Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C3×#390 ⋊ C2 |
| Sylow | C3 ⋊ #34310 |
3764 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=h,c^2=g,d^2=f,e^2=h,b^a=bf,c^a=cg,e^a=ef,i^a=i^2,d^b=df,i^d=i^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #72270674, #72270695, D3×#34310 |
| maximal normal subgroup of | #72270674, #72270695, D3×#34310 |
| maximal quotient of | #72270978 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 331625);