Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×C3×#131 ⋊ C2 |
| Sylow | C3 ⋊ #20899 |
1938 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=eg,g^2=h,b^a=be,c^a=cf,i^a=i^2,d^c=dh156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 170725);