Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C3×D4×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #34362 |
2586 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=h,d^2=f,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,i^a=i^2,c^b=cg,d^b=df,i^d=i^2126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 332366);