Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×C3×#100 ⋊ C2 |
| Sylow | C3 ⋊ #21005 |
1782 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=eg,d^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,d^b=dh,e^b=eh,f^b=fh,g^b=gh,e^c=eh,f^c=fh,g^c=gh,i^c=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #72253366, D3×#21005, #72253375, … |
| maximal normal subgroup of | #72253366, D3×#21005, #72253375, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 171522);