Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#1272 ⋊ C2 |
| Sylow | C3 ⋊ #7595 |
630 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 117 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=e,b^2=g,d^2=g,e^2=h,b^a=bd,c^a=cg,d^a=df,d^b=dg,e^b=efg,i^c=i^290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 57655);