Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #7132 |
368 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 83 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,b^2=fh,c^2=f,d^2=g,b^a=bc,c^a=ce,e^a=eh,c^b=cf,d^b=def,i^b=i^2,d^c=dh90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 56387);