Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#3025 ⋊ C2 |
| Sylow | C3 ⋊ #33556 |
1134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|b^2=h,c^2=h,d^2=h,b^a=be,c^a=cf,g^a=gh,d^b=dh,f^b=fgh,i^b=i^2,e^c=eg,f^e=fh66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#33556, #72253837, #72253895 |
| maximal normal subgroup of | D3×#33556, #72253837, #72253895 |
| maximal quotient of | #72253973 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323674);