Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×H(3,ℤ/4) ⋊ C2 |
| Sylow | C3 ⋊ #10785 |
1394 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^2,d^b=dh,f^b=fh,i^b=i^2,e^c=eh,f^c=fh,i^c=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #72248555, #72248570, #72248584, … |
| maximal normal subgroup of | #72248555, #72248570, #72248584, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 75116);