Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C3×#3264 ⋊ C2 |
| Sylow | C3 ⋊ #61079 |
2826 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|f^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,d^b=df,f^b=fh,e^c=eh,f^d=fh,i^e=i^281 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#61079, #72249276, #72249279 |
| maximal normal subgroup of | D3×#61079, #72249276, #72249279 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1045450);