Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×#353 ⋊ C2 |
| Sylow | C3 ⋊ #33359 |
1356 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|a^2=f,e^2=h,b^a=be,e^a=eg,g^a=gh,e^b=eh,f^b=fgh,d^c=dh,i^d=i^2,f^e=fh72 conjugacy classes — view the full character table.
| maximal subgroup of | #72255219, #72255227, D3×#33359, … |
| maximal normal subgroup of | #72255219, #72255227, D3×#33359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322368);