Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C3×#342 ⋊ C2 |
| Sylow | C3 ⋊ #20354 |
2410 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,b^a=be,e^a=eh,f^b=fh,d^c=dh,i^d=i^2126 conjugacy classes — view the full character table.
| maximal subgroup of | #72270111, #72270162, #72270181, … |
| maximal normal subgroup of | #72270111, #72270162, #72270181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 167001);