Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C3×#453 ⋊ C2 |
| Sylow | C3 ⋊ #61110 |
2684 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|a^2=h,f^2=h,g^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,g^a=gh,i^a=i^2,d^b=df,e^b=eh,f^b=fh,g^c=gh,i^c=i^2,f^d=fh,i^d=i^284 conjugacy classes — view the full character table.
| maximal subgroup of | #72214505, C3×#11671496, #72214975, … |
| maximal normal subgroup of | C3×#11671496, D3×#61110 |
| maximal quotient of | #72214505, C3×#11671496, #72214975, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1045877);