Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #7464 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=d,b^2=ceg,c^2=egh,d^2=f,e^2=gh,f^2=h,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,d^b=dh,i^b=i^296 conjugacy classes — view the full character table.
| maximal subgroup of | #72245453, #72245476, D3×#7464 |
| maximal normal subgroup of | #72245453, #72245476, D3×#7464 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 57252);