Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C23×C3×#41 ⋊ C2 |
| Sylow | C3 ⋊ #60359 |
5098 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|e^2=h,f^2=h,b^a=bf,c^a=cg,d^a=dh,f^a=fh,i^a=i^2,f^b=fh144 conjugacy classes — view the full character table.
| maximal subgroup of | #72253813, #72253829, #72253857, … |
| maximal normal subgroup of | #72253813, #72253829, #72253857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1035962);