Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#2153 ⋊ C2 |
| Sylow | C3 ⋊ #13200 |
438 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 111 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=f,b^2=df,c^2=e,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eh,c^b=cg,e^b=eh,i^b=i^2,d^c=dh96 conjugacy classes — view the full character table.
| maximal subgroup of | #72270338, #72270365, D3×#13200, … |
| maximal normal subgroup of | #72270338, #72270365, D3×#13200, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 87771);