Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #8276 |
414 conjugacy classes of subgroups.
| transitive degree | μt(G) = 768 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,c^2=de,d^2=g,e^2=g,f^2=h,b^a=bd,c^a=cg,i^a=i^2,c^b=ch,d^b=dg,e^b=eg,i^c=i^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #72226304 |
| maximal normal subgroup of | #72226304 |
| maximal quotient of | #72226301 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 60772);