Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C3×#3184 ⋊ C2 |
| Sylow | C3 ⋊ #61451 |
2178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|e^2=f,g^2=h,b^a=bf,c^a=cg,e^a=eh,g^a=gh,d^b=df,i^b=i^2,g^c=gh,i^c=i^2,i^d=i^287 conjugacy classes — view the full character table.
| maximal subgroup of | #72225877, #72248841, #72249276, … |
| maximal normal subgroup of | D3×#61451, #72225877, #72248841, … |
| maximal quotient of | #72269976 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1051489);