Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #10663 |
320 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=dg,b^2=de,c^2=g,d^2=g,e^2=h,b^a=bd,c^a=ce,f^a=fgh,c^b=cf,d^b=dg,e^b=eg,i^b=i^2,d^c=dh,e^c=eh78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 74559);