Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C3 ⋊ #12523 |
262 conjugacy classes of subgroups.
| transitive degree | μt(G) = 768 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=df,c^2=egh,d^2=f,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,g^a=gh,i^a=i^2198 conjugacy classes — view the full character table.
| maximal subgroup of | #72225820, #72225948, D3×#12523, … |
| maximal normal subgroup of | #72225820, #72225948, D3×#12523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84312);