 ⋊ #20945 |
1862 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=egh,d^2=h,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,f^a=fh,e^b=eh,g^b=gh,f^c=fh,i^d=i^290 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#20945, #72254868, #72254904 |
| maximal normal subgroup of | D3×#20945, #72254868, #72254904 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 171096);