Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
No aliases for this group.
| Fitting | C22×C3×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ #60644 |
3350 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|b^2=f,c^2=g,f^2=h,b^a=bf,c^a=cg,f^a=fh,e^b=eh,d^c=dh,i^c=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #72248864, #72248896, #72248906, … |
| maximal normal subgroup of | #72248864, #72248896, #72248906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1039082);