Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #11404 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=d,b^2=e,d^2=f,e^2=g,f^2=h,b^a=bf,c^a=ch,e^a=eh,i^a=i^2,d^b=dh,i^b=i^2168 conjugacy classes — view the full character table.
| maximal subgroup of | #72225844, D3×#11404, #72225847, … |
| maximal normal subgroup of | #72225844, D3×#11404, #72225847, … |
| maximal quotient of | #72226207 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 78570);