Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #7182 |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=d,b^2=e,c^2=f,d^2=g,e^2=fg,f^2=h,g^2=h,b^a=bc,c^a=cf,e^a=efh,f^a=fh,i^a=i^2,c^b=ch,d^b=dh,i^b=i^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #72226060, #72226145, D3×#7182, … |
| maximal normal subgroup of | #72226060, #72226145, D3×#7182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 56517);