Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Fitting | C3×#1436 ⋊ C2 |
| Sylow | C3 ⋊ C22⋊C4×C4⋊C4 |
2574 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=h,d^2=e,b^a=be,c^a=cf,d^b=de,i^c=i^2,i^d=i^2156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 90982);