Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C3×D4×SD16 ⋊ C2 |
| Sylow | C3 ⋊ #61050 |
2870 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|b^2=h,f^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,d^b=df,f^b=fh,f^d=fh,i^d=i^2,i^e=i^293 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#61050, #72253889, #72253905 |
| maximal normal subgroup of | D3×#61050, #72253889, #72253905 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1044888);