Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#2178 ⋊ C2 |
| Sylow | C3 ⋊ #33860 |
636 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 143 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=h,b^2=h,c^2=h,e^2=gh,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fh,g^a=gh,i^a=i^2,c^b=ch,d^b=de,e^b=eg,g^b=gh,f^c=fh,i^c=i^2,e^d=eg,g^d=gh87 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 326382);