Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#3584 ⋊ C2 |
| Sylow | C3 ⋊ #33531 |
1122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|e^2=gh,g^2=h,b^a=be,c^a=cf,e^a=eg,g^a=gh,i^a=i^2,e^b=eg,f^b=fh,g^b=gh,d^c=dh,e^c=eh84 conjugacy classes — view the full character table.
| maximal subgroup of | #72270114, #72270139, #72270144, … |
| maximal normal subgroup of | #72270114, #72270139, #72270144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323471);