Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C2×C3×#433 ⋊ C2 |
| Sylow | C3 ⋊ #60797 |
2062 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|b^2=f,e^2=h,g^2=h,b^a=bf,c^a=cg,d^a=df,g^a=gh,i^a=i^2,c^b=cf,d^b=dh,g^c=gh,i^c=i^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1040983);