Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C3×#1762 ⋊ C2 |
| Sylow | C3 ⋊ #20739 |
1738 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,d^2=eh,f^2=h,b^a=be,c^a=cf,f^a=fh,i^b=i^2,d^c=dh,f^c=fh108 conjugacy classes — view the full character table.
| maximal subgroup of | #72269938, #72269976, D3×#20739 |
| maximal normal subgroup of | #72269938, #72269976, D3×#20739 |
| maximal quotient of | #72269973, #72269985 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 169617);