Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#1309 ⋊ C2 |
| Sylow | C3 ⋊ #8130 |
520 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 151 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=e,b^2=f,c^2=gh,e^2=g,f^2=h,b^a=bd,c^a=cg,d^a=dg,f^a=fh,d^b=dh,e^b=eg,i^c=i^278 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 59988);