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×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C3 ⋊ #33348 |
1410 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|a^2=f,b^a=be,e^a=eg,g^a=gh,f^b=fg,d^c=dh,i^d=i^2,f^e=fh72 conjugacy classes — view the full character table.
| maximal subgroup of | #72255218, #72255219, D3×#33348, … |
| maximal normal subgroup of | #72255218, #72255219, D3×#33348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322314);