Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C23×C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ #60444 |
2918 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|b^2=f,e^2=h,f^2=h,b^a=bf,c^a=cg,f^a=fh,i^a=i^2,d^b=dh144 conjugacy classes — view the full character table.
| maximal subgroup of | #72253916, #72253933, #72253948, … |
| maximal normal subgroup of | #72253916, #72253933, #72253948, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036737);