Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #7097 |
142 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 768 |
Polycyclic presentation:
2^8,3|a^2=d,b^2=g,c^2=fh,d^2=efh,e^2=g,f^2=h,b^a=bc,c^a=ce,e^a=eg,f^a=fg,i^a=i^2,c^b=cf,d^b=defg,e^b=eg,f^b=fh,i^b=i^299 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 56302);