Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C3×#1904 ⋊ C2 |
| Sylow | C3 ⋊ #23883 |
1696 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|c^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,g^a=gh,c^b=cg,e^b=eh,i^b=i^2,e^c=eh,f^c=fh,i^c=i^2,e^d=eh,f^d=fh69 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#23883, #72253870, #72253888 |
| maximal normal subgroup of | D3×#23883, #72253870, #72253888 |
| maximal quotient of | #72248194 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 200989);