Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Fitting | C2×C3×#535 ⋊ C2 |
| Sylow | C3 ⋊ #23445 |
2282 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,d^b=dh,e^c=eh,i^c=i^290 conjugacy classes — view the full character table.
| maximal subgroup of | #72270558, #72270651, D3×#23445 |
| maximal normal subgroup of | #72270558, #72270651, D3×#23445 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 196823);