Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #23197 |
880 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 263 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=eg,c^2=f,d^2=e,e^2=h,f^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^2,d^b=de,e^b=eh,g^b=gh,i^b=i^2,d^c=dh84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 194296);