Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #7514 |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=d,c^2=h,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bc,i^a=i^2,c^b=ch,d^b=dh192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 57381);