Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×M128 ⋊ C2 |
| Sylow | C3 ⋊ #7541 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=d,c^2=efh,d^2=h,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^2,c^b=ceh,d^b=dh,e^b=ef,f^b=fg,g^b=gh,i^b=i^2126 conjugacy classes — view the full character table.
| maximal subgroup of | #72255000, #72255023, D3×#7541 |
| maximal normal subgroup of | #72255000, #72255023, D3×#7541 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 57459);