Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C3×#2311 ⋊ C2 |
| Sylow | C3 ⋊ #20610 |
3754 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,d^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,f^b=fh,g^b=gh,i^b=i^2,e^c=eh102 conjugacy classes — view the full character table.
| maximal subgroup of | #72253913, #72253915, #72253927, … |
| maximal normal subgroup of | #72253913, #72253915, #72253927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 168839);