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×#1823 ⋊ 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,d^c=dh,f^c=fh,i^c=i^2,i^d=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #72269936, D3×#20739, #72270008 |
| maximal normal subgroup of | #72269936, D3×#20739, #72270008 |
| maximal quotient of | #72269947, #72269969 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 169616);