Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#2134 ⋊ C2 |
| Sylow | C3 ⋊ #33570 |
1212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,g^a=gh,i^a=i^2,d^b=dh,e^b=eh,f^b=fgh,e^c=eg,f^c=fh,i^c=i^2,f^e=fh57 conjugacy classes — view the full character table.
| maximal subgroup of | #72245876, #72245915, D3×#33570, … |
| maximal normal subgroup of | #72245876, #72245915, D3×#33570, … |
| maximal quotient of | #72248107, #72253909, #72254198 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323770);