Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#327 ⋊ C2 |
| Sylow | C3 ⋊ #9920 |
856 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|b^2=gh,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fh,c^b=cf,d^b=dg,i^b=i^2,d^c=dh,i^c=i^278 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 69805);