Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×#1322 ⋊ C2 |
| Sylow | C3 ⋊ #7056 |
248 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 53 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|a^2=d,c^2=g,d^2=f,f^2=h,b^a=bc,c^a=ce,e^a=eg,c^b=cg,d^b=deg,i^b=i^2,d^c=dg96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 56190);